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Journal articles on the topic 'Form Brunovsky'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Yakovenko, Gennadii Nikolaevich. "Control systems in Brunovsky form: symmetries, controllability." Computer Research and Modeling 1, no. 2 (June 2009): 147–59. http://dx.doi.org/10.20537/2076-7633-2009-1-2-147-159.

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2

Baragaña, Itziar, M. Asunción Beitia, and Inmaculada de Hoyos. "Structured perturbation of the Brunovsky form: A particular case." Linear Algebra and its Applications 430, no. 5-6 (March 2009): 1613–25. http://dx.doi.org/10.1016/j.laa.2008.05.022.

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3

THEODORIDIS, DIMITRIOS, YIANNIS BOUTALIS, and MANOLIS CHRISTODOULOU. "A NEW DIRECT ADAPTIVE REGULATOR WITH ROBUSTNESS ANALYSIS OF SYSTEMS IN BRUNOVSKY FORM." International Journal of Neural Systems 20, no. 04 (August 2010): 319–39. http://dx.doi.org/10.1142/s0129065710002449.

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The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro–fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONN's).

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4

Kamachkin, Alexander M., Nikolai A. Stepenko, and Gennady M. Chitrov. "On the theory of constructive construction of a linear controller." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 16, no. 3 (2020): 326–44. http://dx.doi.org/10.21638/11701/spbu10.2020.309.

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The classical problem of stationary stabilization with respect to the state of a linear stationary control system is investigated. Efficient, easily algorithmic methods for constructing controllers of controlled systems are considered: the method of V. I. Zubov and the method of P. Brunovsky. The most successful modifications are indicated to facilitate the construction of a linear controller. A new modification of the construction of a linear regulator is proposed using the transformation of the matrix of the original system into a block-diagonal form. This modification contains all the advantages of both V. I. Zubov’s method and P. Brunovsky’s method, and allows one to reduce the problem with multidimensional control to the problem of stabilizing a set of independent subsystems with scalar control for each subsystem.

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5

Gardner, R. B., and W. F. Shadwick. "The GS algorithm for exact linearization to Brunovsky normal form." IEEE Transactions on Automatic Control 37, no. 2 (1992): 224–30. http://dx.doi.org/10.1109/9.121623.

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6

Ghanooni, Pooria, Hamed Habibi, Amirmehdi Yazdani, Hai Wang, Somaiyeh MahmoudZadeh, and Amin Mahmoudi. "Rapid Detection of Small Faults and Oscillations in Synchronous Generator Systems Using GMDH Neural Networks and High-Gain Observers." Electronics 10, no. 21 (October 28, 2021): 2637. http://dx.doi.org/10.3390/electronics10212637.

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This paper presents a robust and efficient fault detection and diagnosis framework for handling small faults and oscillations in synchronous generator (SG) systems. The proposed framework utilizes the Brunovsky form representation of nonlinear systems to mathematically formulate the fault detection problem. A differential flatness model of SG systems is provided to meet the conditions of the Brunovsky form representation. A combination of high-gain observer and group method of data handling neural network is employed to estimate the trajectory of the system and to learn/approximate the fault- and uncertainty-associated functions. The fault detection mechanism is developed based on the output residual generation and monitoring so that any unfavorable oscillation and/or fault occurrence can be detected rapidly. Accordingly, an average L1-norm criterion is proposed for rapid decision making in faulty situations. The performance of the proposed framework is investigated for two benchmark scenarios which are actuation fault and fault impact on system dynamics. The simulation results demonstrate the capacity and effectiveness of the proposed solution for rapid fault detection and diagnosis in SG systems in practice, and thus enhancing service maintenance, protection, and life cycle of SGs.

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7

Zeng, Wei, and Cong Wang. "Learning from NN output feedback control of nonlinear systems in Brunovsky canonical form." Journal of Control Theory and Applications 11, no. 2 (May 2013): 156–64. http://dx.doi.org/10.1007/s11768-013-1124-0.

