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Journal articles on the topic 'Uncertain time-Varying parameter'

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Published: 8 June 2024

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1

Yang, Fan, Wen Wang, Lixiang Li, Mingwen Zheng, Yanping Zhang, and Zhenying Liang. "Finite-time parameter identification of fractional-order time-varying delay neural networks based on synchronization." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 3 (March 2023): 033146. http://dx.doi.org/10.1063/5.0137598.

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We research the finite-time parameter identification of fractional-order time-varying delay neural networks (FTVDNNs) based on synchronization. First, based on the fractional-order Lyapunov stability theorem and feedback control idea, we construct a synchronous controller and some parameter update rules, which accomplish the synchronization of the drive-response FTVDNNs and complete the identification of uncertain parameters. Second, the theoretical analysis of the synchronization method is carried out, and the stable time is calculated. Finally, we give two examples for simulation verification. Our method can complete the synchronization of the FTVDNNs in finite time and identify uncertain parameters while synchronizing.

2

Chen, Y. H. "Decentralized Adaptive Robust Control Design: The Uncertainty is Time Varying." Journal of Dynamic Systems, Measurement, and Control 113, no. 3 (September 1, 1991): 515–18. http://dx.doi.org/10.1115/1.2896441.

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We consider a class of nonlinear uncertain interconnected systems with time-varying uncertainty. The uncertainty may arise within each system as well as in the interconnections. The uncertainty is assumed bounded but the bound is unknown. No a priori statistical information is imposed. Decentralized adaptive robust control is proposed for each system. The control has two parts. First, an adaptive scheme for the estimation of the bound is constructed. Second, a robust control, which is based on the adaptive parameter, is adopted for each system.

3

HUANG, HE, HAN-XIONG LI, and JUE ZHONG. "MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY AND PARAMETER UNCERTAINTY." International Journal of Bifurcation and Chaos 16, no. 02 (February 2006): 281–94. http://dx.doi.org/10.1142/s0218127406014800.

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This paper deals with the problem of master-slave synchronization for uncertain Lur'e systems via time-varying delay feedback control. The parametric uncertainty is assumed to be norm bounded. Several new and sufficient conditions are presented such that the uncertain Lur'e master and slave systems are synchronous for all admissible uncertainties. These synchronization criteria are dependent on the size of time delay, which can be expressed by means of matrix inequalities. The adopted method is based on defining a new Lyapunov–Krasovskii function and using some inequalities techniques. Our results obtained here extend and improve some previously related results. Finally, two numerical examples are provided to demonstrate the applications of our proposed results.

4

Mukdasai, Kanit. "Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/237430.

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This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

5

Iqbal, Muhammad Naveed, Jian Xiao, and Weiming Xiang. "Parameter-dependent finite-time observer design for time-varying polytopic uncertain switched systems." Journal of the Franklin Institute 351, no. 3 (March 2014): 1657–72. http://dx.doi.org/10.1016/j.jfranklin.2013.12.007.

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6

Hu, Jingting, Guixia Sui, Shengli Du, and Xiaodi Li. "Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/2538904.

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The problem of finite-time stability for a class of uncertain nonlinear systems with time-varying delay and external disturbances is investigated. By using the Lyapunov stability theory, sufficient conditions for the existence of finite-time state feedback controller for this class of systems are derived. The results can be applied to finite-time stability problems of linear time-delay systems with parameter uncertainties and external disturbances. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

7

Shao, Xueying, Qing Lu, Hamid Reza Karimi, and Jin Zhu. "New Results on Passivity Analysis for Uncertain Neural Networks with Time-Varying Delay." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/303575.

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The paper investigates the stability and passivity analysis problems for a class of uncertain neural networks with time-delay via delta operator approach. Both the parameter uncertainty and the generalized activation functions are considered in this paper. By constructing an appropriate Lyapunov-Krasovskii functional, some new stability and passivity conditions are obtained in terms of linear matrix inequalities (LMIs). The main characteristic of this paper is to obtain novel stability and passivity analysis criteria for uncertain neural networks with time-delay in the delta operator system framework. A numerical example is presented to demonstrate the effectiveness of the proposed results.

8

Chen, Fu, Shugui Kang, and Fangyuan Li. "Stability and Stabilization for Polytopic LPV Systems with Parameter-Varying Time Delays." Mathematical Problems in Engineering 2019 (May 5, 2019): 1–12. http://dx.doi.org/10.1155/2019/4924963.

