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Journal articles on the topic 'Probabilistic robust controller synthesis'

Author: Grafiati

Published: 25 January 2025

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1

Badings, Thom, Licio Romao, Alessandro Abate, David Parker, Hasan A. Poonawala, Marielle Stoelinga, and Nils Jansen. "Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions." Journal of Artificial Intelligence Research 76 (January 21, 2023): 341–91. http://dx.doi.org/10.1613/jair.1.14253.

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Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

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2

Kanev, S., B. De Schutter, and M. Verhaegen. "An ellipsoid algorithm for probabilistic robust controller design." Systems & Control Letters 49, no. 5 (August 2003): 365–75. http://dx.doi.org/10.1016/s0167-6911(03)00115-4.

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3

Bakumenko, N. S., V. Y. Strilets, M. L. Ugryumov, R. O. Zelenskyi, K. M. Ugryumova, V. P. Starenkiy, S. V. Artiukh, and A. M. Nasonova. "COMPUTATIONAL INTELLIGENCE METHODS TO PATIENTS STRATIFICATION IN THE MEDICAL MONITORING SYSTEMS." Radio Electronics, Computer Science, Control, no. 1 (February 24, 2023): 24. http://dx.doi.org/10.15588/1607-3274-2023-1-3.

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Context. In modern medical practice the automation and information technologies are increasingly being implemented for diagnosing diseases, monitoring the condition of patients, determining the treatment program, etc. Therefore, the development of new and improvement of existing methods of the patient stratification in the medical monitoring systems is timely and necessary. Objective. The goal of intelligent diagnostics of patient’s state in the medical monitoring systems – reducing the likelihood of adverse states based on the choice of an individual treatment program: − reducing the probability of incorrectly determining the state of the patients when monitoring patients; − obtaining stable effective estimates of unknown values of treatment actions for patients (corresponding to the found state); − the choice of a rational individual treatment program for the patients, identified on the basis of the forecasted state. Method. Proposed methodology, which includes the following computational intelligence methods to patient’s stratification in the medical monitoring systems: 1) method of cluster analysis based on the agent-based approach – the determination of the possible number of patient’s states using controlled variables of state; 2) method of robust metamodels development by means artificial neuron networks under a priori data uncertainty (only accuracy of measurements is known) in the monitoring data: a) a multidimensional logistic regression model in the form of analytical dependences of the posterior probabilities of different states of the patients on the control and controlled variables of state; b) a multidimensional diagnostic model in the form of analytical dependences of the objective functions (quality criteria of the patient’s state) on the control and controlled variables of state; 3) method of estimating informativeness controlled variables of state at a priori data uncertainty; 4) method of robust multidimensional models development for the patient’s state control under a priori data uncertainty in the monitoring data in the form of analytical dependencies predicted from the measured values of the control and controlled variables of state in the monitoring process; 5) method of reducing the controlled state variables space dimension based on the analysis of the variables informativeness of the robust multidimensional models for the patient’s state control; 6) method of patient’s states determination based on the classification problem solution with the values of the control and forecasted controlled variables of state with using the probabilistic neural networks; 7) method of synthesis the rational individual patient’s treatment program in the medical monitoring system, for the state identified on the basis of the forecast. Proposed the structure of the model for choosing the rational individual patient’s treatment program based on IT Data Stream Mining, which implements the «Big Data for Better Outcomes» concept. Results. The developed advanced computational intelligence methods for forecast states were used in choosing the tactics of treating patients, to forecast treatment complications and assess the patient’s curability before and during special treatment. Conclusions. Experience in the implementation of “Big Data for Better Outcomes” concept for the solution of the problem of computational models for new patient stratification strategies is presented. Advanced methodology, computational methods for a patient stratification in the medical monitoring systems and applied information technology realizing them have been developed. The developed methods for forecast states can be used in choosing the tactics of treating patients, to forecast treatment complications and assess the patient’s curability before and during special treatment.

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4

Bao, Jie, Peter L. Lee, Fuyang Wang, and Weibiao Zhou. "New robust stability criterion and robust controller synthesis." International Journal of Robust and Nonlinear Control 8, no. 1 (January 1998): 49–59. http://dx.doi.org/10.1002/(sici)1099-1239(199801)8:1<49::aid-rnc309>3.0.co;2-h.

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5

Bernstein, D. S., and W. M. Haddad. "Robust controller synthesis using Kharitonov's theorem." IEEE Transactions on Automatic Control 37, no. 1 (1992): 129–32. http://dx.doi.org/10.1109/9.109648.

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6

Oya, Hidetoshi, Daisuke Yamasaki, Shunya Nagai, and Kojiro Hagino. "Synthesis of Adaptive Gain Robust Controllers for Polytopic Uncertain Systems." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/854306.

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We present a new adaptive gain robust controller for polytopic uncertain systems. The proposed adaptive gain robust controller consists of a state feedback law with a fixed gain and a compensation input with adaptive gains which are tuned by updating laws. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust controller are given in terms of LMIs. Finally, illustrative examples are presented to show the effectiveness of the proposed adaptive gain robust controller.