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8

Boulkroune, Abdesselem, Sarah Hamel, Farouk Zouari, Abdelkrim Boukabou, and Asier Ibeas. "Output-Feedback Controller Based Projective Lag-Synchronization of Uncertain Chaotic Systems in the Presence of Input Nonlinearities." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/8045803.

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This paper solves the problem of projective lag-synchronization based on output-feedback control for chaotic drive-response systems with input dead-zone and sector nonlinearities. This class of the drive-response systems is assumed in Brunovsky form but with unavailable states and unknown dynamics. To effectively deal with both dead-zone and sector nonlinearities, the proposed controller is designed in a variable-structure framework. To online learn the uncertain dynamics, adaptive fuzzy systems are used. And to estimate the unavailable states, a simple synchronization error is constructed. To prove the stability of the overall closed-loop system (controller, observer, and drive-response system) and to design the adaptation laws, a Lyapunov theory and strictly positive real (SPR) approach are exploited. Finally, three academic examples are given to show the effectiveness of this proposed lag-synchronization scheme.

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9

Cong, Lanmei, Xiaocong Li, and Ancai Zhang. "Multiobject Holographic Feedback Control of Differential Algebraic System with Application to Power System." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/415281.

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A multiobject holographic feedback (MOHF) control method for studying the nonlinear differential algebraic (NDA) system is proposed. In this method, the nonlinear control law is designed in a homeomorphous linear space by means of constructing the multiobject equations (MOEq) which is in accord with Brunovsky normal form. The objective functions of MOEq are considered to be the errors between the output functions and their references. The relative degree for algebraic system is defined that is key to connecting the nonlinear and the linear control laws. Pole assignment method is addressed for the stability domain of this MOHF control. Since there is no any approximation, the MOHF control is effective in governing the dynamic performance stably both to the small and major disturbance. The application in single machine infinite system (SMIS) shows that this approach is effective in the improvement of stable and transient stability for power system on the disturbance of active power or three-phase short circuit fault.

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10

RIGATOS, GERASIMOS, and EFTHYMIA RIGATOU. "SYNCHRONIZATION OF CIRCADIAN OSCILLATORS AND PROTEIN SYNTHESIS CONTROL USING THE DERIVATIVE-FREE NONLINEAR KALMAN FILTER." Journal of Biological Systems 22, no. 04 (November 11, 2014): 631–57. http://dx.doi.org/10.1142/s0218339014500259.

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The paper proposes a new method for synchronization of coupled circadian cells and for nonlinear control of the associated protein synthesis process using differential flatness theory and the derivative-free nonlinear Kalman filter. By proving that the dynamic model of the FRQ protein synthesis is a differentially flat one, its transformation to the linear canonical (Brunovsky) form becomes possible. For the transformed model, one can find a state feedback control input that makes the oscillatory characteristics in the concentration of the FRQ protein vary according to desirable setpoints. To estimate nonmeasurable elements of the state vector, the derivative-free nonlinear Kalman filter is used. The derivative-free nonlinear Kalman filter consists of the standard Kalman filter recursion on the linearized equivalent model of the coupled circadian cells and on computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. Moreover, to cope with parametric uncertainties in the model of the FRQ protein synthesis and with stochastic disturbances in measurements, the derivative-free nonlinear Kalman filter is redesigned in the form of a disturbance observer. The efficiency of the proposed Kalman filter-based control scheme is tested through simulation experiments.

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11

Pérez-Cruz, J. Humberto, E. Ruiz-Velázquez, José de Jesús Rubio, and Carlos A. de Alba-Padilla. "Robust Adaptive Neurocontrol of SISO Nonlinear Systems Preceded by Unknown Deadzone." Mathematical Problems in Engineering 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/342739.