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In this paper, we deal with the problem of stability and stabilization for linear parameter-varying (LPV) systems with time-varying time delays. The uncertain parameters are assumed to reside in a polytope with bounded variation rates. Being main difference from the existing achievements, the representation of the time derivative of the time-varying parameter is under a polytopic structure. Based on the new representation, delay-dependent sufficient conditions of stability and stabilization are, respectively, formulated in terms of linear matrix inequalities (LMI). Simulation examples are then provided to confirm the effectiveness of the given approach.

9

Lou, Xuyang, Qian Ye, and Baotong Cui. "Parameter-dependent robust stability of uncertain neural networks with time-varying delay." Journal of the Franklin Institute 349, no. 5 (June 2012): 1891–903. http://dx.doi.org/10.1016/j.jfranklin.2012.02.015.

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10

Hashimoto, Tomoaki, and Takashi Amemiya. "Output Feedback Stabilization of Linear Time-Varying Uncertain Delay Systems." Mathematical Problems in Engineering 2009 (2009): 1–14. http://dx.doi.org/10.1155/2009/457468.

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This paper investigates the output feedback stabilization problem of linear time-varying uncertain delay systems with limited measurable state variables. Each uncertain parameter and each delay under consideration may take arbitrarily large values. In such a situation, the locations of uncertain entries in the system matrices play an important role. It has been shown that if a system has a particular configuration called a triangular configuration, then the system is stabilizable irrespective of the given bounds of uncertain variations. In the results so far obtained, the stabilization problem has been reduced to finding the proper variable transformation such that anM-matrix stability criterion is satisfied. However, it still has not been shown whether the constructed variable transformation enables the system to satisfy theM-matrix stability condition. The objective of this paper is to show a method that enables verification of whether the transformed system satisfies theM-matrix stability condition.

11

Li, Chong. "Robust Reliable Control for a Class of Uncertain Discrete-Time Systems with Multiple Time-Varying Delays." Advanced Materials Research 630 (December 2012): 396–401. http://dx.doi.org/10.4028/www.scientific.net/amr.630.396.

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The robust reliable control design problem of uncertain discrete-time control systems with multiple time-varying delays is addressed in this article. Uncertainty in system is assumed to satisfy the norm-bounded condition and the time-delay parameter is time-varying unstructured. Under the proposed concepts of exponentially robust stability and exponentially robust stabilization, the delay-dependent exponential stability condition for the robust reliable control system is derived and a new delay-dependent state feedback controller design method is provided. The relationship between system stability and time-delays is also studied. Simulation study shows the effectiveness and feasibility of the proposed controller design method.

12

Liu, Yan, Hong Sheng Lin, Li Mei Liu, and Ying Li. "A Parameter-Dependent Approach to Robust H_∞ Control of Norm Bounded Uncertain Systems." Applied Mechanics and Materials 701-702 (December 2014): 645–53. http://dx.doi.org/10.4028/www.scientific.net/amm.701-702.645.

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A new approach to analyze and synthesize linear uncertain systems with time varying norm bounded uncertainty is presented in this paper. First, the uncertainty set is separated into several different sets according to the maximum singular value of uncertainty.Based on the new classification, the original uncertain system is transformed into a Markovian jump system. Second, via a parameter-dependent Lyapunov function, the problems of robust H∞ analysis and synthesis is studied.Based on this, two sufficient conditions for designing parameter-dependent controllers are established. Finally, numerical simulations are used to illustrate the developed method.

13

Rodriguez, Carlos, Karina A. Barbosa, and Daniel Coutinho. "Robust Filtering for Discrete-Time Linear Parameter-Varying Descriptor Systems." Symmetry 12, no. 11 (November 13, 2020): 1871. http://dx.doi.org/10.3390/sym12111871.