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7

Mihaly, Vlad, Mircea Şuşcă, Dora Morar, Mihai Stănese, and Petru Dobra. "μ-Synthesis for Fractional-Order Robust Controllers." Mathematics 9, no. 8 (April 20, 2021): 911. http://dx.doi.org/10.3390/math9080911.

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The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with D–K iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets the stability and performance criteria for a family of plants. Because this control problem is NP-hard, it is usually solved using an approximation, the most common being the D–K iteration algorithm, but, this approximation leads to high-order controllers, which are not practically feasible. If a desired structure is imposed to the controller, the corresponding K step is a non-convex problem. The novelty of the paper consists in an artificial bee colony swarm optimization approach to compute the nearly optimal controller parameters. Further, a mixed-sensitivity μ-synthesis control problem is solved with the proposed approach for a two-axis Computer Numerical Control (CNC) machine benchmark problem. The resulting controller using the described algorithm manages to ensure, with mathematical guarantee, both robust stability and robust performance, while the high-order controller obtained with the classical μ-synthesis approach in MATLAB does not offer this.

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8

Field, R. V., P. G. Voulgaris, and L. A. Bergman. "Methods to Compute Probabilistic Measures of Robustness for Structural Systems." Journal of Vibration and Control 2, no. 4 (October 1996): 447–63. http://dx.doi.org/10.1177/107754639600200405.

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Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst- case analyses. These traditional methods include the use of the structured singular value (μ-analysis), as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. Because of this, an attempt to view controller robustness as a probability measure is presented. As a result, a much more intuitive insight into controller robustness can be obtained. In this context, the joint probability distribution is of dimension equal to the number of uncertain parameters, and the failure hypersurface is defined by the onset of instability of the closed-loop system in the eigenspace. A first-order reliability measure (FORM) of the system is computed and used to estimate controller robustness. It is demonstrated via an example that this FORM method can provide accurate results on the probability of failure despite the potential complexity of the closed-loop. In addition to the FORM method, a probabilistic measure of robustness is developed based on the fundamentals of μ-analysis. It is shown that the μ-analysis based method is inferior to the FORM method and can only have qualitative value when assessing control system robustness in a probabilistic framework.

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9

Li, Ying, and Xue Gong Ding. "Robust μ-Synthesis Control for Parameter Variations." Advanced Materials Research 546-547 (July 2012): 850–55. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.850.

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The robust ASAC(active structure acoustic control) model for the system of structural acoustical coupling is established and the μ-synthesis design is presented in the paper. The main idea is as follows: First, the robust performance problem of this system is transformed into the robust stability problem of an augmented system. Through the robust stability controller for this augmented system is solved by the standard D-K iteration. Simulation results show that μ-controller can provide good disturbance rejection and is more robust to parameter variations.

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10

Amin, Rooh ul, and Aijun Li. "Modelling and robust attitude trajectory tracking control of 3-DOF four rotor hover vehicle." Aircraft Engineering and Aerospace Technology 89, no. 1 (January 3, 2017): 87–98. http://dx.doi.org/10.1108/aeat-11-2015-0236.

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Purpose The purpose of this paper is to present μ-synthesis-based robust attitude trajectory tracking control of three degree-of-freedom four rotor hover vehicle. Design/methodology/approach Comprehensive modelling of hover vehicle is presented, followed by development of uncertainty model. A μ-synthesis-based controller is designed using the DK iteration method that not only handles structured and unstructured uncertainties effectively but also guarantees robust performance. The performance of the proposed controller is evaluated through simulations, and the controller is also implemented on experimental platform. Simulation and experimental results validate that μ-synthesis-based robust controller is found effective in: solving robust attitude trajectory tracking problem of multirotor vehicle systems, handling parameter variations and dealing with external disturbances. Findings Performance analysis of the proposed controller guarantees robust stability and also ensures robust trajectory tracking performance for nominal system and for 15-20 per cent variations in the system parameters. In addition, the results also ensure robust handling of wind gusts disturbances. Originality/value This research addresses the robust performance of hover vehicle’s attitude control subjected to uncertainties and external disturbances using μ-synthesis-based controller. This is the only method so far that guarantees robust stability and performance simultaneously.

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11

Qi, Xiaomei, Chengjin Zhang, and Jason Gu. "Robust Fault-Tolerant Control for Uncertain Networked Control Systems with State-Delay and Random Data Packet Dropout." Journal of Control Science and Engineering 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/734758.

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A robust fault-tolerant controller design problem for networked control system (NCS) with random packet dropout in both sensor-to-controller link and controller-to-actuator link is investigated. A novel stochastic NCS model with state-delay, model uncertainty, disturbance, probabilistic sensor failure, and actuator failure is proposed. The random packet dropout, sensor failures, and actuator failures are characterized by a binary random variable. The sufficient condition for asymptotical mean-square stability of NCS is derived and the closed-loop NCS satisfiesH∞performance constraints caused by the random packet dropout and disturbance. The fault-tolerant controller is designed by solving a linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the proposed method.