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In this study, the problem of controlling an unknown SISO nonlinear system in Brunovsky canonical form with unknown deadzone input in such a way that the system output follows a specified bounded reference trajectory is considered. Based on universal approximation property of the neural networks, two schemes are proposed to handle this problem. The first scheme utilizes a smooth adaptive inverse of the deadzone. By means of Lyapunov analyses, the exponential convergence of the tracking error to a bounded zone is proven. The second scheme considers the deadzone as a combination of a linear term and a disturbance-like term. Thus, the estimation of the deadzone inverse is not required. By using a Lyapunov-like analyses, the asymptotic converge of the tracking error to a bounded zone is demonstrated. Since this control strategy requires the knowledge of a bound for an uncertainty/disturbance term, a procedure to find such bound is provided. In both schemes, the boundedness of all closed-loop signals is guaranteed. A numerical experiment shows that a satisfactory performance can be obtained by using any of the two proposed controllers.

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12

Rigatos, Gerasimos G. "Differential flatness theory-based control and filtering for a mobile manipulator." Cybernetics and Physics, Volume 9, 2020, Number 1 (June 30, 2020): 57–68. http://dx.doi.org/10.35470/2226-4116-2020-9-1-57-68.

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The article proposes a differential flatness theory based control and filtering method for the model of a mobile manipulator. This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. Using the Euler-Lagrange approach, the dynamic model of the mobile manipulator is obtained. This is proven to be a differentially flat one, thus confirming that it can be transformed into an input-output linearized form. Through a change of state and control inputs variables the dynamic model of the manipulator is finally written into the linear canonical (Brunovsky) form. For the latter representation of the system’s dynamics the solution of both the control and filtering problems becomes possible. The global asymptotic stability properties of the control loop are proven. Moreover, a differential flatness theory-based state estimator, under the name of Derivative-free nonlinear Kalman Filter, is developed. This comprises (i) the standard Kalman Filter recursion on the linearized equivalent model of the mobile manipulator and (ii) an inverse transformation, relying on the differential flatness properties of the system which allows for estimating the state variables of the initial nonlinear model. Finally, by redesigning the aforementioned Kalman Filter as a disturbance observer one can achieve estimation and compensation of the disturbance inputs that affect the model of the mobile manipulator.

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13

Rigatos, Gerasimos G., and Guilherme V. Raffo. "Input–Output Linearizing Control of the Underactuated Hovercraft Using the Derivative-Free Nonlinear Kalman Filter." Unmanned Systems 03, no. 02 (April 2015): 127–42. http://dx.doi.org/10.1142/s2301385015500089.

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The paper proposes a nonlinear control approach for the underactuated hovercraft model based on differential flatness theory and uses a new nonlinear state vector and disturbances estimation method under the name of derivative-free nonlinear Kalman filter. It is proven that the nonlinear model of the hovercraft is a differentially flat one. It is shown that this model cannot be subjected to static feedback linearization, however it admits dynamic feedback linearization which means that the system's state vector is extended by including as additional state variables the control inputs and their derivatives. Next, using the differential flatness properties it is also proven that this model can be subjected to input–output linearization and can be transformed to an equivalent canonical (Brunovsky) form. Based on this latter description the design of a state feedback controller is carried out enabling accurate maneuvering and trajectory tracking. Additional problems that are solved in the design of this feedback control scheme are the estimation of the nonmeasurable state variables in the hovercraft's model and the compensation of modeling uncertainties and external perturbations affecting the vessel. To this end, the application of the derivative-free nonlinear Kalman filter is proposed. This nonlinear filter consists of the Kalman Filter's recursion on the linearized equivalent model of the vessel and of an inverse nonlinear transformation based on the differential flatness features of the system which enables to compute estimates for the state variables of the initial nonlinear model. The redesign of the filter as a disturbance observer makes possible the estimation and compensation of additive perturbation terms affecting the hovercraft's model. The efficiency of the proposed nonlinear control and state estimation scheme is confirmed through simulation experiments.

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14

Tahri, Omar, Driss Boutat, and Youcef Mezouar. "Brunovsky's Linear Form of Incremental Structure From Motion." IEEE Transactions on Robotics 33, no. 6 (December 2017): 1491–99. http://dx.doi.org/10.1109/tro.2017.2715344.

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15

Aranda-Bricaire, E., C. Moog, and J. Pomet. "Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization." Banach Center Publications 32, no. 1 (1995): 19–33. http://dx.doi.org/10.4064/-32-1-19-33.