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This paper deals with robust state estimation for discrete-time, linear parameter varying (LPV) descriptor systems. It is assumed that all the system state-space matrices are affine functions of the uncertain parameters and both the parameters and their variations are bounded functions of time with known minimum and maximum values. First, necessary and sufficient conditions are proposed for admissibility and bounded realness for discrete linear time-varying (DLTV) descriptor systems. Next, two convex optimisation based methods are proposed for designing admissible stationary linear descriptor filters for LPV descriptor systems which ensure a prescribed upper bound on the ℓ2-induced gain from the noise signal to the estimation error regardless of model uncertainties. The proposed filter design results were based on parameter-dependent generalised Lyapunov functions, and full-order, augmented-order and reduced-order filters were considered. Numerical examples are presented to show the effectiveness of the proposed filtering scheme. In particular, the proposed approach was used to estimate the state variables of a controlled horizontal 2-DOF robotic manipulator based on noisy measurements.

14

Aeinfar, Vahid, Javad Askari, Arash Sadeghzadeh, and Mohsen Mojiri. "Parameter dependent filter design for linear continuous-time uncertain systems with arbitrarily time-varying parameters in polytopic domains." Signal Processing 165 (December 2019): 83–89. http://dx.doi.org/10.1016/j.sigpro.2019.06.021.

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15

Chen, Y. H., and Chieh Hsu. "Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems." Journal of Applied Mechanics 55, no. 4 (December 1, 1988): 992–94. http://dx.doi.org/10.1115/1.3173756.

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The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.

16

Kwon, O. M., M. J. Park, Ju H. Park, S. M. Lee, and E. J. Cha. "Analysis on Passivity for Uncertain Neural Networks with Time-Varying Delays." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/602828.

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The problem of passivity analysis for neural networks with time-varying delays and parameter uncertainties is considered. By the consideration of newly constructed Lyapunov-Krasovskii functionals, improved sufficient conditions to guarantee the passivity of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum allowable delay bounds.

17

Shi, Peng, Shyh-Pyng Shue, Yan Shi, and Ramesh K. Agarwal. "Controller design for bilinear systems with parametric uncertainties." Mathematical Problems in Engineering 4, no. 6 (1999): 505–28. http://dx.doi.org/10.1155/s1024123x98000945.

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This paper studies the problem of robust control of a class of uncertain bilinear continuous-time systems. The class of uncertain systems is described by a state space model with time-varying norm-bounded parameter uncertainty in the state equation. We address the problem of robustH∞control in which both robust stability and a prescribedH∞performance are required to be achieved irrespective of the uncertainties. Both state feedback and output feedback controllers are designed. It has been shown that the above problems can be recast intoH∞syntheses for related bilinear systems without parameter uncertainty, which can be solved via a Riccati inequality approach. Two examples are given to show the potential of the proposed technique.

18

Chen, Y. H., and J. S. Chen. "Robust Composite Control for Singularly Perturbed Systems With Time-Varying Uncertainties." Journal of Dynamic Systems, Measurement, and Control 117, no. 4 (December 1, 1995): 445–52. http://dx.doi.org/10.1115/1.2801099.

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A two-time-scale linear system with uncertain time-varying parameter is to be stabilized. A class of robust composite controls is proposed. The control renders the system practically stable regardless of the true value of the parameter. The control scheme consists of linear and nonlinear parts. The linear part is designed via a two-level optimization setting. No matching condition is needed for the linear control. The nonlinear part is of continuous saturation type. Matching condition is needed for the nonlinear control. However, it can be achieved by choosing the boundary layer model appropriately.

19

CHEN, MOU, CHANG-SHENG JIANG, QING-XIAN WU, and WEN-HUA CHEN. "MAINTAINING SYNCHRONIZATION BY DECENTRALIZED FEEDBACK CONTROL IN TIME DELAY NEURAL NETWORKS WITH PARAMETER UNCERTAINTIES." International Journal of Neural Systems 17, no. 02 (April 2007): 115–22. http://dx.doi.org/10.1142/s0129065707000981.

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A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.

20

Kasimu, Yakufu, and Gulijiamali Maimaitiaili. "Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays." AIMS Mathematics 9, no. 6 (2024): 15559–83. http://dx.doi.org/10.3934/math.2024752.

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<abstract> <p>This paper deals with the problem of non-fragile ${H_\infty }$ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed ${H_\infty }$ performance level $\gamma $. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified.</p> </abstract>

21

Li, Yi Min, and Yuan Yuan Li. "Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays." Applied Mechanics and Materials 341-342 (July 2013): 668–73. http://dx.doi.org/10.4028/www.scientific.net/amm.341-342.668.