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12

Zhu, Shenjin, and Yuping He. "A Design Synthesis Method for Robust Controllers of Active Vehicle Suspensions." Designs 6, no. 1 (February 11, 2022): 14. http://dx.doi.org/10.3390/designs6010014.

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This paper presents a design synthesis method for robust controllers of active vehicle suspensions (AVSs). Various control techniques have been applied to the design of AVSs for enhancing ride comfort and handling performance of ground vehicles. However, most of these model-based controller designs show poor robustness when the vehicle models are not accurate and operating conditions vary. To address the poor robustness problem of AVSs, a new controller is designed using the H∞ loop-shaping control technique. The controller targets robustness issues on vehicle models with parametric uncertainties and unmodelled dynamics. To facilitate the robust controller design, a design synthesis method is proposed: the H∞ loop-shaping controller design is formulated as a multi-objective optimization problem, the weighting functions’ parameters of the controller are treated as design variables, the expensive computing loads are handled by a parallel computing technique, and the solution of the optimization problem is the desired robust AVS controller. Simulation results demonstrate the benefits of the proposed AVS design.

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13

Nagai, Shunya, and Hidetoshi Oya. "Synthesis of Decentralized Variable Gain Robust Controllers for Large-Scale Interconnected Systems with Structured Uncertainties." Journal of Control Science and Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/848465.

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In this paper, we propose a decentralized variable gain robust controller which achieves not only robust stability but also satisfactory transient behavior for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. The proposed decentralized robust controller consists of a fixed feedback gain controller and a variable gain one determined by a parameter adjustment law. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller are given in terms of LMIs. Finally, a simple numerical example is included.

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14

Hu, Jinglu, Kotaro Hirasawa, Junichi Murata, Chunzhi Jin, and Takuya Matsuoka. "Probabilistic Learning-Network-Based Robust Control Scheme for Nonlinear Systems." Journal of Advanced Computational Intelligence and Intelligent Informatics 3, no. 6 (December 20, 1999): 485–90. http://dx.doi.org/10.20965/jaciii.1999.p0485.

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We present a control design scheme for nonlinear systems based on a probability learning network (ProNet). ProNet is a learning network equipped with the capability to deal with stochastic signals. A plant and its controllers are described by using a set of related equations and form a unified learning network-ProNet where disturbances are considered as external inputs. In this way, controller design is transferred to ProNet learning. By including an effort to reduce variances of ProNet output in the criterion function for training, the trained ProNet has different sensitivities to signals of different frequencies. A ProNet control system is designed by taking this advantage to increase its robustness against disturbances. Computer simulations confirm the effectiveness of the ProNet control scheme.

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15

N. A., Tseligorov, Chubukin A. V., Ozersky A. I., Lebedev A. R., and Tseligorova E. N. "Development of a Ship's Course Controller using μ-synthesis." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 18 (December 31, 2023): 663–68. http://dx.doi.org/10.37394/23203.2023.18.67.

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The article describes the procedure for designing a robust controller for controlling the course of sea vessels exposed to sea waves using µ-synthesis. To this end, practical knowledge of the vessel is used to obtain a linear design model with parametric uncertainties describing the dynamics of the vessel. Appropriate frequency weighting functions are selected to provide the required performance characteristics during the controller design phase. The proposed model and then the weighting functions are used to design a robust controller. The problem of wave filtering in the low-frequency range is also considered during the modeling and design of the controller. The key contribution of the paper is that it provides system designers with a methodology for obtaining uncertain linearized ship models that naturally fit within the framework of µ-synthesis control theory, and it describes, in a systematic manner, the various stages of the controller design process. In addition, the document contains detailed information on methods for analyzing robust systems and their modeling.

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16

Ulusoy, Alphan, Tichakorn Wongpiromsarn, and Calin Belta. "Incremental controller synthesis in probabilistic environments with temporal logic constraints." International Journal of Robotics Research 33, no. 8 (May 19, 2014): 1130–44. http://dx.doi.org/10.1177/0278364913519000.

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17

Degtyarev, G. L., R. N. Faizutdinov, and I. O. Spiridonov. "Multiobjective Robust Controller Synthesis for Nonlinear Mechanical System." Mekhatronika, Avtomatizatsiya, Upravlenie 19, no. 11 (November 8, 2018): 691–98. http://dx.doi.org/10.17587/mau.19.691-698.