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16

Hermida-Alonso, Jose A., M. Pilar Perez, and Tomas Sanchez-Giralda. "Brunovsky's canonical form for linear dynamical systems over commutative rings." Linear Algebra and its Applications 233 (January 1996): 131–47. http://dx.doi.org/10.1016/0024-3795(94)00062-x.

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17

ДМИТРИЕНКО, В. Д., and А. Ю. ЗАКОВОРОТНЫЙ. "Automation processes of transformation of non-linear models to equivalent linear form Brunovsky." Bulletin of the National Technical University "KhPI". A series of "Information and Modeling", no. 62 (December 30, 2014). http://dx.doi.org/10.20998/2411-0558.2014.62.03.

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18

Ray, Anirban, A. RoyChowdhury, and Indranil Mukherjee. "Nonlinear Control of Hyperchaotic System, Lie Derivative, and State Space Linearization." Journal of Computational and Nonlinear Dynamics 7, no. 3 (March 19, 2012). http://dx.doi.org/10.1115/1.4005926.

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State space linearization using the concept of Brunovsky form and Lie derivative is applied to the case of a Hyperchaotic Lorentz System. It is observed that the necessary and sufficient conditions can be satisfied, the analytic form of the controller ‘u’ and the final form of the linearized equations can be obtained. Numerical simulation is used to ascertain the feasibility of the procedure in practice. It may be added that the case of an ordinary Lorentz equation is distinctively different as the controller is to be added in a different manner. The most important aspect of the present analysis is that the controller can be determined and not chosen ad hoc.

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19

Sariyildiz, Emre, Rahim Mutlu, and Chuanlin Zhang. "Active Disturbance Rejection Based Robust Trajectory Tracking Controller Design in State Space." Journal of Dynamic Systems, Measurement, and Control 141, no. 6 (March 13, 2019). http://dx.doi.org/10.1115/1.4042878.

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This paper proposes a new active disturbance rejection (ADR) based robust trajectory tracking controller design method in state space. It can compensate not only matched but also mismatched disturbances. Robust state and control input references are generated in terms of a fictitious design variable, namely differentially flat output, and the estimations of disturbances by using differential flatness (DF) and disturbance observer (DOb). Two different robust controller design techniques are proposed by using Brunovsky canonical form and polynomial matrix form approaches. The robust position control problem of a two mass-spring-damper system is studied to verify the proposed ADR controllers.

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20

Delavari, Hadi, Danial Senejohnny, and Dumitru Baleanu. "Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter." Open Physics 10, no. 5 (January 1, 2012). http://dx.doi.org/10.2478/s11534-012-0073-4.

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AbstractIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

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21

Дмитриенко, В. Д., А. Ю. Заковоротный, and А. О. Нестеренко. "Developing software tools that automate the conversion nonlinear systems to equivalent linear system in form Brunovsky." Bulletin of the National Technical University "KhPI". A series of "Information and Modeling", no. 35 (July 30, 2014). http://dx.doi.org/10.20998/2411-0558.2014.35.08.

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22

López-Morales, V., and R. Valdés-Asiain. "Robust control of a MIMO thermal-hidraulic process with sensor compensation in real time." Journal of Applied Research and Technology 3, no. 01 (April 1, 2005). http://dx.doi.org/10.22201/icat.16656423.2005.3.01.565.

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The main goal of this paper is twofold: To show a kind of robustness in a nonlinear multivariable (NL MIMO) system with feedback control, by employing some linearization and observation techniques well known in reference kind of model; and at the same time it is a proposal to immunize the measurements of a level capacitance-based sensor when there are changes in the measured variables properties, by employing an on-line compensation. The MIMO thermal-hydraulic nonlinear system is stabilized when some linearizing conditions are met and a design methodology for using a state feedback scheme is established. In order to assign poles to the control system, the Jacobian linearization is transformed to the controllable canonical form. This is accomplished by the Brunovsky similarity transformation, and by a static state feedback. A Luenberger observer is added to the control system in order to improve its stability. Illustrations of these techniques are shown via numerical and practical simulations carried out directly in the inexpensive physical process.

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