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This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

22

Yang, Xianqiang, Weili Xiong, Zeyuan Wang, and Xin Liu. "Parameter identification of nonlinear multirate time-delay system with uncertain output delays." Transactions of the Institute of Measurement and Control 40, no. 12 (October 16, 2017): 3498–506. http://dx.doi.org/10.1177/0142331217733326.

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The joint parameter and time-delay estimation problems for a class of nonlinear multirate time-delay system with uncertain output delays are addressed in this paper. The practical process typically has time-delay properties and the process data are often multirate, sampled with output data inevitably corrupted by uncertain delays. The linear parameter varying (LPV) finite impulse response (FIR) multirate time-delay model is initially built to describe the considered system. The problems of over-parameterization and the existence of both continuous model parameters and discrete time-delays have made the conventional maximum likelihood difficult to solve the considered problems. In order to handle these problems, the joint parameter and time-delay estimation for the LPV FIR multirate time-delay model are formulated in the expectation-maximization scheme, and the algorithm to estimate the model parameters and time-delays is derived, simultaneously based on multirate process data. The efficacy of the proposed method is verified through a numerical simulation and a practical chemical plant.

23

ZHANG, BAOYONG, SHENGYUAN XU, and YONGMIN LI. "DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS." International Journal of Neural Systems 17, no. 03 (June 2007): 207–18. http://dx.doi.org/10.1142/s012906570700107x.

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This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

24

Chi, Ronghu, Zhongsheng Hou, and Shangtai Jin. "Data-Weighting Periodic RLS Based Adaptive Control Design and Analysis without Linear Growth Condition." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/191256.

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A new periodic recursive least-squares (PRLS) estimator is developed with data-weighting factors for a class of linear time-varying parametric systems where the uncertain parameters are periodic with a known periodicity. The periodical time-varying parameter can be regarded as a constant in the time interval of a periodicity. Then the proposed PRLS estimates the unknown time-varying parameter from period to period in batches. By using equivalent feedback principle, the feedback control law is constructed for the adaptive control. Another distinct feature of the proposed PRLS-based adaptive control is that the controller design and analysis are done via Lyapunov technology without any linear growth conditions imposed on the nonlinearities of the control plant. Simulation results further confirm the effectiveness of the presented approach.

25

Xing, Hailong, C. C. Gao, and Donghai Li. "Sliding mode variable structure control for parameter uncertain stochastic systems with time-varying delay." Journal of Mathematical Analysis and Applications 355, no. 2 (July 2009): 689–99. http://dx.doi.org/10.1016/j.jmaa.2009.02.005.

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26

Fan, Yongqing, Wenqing Wang, Ying Liu, and Minjuan Wang. "Fuzzy Adaptive Switching Control for an Uncertain Robot Manipulators with Time-Varying Output Constraint." Complexity 2018 (July 22, 2018): 1–10. http://dx.doi.org/10.1155/2018/8275296.

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An adaptive control strategy based on a fuzzy logic system by introducing a nonzero time-varying parameter is studied for an n-link manipulator system with the condition of a complex environment. At the beginning, a universal approximator with a one time-varying parameter is proposed based on the analysis of the fuzzy logic system, which is utilized to equalize uncertainties in robot manipulators with time-varying output constraints. The novel design method is used to reduce greatly the online learning computation burden compared with traditional fuzzy adaptive control. The output and the position of robotic manipulators are constrained with time-varying, a good tracking performance can be guaranteed with the condition of unknown dynamics of robot manipulators, and the violation of constraints can be conquered by the analysis based on the barrier Lyapunov function. A switching adaptive control is proposed to extend the semiglobal stability to global stability. Effectiveness of the approach is demonstrated by simulation results.

27

Hua, Mingang, Pei Cheng, Juntao Fei, Jianyong Zhang, and Junfeng Chen. "RobustH∞Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay." Journal of Applied Mathematics 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/402480.

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The robust filtering problem for a class of uncertain discrete-time fuzzy stochastic systems with sensor nonlinearities and time-varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribedH∞performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time-varying delays. These conditions are dependent on the lower and upper bounds of the time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

28

Zong, Guangdeng, Linlin Hou, and Hongyong Yang. "Further Results Concerning Delay-DependentH∞Control for Uncertain Discrete-Time Systems with Time-Varying Delay." Mathematical Problems in Engineering 2009 (2009): 1–24. http://dx.doi.org/10.1155/2009/732181.