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In the paper multiobjective robust controller synthesis problem for nonlinear mechanical system described by Lagrange’s equations of the second kind is considered. Such tasks have numerous practical applications, for example in controller design of robotic systems and gyro-stabilized platforms. In practice, we often have to use uncertain mathematical plant models in controller design. Therefore, ensuring robustness in presence of parameters perturbations and unknown external disturbances is an important requirement for designed systems. Much of modern robust control theory is linear. When the actual system exhibits nonlinear behavior, nonlinearities are usually included in the uncertainty set of the plant. A disadvantage of this approach is that resulting controllers may be too conservative especially when nonlinearities are significant. The nonlinear H∞ optimal control theory developed on the basis of differential game theory is a natural extension of the linear robust control theory. Nonlinear theory methods ensure robust stability of designed control systems. However, to determine nonlinear H∞-control law, the partial differential equation have to be solved which is a rather complicated task. In addition, it is difficult to ensure robust performance of controlled processes when using this method. In this paper, methods of linear parameter-varying (LPV) systems are used to synthesize robust control law. It is shown, that Lagrange system may be adequately represented in the form of quasi-LPV model. From the computational point of view, the synthesis procedure is reduced to convex optimization techniques under constraints expressed in the form of linear matrix inequalities (LMIs). Measured parameters are incorporated in the control law, thus ensuring continuous adjustment of the controller parameters to the current plant dynamics and better performance of control processes in comparison with H∞-regulators. Furthermore, the use of the LMIs allows to take into account the transient performance requirements in the controller synthesis. Since the quasi-LPV system depends continuously on the parameter vector, the LMI system is infinite-dimensional. This infinitedimensional system is reduced to a finite set of LMIs by introducing a polytopic LPV representation. The example of multiobjective robust control synthesis for electro-optical device’s line of sight pointing and stabilization system suspended in two-axes inertially stabilized platform is given.

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18

CHANG, JIN-WEN, and CHENG-CHING YU. "Synthesis of controller structures for robust load performance." International Journal of Control 60, no. 6 (December 1994): 1353–69. http://dx.doi.org/10.1080/00207179408921526.

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19

Collins, Emmanuel G., Debashis Sadhukhan, and Layne T. Watson. "Robust controller synthesis via non-linear matrix inequalities." International Journal of Control 72, no. 11 (January 1999): 971–80. http://dx.doi.org/10.1080/002071799220515.

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20

Pirie, Carol, and Geir E. Dullerud. "Robust Controller Synthesis for Uncertain Time-Varying Systems." SIAM Journal on Control and Optimization 40, no. 4 (January 2002): 1312–31. http://dx.doi.org/10.1137/s0363012900369630.

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21

Wang, Y. W., W. M. Haddad, and D. S. Bernstein. "Robust strong stabilization via modified Popov controller synthesis." IEEE Transactions on Automatic Control 39, no. 11 (1994): 2284–87. http://dx.doi.org/10.1109/9.333777.

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22

Manousiouthakis, V. "A game theoretic approach to robust controller synthesis." Computers & Chemical Engineering 14, no. 4-5 (May 1990): 381–89. http://dx.doi.org/10.1016/0098-1354(90)87014-g.

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23

Taher, Seyed Abbas, Shahabeddin Akbari, Ali Abdolalipour, and Reza Hematti. "Robust decentralized controller design for UPFC using -synthesis." Communications in Nonlinear Science and Numerical Simulation 15, no. 8 (August 2010): 2149–61. http://dx.doi.org/10.1016/j.cnsns.2009.08.006.

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24

Chowdhury, Amor, Andrej Sarjaš, Peter Cafuta, and Rajko Svečko. "Robust controller synthesis with consideration of performance criteria." Optimal Control Applications and Methods 32, no. 6 (December 3, 2010): 700–719. http://dx.doi.org/10.1002/oca.970.

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25

Ukpai, Ukpai I., and Suhada Jayasuriya. "Using Controller Reduction Techniques for Efficient PID Controller Synthesis." Journal of Dynamic Systems, Measurement, and Control 126, no. 3 (September 1, 2004): 692–96. http://dx.doi.org/10.1115/1.1790541.

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Balanced reduction relies on the internal balancing of the controllability and observability grammians to eliminate weakly observable and controllable modes. Weighting functions are often used to improve this procedure. Several benefits exist in implementing low-order rather than high-order controllers. It is, therefore, imperative to reduce any errors that result from using the infinite grammians in the controller reduction process. By fixing the structure of the high-order controller and choosing an appropriate frequency interval for the balanced reduction a system that assumes a second-order controller is obtained, forming the basis for an efficient approximation/optimization towards obtaining a robust PID controller. This paper establishes a procedure for choosing the weighting functions.

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26

Ocaña, M., L. M. Bergasa, M. A. Sotelo, R. Flores, D. F. Llorca, and D. Schleicher. "Automatic training method applied to a WiFi+ultrasound POMDP navigation system." Robotica 27, no. 7 (March 9, 2009): 1049–61. http://dx.doi.org/10.1017/s0263574709005463.

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SUMMARYThis paper presents an automatic training method based on the Baum–Welch algorithm (also known as EM algorithm) and a robust low-level controller. The method has been applied to the indoor autonomous navigation of a surveillance robot that utilizes a WiFi+Ultrasound Partially Observable Markov Decision Process (POMDP). This method uses a robust local navigation system to automatically provide some WiFi+Ultrasound maps. These maps could be employed within probabilistic global robot localization systems. These systems use a priori probabilistic map in order to estimate the global robot position. The method has been tested in a real environment using two commercial Pioneer 2AT robotic platforms in the premises of the Department of Electronics at the University of Alcalá. Some experimental results and conclusions are presented.

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Oya, Hidetoshi, and Kojiro Hagino. "Synthesis of Adaptive Gain Robust Output Feedback Controllers for a Class of Lipschitz Nonlinear Systems with Unknown Upper Bound of Uncertainty." Journal of Control Science and Engineering 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/902576.

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We propose a new adaptive gain robust output feedback controller for a class of the Lipschitz nonlinear systems with unknown upper bound of uncertainty. The proposed adaptive gain robust output feedback controller is designed so as to reduce the effect of uncertainties and Lipschitz nonlinearities. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust output feedback controller are reduced to LMI conditions. Finally, the effectiveness of the proposed robust output feedback controller is demonstrated by numerical simulations.

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Ur Rahman, Muhammad Zia, Muhammad Tanveer Riaz, M. M. Sayed Al Mahmud, Mohsin Rizwan, and Muhammad Ahmad Choudhry. "The Prescribed Fixed Structure Intelligent Robust Control of an Electrohydraulic Servo System." Mathematical Problems in Engineering 2022 (March 8, 2022): 1–12. http://dx.doi.org/10.1155/2022/5144602.

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The paper is focused to design a robust and a simple fixed structure H ∞ control synthesis for an Electrohydraulic Servo System (EHSS) and comparing its performance with the conventional H ∞ controller and the classical proportional integral derivative (PID) controller. The precise position tracking of the piston load of EHSS system using classical PID controller is a difficult task due to some non-linear properties of EHSS and the dynamic behaviour of its parameters. The conventional H ∞ controllers also have constraints on gain ( H ∞ norm) for typical design requirement such as the speed of response, higher order, complex structure, control bandwidth, and robust stability. To overcome the above limitations, the proposed synthesis is formulated in the MATLAB. The proposed synthesis has fixed order and fixed structure and is also a linear robust controller. The control parameters of proposed synthesis are tuned using Genetic Algorithm optimization in MATLAB. Another advantage of this design is to use higher order complex shaping fillers to shape the close loop sensitivity S s and complementary sensitivity T s for the desired robust performance, without effecting the structure fixed of proposed synthesis. The order of the proposed controller is not affected by using the higher order complex weights transfer functions W s s and W T s on sensitivity and complementary sensitivity, respectively, whereas the structure of the conventional H ∞ controller becomes more complex due to higher order shaping weights. Model of the Electrohydraulic Servo System is validated experimentally, and results of proposed robust synthesis are compared with conventional H ∞ controller and the classical PID.

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Badings, Thom S., Alessandro Abate, Nils Jansen, David Parker, Hasan A. Poonawala, and Marielle Stoelinga. "Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 9669–78. http://dx.doi.org/10.1609/aaai.v36i9.21201.

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Controllers for autonomous systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel planning method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target. First, we abstract the continuous system into a discrete-state model that captures noise by probabilistic transitions between states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP, and compute a controller for which these guarantees carry over to the autonomous system. Realistic benchmarks show the practical applicability of our method, even when the iMDP has millions of states or transitions.

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30

Rouamel, Mohamed, Sofiane Gherbi, and Fayçal Bourahala. "Robust stability and stabilization of networked control systems with stochastic time-varying network-induced delays." Transactions of the Institute of Measurement and Control 42, no. 10 (January 27, 2020): 1782–96. http://dx.doi.org/10.1177/0142331219895931.

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This paper investigates the robust stability analysis and state feedback controller design of networked control systems (NCSs). A stochastic network-induced delay in given interval with known lower and upper bounds is considered. Therefore, the NCS is modeled as linear system with probabilistic time-varying delay distribution. Then, the Lyapunov-Krasovskii functional (LKF) is formulated using probabilistic informations of both lower and upper bounds of the time-varying network-induced delay, and Wirtinger-based integral inequalities are used to estimate the accuracy of the resulting time derivatives and also to reduce conservatism by introducing some new cross terms. Afterwards, stability condition based on [Formula: see text] disturbance attenuation level is expressed in terms of a set of linear matrix inequalities (LMIs), and Finsler’s lemma is used to relax it by adding slack decision variables and decoupling the systems matrices from those of Lyapunov-Krasovskii. This procedure makes the state feedback controller design as simple as a variables change. Finally, a maximum allowable upper bound of the network-induced delay and state feedback controller gains are calculated by resolving the above relaxed LMIs’ convex optimization problem. Practical numerical examples are provided to validate the proposed approach; the results show that the negative effects of the unpredictable network-induced delays are compensated and the stability of NCSs with high disturbance attenuation level is guaranteed. A comparative study with other results in recent researches is also given and the superiority of the proposed method in terms of robustness and conservatism reduction is shown.

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31

Yaniv, Oded. "Robust LTV Feedback Synthesis for Nonlinear MIMO Plants." Journal of Dynamic Systems, Measurement, and Control 121, no. 2 (June 1, 1999): 226–32. http://dx.doi.org/10.1115/1.2802459.