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This paper addresses the problem ofH∞control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.

29

Wu, Bing, Jiale Wu, Jian Zhang, Guojian Tang, and Zhijia Zhao. "Adaptive Neural Control of a 2DOF Helicopter with Input Saturation and Time-Varying Output Constraint." Actuators 11, no. 11 (November 18, 2022): 336. http://dx.doi.org/10.3390/act11110336.

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An adaptive neural control for uncertain 2DOF helicopter systems with input saturation and time-varying output constraints is provided. A radial basis function neural network is used to estimate the uncertainty terms present in the system. The saturation error and the external disturbance are considered as a composite disturbance, and an adaptive auxiliary parameter is introduced to compensate it. An asymmetric barrier Lyapunov function is employed to address the constraint violation of the system output. The closed-loop stability of the system is then demonstrated by Lyapunov theory analysis. Simulation results demonstrate the effectiveness of the control strategy.

30

Chołodowicz, Ewelina, and Przemysław Orłowski. "Neural Network Control of Perishable Inventory with Fixed Shelf Life Products and Fuzzy Order Refinement under Time-Varying Uncertain Demand." Energies 17, no. 4 (February 11, 2024): 849. http://dx.doi.org/10.3390/en17040849.

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Many control algorithms have been applied to manage the flow of products in supply chains. However, in the era of thriving globalization, even a small disruption can be fatal for some companies. On the other hand, the rising environmental impact of a rapid industry is imposing limitations on energy usage and waste generation. Therefore, taking into account the mentioned perspectives, there is a need to explore the research directions that concern product perishability together with different demand patterns and their uncertain character. This study aims to propose a robust control approach that combines neural networks and optimal controller tuning with the use of both different demand patterns and fuzzy logic. Firstly, the demand forecast is generated, following which the parameters of the neural controller are optimized, taking into account the different demand patterns and uncertainty. As part of the verification of the designated controller, the sensitivity to parameter changes has been determined using the OAT method. It turns out that the proposed approach can provide significant waste reductions compared to the well-known POUT method while maintaining low stocks, a high fill rate, and providing lower sensitivity for parameter changes in most considered cases. The effectiveness of this approach is verified by using a dataset from a worldwide retailer. The simulation results show that the proposed approach can effectively improve the control of uncertain perishable inventories.

31

Zhou, Qi, Xueying Shao, Jin Zhu, and Hamid Reza Karimi. "Stability Analysis for Uncertain Neural Networks of Neutral Type with Time-Varying Delay in the Leakage Term and Distributed Delay." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/517604.

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The stability problem is investigated for a class of uncertain networks of neutral type with leakage, time-varying discrete, and distributed delays. Both the parameter uncertainty and the generalized activation functions are considered in this paper. New stability results are achieved by constructing an appropriate Lyapunov-Krasovskii functional and employing the free weighting matrices and the linear matrix inequality (LMI) method. Some numerical examples are given to show the effectiveness and less conservatism of the proposed results.

32

Wang, Bao Feng. "Robust Estimation for Discrete Time-Varying Uncertain Systems with Observation Losses in Networked Control System." Applied Mechanics and Materials 336-338 (July 2013): 628–32. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.628.

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In this paper, we deal with the robust minimum variance filtering problem for discrete time-varying systems with observation losses. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and output matrices, and the observation losses are described by a Bernoulli process with a known probability. An upper bound on the variance of the state estimation error is first found under certain probability of missing observations and admissible parameter uncertainties. Then, a robust filter is derived by minimizing the prescribed upper bound in the sense of the matrix norm. It is shown that the desired filter can be obtained in terms of the solutions to two discrete Riccati difference equations.

33

HAYASHIDA, Yasutaka, and Toshiki OGUCHI. "Control Design of Sampled-data Uncertain Systems with Time-varying Input Delay and Parameter Perturbations." Transactions of the Society of Instrument and Control Engineers 54, no. 10 (2018): 757–64. http://dx.doi.org/10.9746/sicetr.54.757.

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Phat, V. N., and P. T. Nam. "Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function." International Journal of Control 80, no. 8 (August 2007): 1333–41. http://dx.doi.org/10.1080/00207170701338867.

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Amato, F., M. Corless, A. Pironti, and R. Setola. "Robust Stability in the Presence of a Bounded and Bounded Rate, Time-Varying, Uncertain Parameter." IFAC Proceedings Volumes 29, no. 1 (June 1996): 3663–67. http://dx.doi.org/10.1016/s1474-6670(17)58247-6.

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Jia, Xiao, Laihong Hu, Fujun Feng, and Jun Xu. "Robust H∞ Consensus Control for Linear Discrete-Time Swarm Systems with Parameter Uncertainties and Time-Varying Delays." International Journal of Aerospace Engineering 2019 (July 24, 2019): 1–16. http://dx.doi.org/10.1155/2019/7278531.

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Robust H∞ consensus control problems of linear swarm systems with parameter uncertainties and time-varying delays are investigated. In this literature, a linear consensus protocol for high-order discrete-time swarm systems is proposed. Firstly, the robust H∞ consensus control problem of discrete-time swarm systems is transformed into a robust H∞ control problem of a set of independent uncertain systems. Secondly, sufficient linear matrix inequality conditions for robust H∞ consensus analysis of discrete-time swarm systems are given by the stability theory, and a H∞ performance level γ is determined meanwhile. Thirdly, the convergence result is derived as a final consensus value of swarm systems. Finally, numerical examples are presented to demonstrate theoretical results.

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Lu, Chien-Yu, Chin-Wen Liao, and Hsun-Heng Tsai. "Delay-Range-Dependent Global Robust Passivity Analysis of Discrete-Time Uncertain Recurrent Neural Networks with Interval Time-Varying Delay." Discrete Dynamics in Nature and Society 2009 (2009): 1–14. http://dx.doi.org/10.1155/2009/430158.

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This paper examines a passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. Based on an appropriate type of Lyapunov functional, sufficient passivity conditions for the DRNNs are derived in terms of a family of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness and applicability.

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Gao, Huijun, James Lam, Tongwen Chen, and Changhong Wang. "STABILITY ANALYSIS OF UNCERTAIN DISCRETE-TIME SYSTEMS WITH TIME-VARYING STATE DELAY: A PARAMETER-DEPENDENT LYAPUNOV FUNCTION APPROACH." Asian Journal of Control 8, no. 4 (October 22, 2008): 433–40. http://dx.doi.org/10.1111/j.1934-6093.2006.tb00296.x.

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Tadepalli, Siva Kumar, V. Krishna Rao Kandanvli, and Abhilav Vishwakarma. "Criteria for stability of uncertain discrete-time systems with time-varying delays and finite wordlength nonlinearities." Transactions of the Institute of Measurement and Control 40, no. 9 (June 26, 2017): 2868–80. http://dx.doi.org/10.1177/0142331217709067.

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This paper considers the problem of global asymptotic stability of a class of uncertain discrete-time systems under the influence of finite wordlength nonlinearities (quantization and/or overflow) and time-varying delays. The parameter uncertainties are assumed to be norm-bounded. Utilizing the concept of a Wirtinger-based inequality and a reciprocally convex method, two delay-dependent stability criteria are presented. The selection of the criteria depends on the type of the nonlinearities, that is, a combination of quantization and overflow or saturation overflow nonlinearities involved in the present systems. The approach presented in this paper yields less conservative results and reduces the computational burden as compared to previously reported criteria. Numerical examples are given to illustrate the effectiveness of the presented approach.

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Adiguzel, Fatih, and Tarik Veli Mumcu. "Robust Discrete-Time Nonlinear Attitude Stabilization of a Quadrotor UAV Subject to Time-Varying Disturbances." Elektronika ir Elektrotechnika 27, no. 4 (August 17, 2021): 4–12. http://dx.doi.org/10.5755/j02.eie.28916.

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A discrete-time improved input/output linearization controller based on a nonlinear disturbance observer is considered to secure the stability of a four-rotor unmanned aerial vehicle under constant and time-varying disturbances, as well as uncertain system parameters for its attitude behaviour. Due to the nature of the quadrotor system, it contains the most extreme high level of nonlinearities, system parameter uncertainties (perturbations), and it has to cope with external disturbances that change over time. In this context, an offset-less tracking for the quadrotor system is provided with the input/output linearization controller together with a discrete-time pre-controller. In addition, the robustness of the system is increased with a discrete-time nonlinear disturbance observer for time-varying disturbances affecting the system. The main contribution of this study is to provide highly nonlinearities cancellation to guarantee the aircraft attitude stability and to propose a robust control structure in discrete-time, considering all uncertainties. Various simulation studies have been carried out to illustrate the robustness and effectiveness of the proposed controller structure.