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An n × n nonlinear plant that is known to be a member of a given set is given. The plant is embedded in a feedback structure in order to achieve desired closed-loop performances. The existing QFT technique for that purpose, based on replacing each nonlinear plant by an uncertain linear time invariant plant, is extended to design LTV controllers. In addition, a more efficient fixed-point theorem based on Homotopic invariance is used. The main results are that: (i) a controller with less control effort compared to a linear time invariant controller is achieved; and (ii) the class of plants and desired closed-loop specifications to which the technique can be applied is enlarged. A detailed design example is included.

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Sariyildiz, Emre, Rahim Mutlu, and Haoyong Yu. "A Sliding Mode Force and Position Controller Synthesis for Series Elastic Actuators." Robotica 38, no. 1 (April 15, 2019): 15–28. http://dx.doi.org/10.1017/s0263574719000420.

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SummaryThis paper deals with the robust force and position control problems of series elastic actuators (SEAs). It is shown that an SEA’s force control problem can be described by a second-order dynamic model which suffers from only matched disturbances. However, the position control dynamics of an SEA is of fourth order and includes matched and mismatched disturbances. In other words, an SEA’s position control is more complicated than its force control, particularly when disturbances are considered. A novel robust motion controller is proposed for SEAs by using disturbance observer (DOb) and sliding mode control. When the proposed robust motion controller is implemented, an SEA can precisely track desired trajectories and safely contact with an unknown and dynamic environment. The proposed motion controller does not require precise dynamic models of environments and SEAs. Therefore, it can be applied to many different advanced robotic systems such as compliant humanoids, industrial robots and exoskeletons. The validity of the proposed motion controller is experimentally verified.

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Pajchrowski, Tomasz, Konrad Urbański, and Krzysztof Zawirski. "Artificial neural network based robust speed control of permanent magnet synchronous motors." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 25, no. 1 (January 1, 2006): 220–34. http://dx.doi.org/10.1108/03321640610634461.

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PurposeThe aim of the paper is to find a simple structure of speed controller robust against drive parameters variations. Application of artificial neural network (ANN) in the controller of PI type creates proper non‐linear characteristics, which ensures controller robustness.Design/methodology/approachThe robustness of the controller is based on its non‐linear characteristic introduced by ANN. The paper proposes a novel approach to neural controller synthesis to be performed in two stages. The first stage consists in training the ANN to form the proper shape of the control surface, which represents the non‐linear characteristic of the controller. At the second stage, the PI controller settings are adjusted by means of the random weight change (RWC) procedure, which optimises the control quality index formulated in the paper. The synthesis is performed using simulation techniques and subsequently the behaviour of a laboratory speed control system is validated in the experimental set‐up. The control algorithms of the system are performed by a microprocessor floating point DSP control system.FindingsThe proposed controller structure with proper control surface created by ANN guarantees expected robustness.Originality/valueThe original method of robust controller synthesis was proposed and validated by simulation and experimental investigations.

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Desai, Ravishankar P., and Narayan S. Manjarekar. "Robust Controller Design for AUV Subsystem Using µ Synthesis." IFAC-PapersOnLine 55, no. 25 (2022): 211–16. http://dx.doi.org/10.1016/j.ifacol.2022.09.349.

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Sellami. "Synthesis of Robust Dynamic Controller, Model Predictive Control Based." American Journal of Applied Sciences 9, no. 6 (June 1, 2012): 851–57. http://dx.doi.org/10.3844/ajassp.2012.851.857.

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Bernstein, D., and S. Greeley. "Robust controller synthesis using the maximum entropy design equations." IEEE Transactions on Automatic Control 31, no. 4 (April 1986): 362–64. http://dx.doi.org/10.1109/tac.1986.1104274.

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Sundararajan, N., S. M. Joshi, and E. S. Armstrong. "Robust controller synthesis for a large flexible space antenna." Journal of Guidance, Control, and Dynamics 10, no. 2 (March 1987): 201–8. http://dx.doi.org/10.2514/3.20203.

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Tyan, Feng, and Dennis S. Bernstein. "Shifted Quadratic Guaranteed Cost Bounds for Robust Controller Synthesis." IFAC Proceedings Volumes 29, no. 1 (June 1996): 3156–61. http://dx.doi.org/10.1016/s1474-6670(17)58161-6.

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Austin, David J., and Brenan J. McCarragher. "Robust Discrete Event Controller Synthesis for Constrained Motion Systems." IFAC Proceedings Volumes 30, no. 20 (September 1997): 801–7. http://dx.doi.org/10.1016/s1474-6670(17)44354-0.

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Tsypkin, Ya Z. "Robust Internal Model Control." Journal of Dynamic Systems, Measurement, and Control 115, no. 2B (June 1, 1993): 419–25. http://dx.doi.org/10.1115/1.2899082.

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This paper discusses the method of control systems design for dynamic plants under bounded uncertainty. The structure of these systems coincides with the structure of systems with an internal model. But the choice of an internal model and a controller depends on the demand of the bounded decrease of system sensitivity to the change of plant characteristics and external action and on the demand of modal control. The absorption principle is used for the synthesis of a controller of such robust modal control systems. The realization conditions of robust systems of modal control are stated.

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Chamanbaz, Mohammadreza, Ehsan Keikha, Venkatakrishnan Venkataramanan, Abdullah Al Mamun, and Qing-Guo Wang. "Design of a probabilistic robust track-following controller for hard disk drive servo systems." Mechatronics 24, no. 6 (September 2014): 582–89. http://dx.doi.org/10.1016/j.mechatronics.2014.02.007.

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Widowati, Widowati, Sutrisno Sutrisno, M. Ivan Azis, and Ikha Magdalena. "Control of Inventory Systems in Probabilistic Environment via Chance Constrained-Based Robust Predictive Controller." International Review of Automatic Control (IREACO) 15, no. 4 (July 31, 2022): 185. http://dx.doi.org/10.15866/ireaco.v15i4.21207.

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Fujimori, A., and P. N. Nikiforuk. "A design of active flutter suppression control systems using μ synthesis and controller reduction." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 211, no. 3 (March 1, 1997): 183–92. http://dx.doi.org/10.1243/0954410971532604.

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This paper presents a control synthesis of a two-dimensional aerofoil active flutter suppression (2D-AFS) using μ synthesis and the extended coprime factorization (weighted) (ECFW) controller reduction method in numerical simulation. A multiplicative uncertainty representation is chosen as a structured uncertainty model of the 2D-AFS system because H∞ norm of the uncertainty due to changes in the flight velocity is calculated small by using the multiplicative uncertainty representation. Controllers are designed by μ synthesis in the frame of the robust stability and the robust control performance problems. Furthermore, using the ECFW controller reduction method, a seventh-order controller whose performances are almost the same as those of the original controller is obtained.

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Zhmud, V. A., A. S. Vostrikov, A. Yu Ivoilov, and G. V. Sablina. "Synthesis of Robust PID Controllers by Double Optimization Method." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 2 (February 10, 2020): 67–74. http://dx.doi.org/10.17587/mau.21.67-73.

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The design of adaptive controllers allows to solve the problem of control of the object with non-stationary parameters. However, if the parameters of the object do not change too much or if only a certain interval of their change is known, it may turn out that an adaptive controller is not required, since the problem can be solved with the help of a robust controller. The robust controller allows to provide an acceptable quality of control even if the parameters of the mathematical model of the object change in some predetermined interval. A method of designing such controllers is known as the method of numerical optimization of the controllers used in the ensemble of systems in which the models of objects are different and the models of controllers are identical. The ensemble uses object models with extreme parameter values. The disadvantages of this method are too many systems that need to be modeled and optimized at the same time if there are several parameters to be changed. In addition, the worst combination of model parameters may not be boundary, but middle, in this case this method is not applicable. This article offers and analyzes an alternative method of designing a robust controller on a numerical example. The essence of this method is the numerical optimization of the regulator for the model with the worst combination of the values of all modifiable parameters. The search for the worst combination of parameters is also carried out using the method of numerical optimization. In this case, a combination of model parameters is found in which the best relation of regulator coefficients gives the worst result of the system. The problem is solved in several optimization cycles with alternating cost functions. The utility of the method is illustrated numerically by an example of a third order dynamic object with a series linked delay element.

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Tissir, El Houssaine. "Robust Control Design for Retarded Discrete-Time Systems." Journal of Dynamic Systems, Measurement, and Control 129, no. 1 (April 28, 2006): 72–76. http://dx.doi.org/10.1115/1.2397154.

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This paper focuses on the analysis and synthesis of a robust stabilizing controller for linear discrete time systems with norm-bounded time varying uncertainties. Delay independent robust stability conditions are derived and two synthesis methods are presented. One method is to construct a robust memoryless state feedback control law from the solutions of linear matrix inequalities. The other method consists of designing robust observer-based output feedback controller. The results are expressed in termes of linear matrix inequalities. A comparison with μ∕LDI tests is presented. Furthermore, numerical examples are given for illustration.

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Aboud, Wajdi S., and Sallehuddin Mohamed Haris. "Performance of Robust μ Synthesis Control for Mechatronic Suspension System." Applied Mechanics and Materials 471 (December 2013): 247–52. http://dx.doi.org/10.4028/www.scientific.net/amm.471.247.

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The main goal of using mechatronic suspensions is to improve the ride comfort and handling performance. In this work, a robust linear controller for such a system was designed based on the μ synthesis method. The performance of a model two degree of freedom quarter car with parameter perturbations, subjected to road disturbances, was simulated and the time domain responses were analyzed. The simulation results indicate that the robust controller improved the vibration isolation performance of the mechatronic suspension system, despite the presence of parameter perturbations and exogenous disturbances. When compared to both LQG active control and to a passive suspension system, the μ synthesis controller also showed super or performance.

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Gayvoronskiy, S. A., T. A. Ezangina, and I. V. Khozhaev. "Parametric Synthesis of a Robust Controller Based on the Method of Dominant Poles." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 1 (January 14, 2020): 14–20. http://dx.doi.org/10.17587/mau.21.14-20.

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In the paper a linear control system described by its characteristic polynomial with interval coefficients including parameters of controller linearly is considered. Problem of the research is finding parameters of a controller guaranteeing dynamic characteristics of a system despite interval parametric uncertainty of its object. It is proposed to base a controller synthesis on root quality indices: minimal stability degree and maximal oscillability degree. Desired values of these indices will be provided with the help of dominant poles method. Applying this method consists in placing a pair of complex-conjugate dominant poles; all other poles — unrestricted poles — will be placed by defining a right border of their allocation area on a complex plane. To apply dominant poles method, a feature of stability degree and oscillability degree to be determined by images of certain vertices of a parametric polytope was used. To synthesize a controller, it is proposed to divide its parameters in two groups: dependent ones and unrestricted ones. The first group of controller parameters is to provide desired allocation of dominant poles in one of vertices of parametric polytope (a dominant vertex). Unrestricted parameters of a controller are to provide desired distance between dominant poles and allocation area of unrestricted poles. To find coordinates of a dominant vertex and verifying vertices providing unrestricted poles allocation, an interval extension of basic phase equation of a root locus theory was developed. This resulted in interval phase inequalities, whose solution allows finding coordinates of desired vertices of characteristic polynomials coeffi cients polytope. Knowing a dominant vertex polynomial and dominant poles allows expressing dependent parameters of a controller from unrestricted ones. Obtained expressions allow placing unrestricted poles in a desired area of a complex plane. To do this, a D-partition by unrestricted parameters of a controller is performed in all verifying vertices of parametric polytope of a system. After choosing values of unrestricted parameters from intersection of all stability domains obtain during D-partition, dependent parameters of a controller can be calculated. An example of synthesizing a PID-controller guaranteeing desired values of dynamics characteristics for an interval control system of the fourth order is provided.

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Abidin, Zainal. "Robust Control Systems Design Using Matlab." Jurnal Elektro 3, no. 1 (May 4, 2018): 13. http://dx.doi.org/10.30736/je.v3i1.213.

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In general, robustness does not “come for free” from a controller designed via optima control and estimation theory (observer design): a controller designed for a nominal process model generally works fine for the nominal plant model, but may fail for even a “nearby” plant model. An important point of all feedback control synthesis methods is the control engineer’s awareness of inherent trade–offs : increasing the robustness will generally make the controller“less aggressive”, and will thereby decrease system performance.Robust control allows to specify more or less directly the plant uncertainty, and allows to predict the possible trade–offs between robustness and closed–loop performance.

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Guan, Wei, Jinghai Sun, Xiang Li, and Zhihao Ren. "Unmanned Surface Vessel Steering L2 Gain Robust Control Based on Closed-Loop Shaping Filter." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 5 (October 2019): 1018–27. http://dx.doi.org/10.1051/jnwpu/20193751018.

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With the introduction of the closed-loop shaping filtering method into the L2 gain robust controller design strategy, a nonlinear robust steering controller for unmanned surface vessel is designed under the planning and control strategy in this paper. The rigorous mathematical analysis and synthesis characteristics of the L2 gain robust control theory and the Lyapunov design method are fully utilized in the controller design process. Furthermore, the concept of the closed-loop shaping filtering based on the classical closed-loop control theory is taken into the controller design strategy. Therefore, the time domain controller design methods integration with the frequency domain controller design strategy are merged togehter to complete the unmanned surface vessel steering controller design in the view of practical engineering and planning and control strategy. Finally, compared with several practical controller design methods in the multi-direction irregular waves, the simulation results show that the proposed steering controller design strategy has concise structure, distinctive physic meanings of the controller parameters and superior comprehensive control performance.

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Keskin, Rıdvan, Ibrahim Aliskan, and Ersin Daş. "Robust structured controller synthesis for interleaved boost converters using an H∞ control method." Transactions of the Institute of Measurement and Control 43, no. 14 (June 10, 2021): 3169–80. http://dx.doi.org/10.1177/01423312211019560.

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The regulation of output voltage and equivalent distribution of phase currents of multi-phase converters which have non-minimum phase characteristic are still challenges, especially in the presence of uncertainties in real parameters, duty cycle, input voltage, and load disturbances. However, in classical third-order integral-lead (Type-III) controller design methodologies, the controller is synthesized considering only the nominal performance conditions. This paper proposes a structured [Formula: see text] synthesis framework based on an optimization methodology to the design of a robust Type-III controller for interleaved boost converters. The structured [Formula: see text] control approach is adapted for optimization of Type-III feedback and feedforward controllers in two-degree-of-freedom (2-DOF) control system configuration. The robust stability of the closed-loop interleaved boost converter system against model uncertainties is ensured via the classical [Formula: see text]-analysis technique. Numerical comparisons are made among the classical, i.e. unstructured or full order, [Formula: see text]-based controller design method, a dual-loop PI controller, and proposed 1-DOF and 2-DOF structured controller synthesis approaches on an interleaved boost converter model. Simulation results verify the effectiveness and advantages of the proposed approach from the viewpoint of the output voltage regulation under different disturbance points.

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