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Chen, Shinn-Horng, Jyh-Horng Chou, and Liang-An Zheng. "Robust Kalman-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems." Journal of Mechanics 16, no. 3 (September 2000): 145–55. http://dx.doi.org/10.1017/s1727719100001805.

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ABSTRACTThis paper presents a time-domain control methodology, which is named as the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method, to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high frequencies unmodelled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise),and noise uncertainties. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rotor system.

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Tang, Chuan Sheng, and Yue Hong Dai. "Novel Active Disturbance Rejection Control for Permanent Magnet Linear Synchronous Motor without Sensor." Advanced Materials Research 335-336 (September 2011): 571–76. http://dx.doi.org/10.4028/www.scientific.net/amr.335-336.571.

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A novel ADRC scheme is proposed for permanent magnet linear synchronous motor without sensor, which has nonlinear, multi-load disturbance and parameter time-varying characteristics. Extended states observer (ESO) in ADRC can real-time estimate speed, location and uncertain disturbance, and the parameters artificial is used to optimize by fish swarm algorithm. Finally, simulation results confirm the proposed strategy has better tracking performance and robustness than the traditional one.

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Dong, Yali, Jing Hao, Yonghong Yao, and Huimin Wang. "Robust Stabilization of Discrete-Time Switched Periodic Systems with Time Delays." Complexity 2019 (February 13, 2019): 1–13. http://dx.doi.org/10.1155/2019/3950848.

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This paper studies the problems of robust stability and robust stabilization for discrete-time switched periodic systems with time-varying delays and parameter uncertainty. We obtain the novel sufficient conditions to ensure the switched system is robustly asymptotically stable in terms of linear matrix inequalities. To obtain these conditions, we utilize a descriptor system method and introduce a switched Lyapunov-Krasovskii functional. The robust stability results are then extended to solve problems of robust stabilization via periodic state feedback. Novel sufficient conditions are established to ensure that the uncertain switched periodic system is robustly asymptotically stabilizable. Finally, we give two numerical examples to illustrate the effectiveness of our method.

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Singkibud, Peerapongpat, Luu Thi Hiep, Piyapong Niamsup, Thongchai Botmart, and Kanit Mukdasai. "Delay-Dependent Robust H∞ Performance for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations." Mathematical Problems in Engineering 2018 (October 16, 2018): 1–16. http://dx.doi.org/10.1155/2018/5721695.

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This paper deals with the problems of delay-dependent stability and H∞ performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved H∞ performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.

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Han, Xudong, Yongling Fu, Yan Wang, Mingkang Wang, and Deming Zhu. "Dynamic Surface-Based Adaptive Active Disturbance Rejection Control of Electrohydrostatic Actuators." Aerospace 10, no. 9 (August 23, 2023): 747. http://dx.doi.org/10.3390/aerospace10090747.

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The control accuracy and stability of the electrohydrostatic actuator (EHA) are directly impacted by parameter uncertainty, disturbance uncertainty, and non-matching disturbance, which negatively impacts aircraft rudder maneuvering performance and even results in rudder chatter. A dynamic surface-based adaptive active disturbance rejection control (DSAADRC) is proposed as a solution for these issues. It does this by developing a novel parametric adaptive law driven by the combination of tracking error, parameter estimation error, and state estimation error to estimate the unknown parameters, using three low-order ESOs to estimate and compensate the uncertain disturbances online, and employing a dynamic surface method to obtain the differential values of virtual control signals in the backstepping method to deal with non-matching disturbances. In this research, a Lyapunov stability analysis demonstrates that the method can achieve the position tracking accuracy of the EHA under time-varying external disturbances after first establishing an EHA dynamics model with nonlinearity and uncertainty, followed by the design of an adaptive active disturbance rejection control method based on dynamic surfaces for the uncertainties and perturbations. In contrast to control strategies like Robust Control (RC) and Adaptive Robust Control (ARC), simulation and experiment comparison shows that the method has stronger anti-disturbance under time-varying external disturbances.

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Souillé, Fabien, Cédric Goeury, and Rem-Sophia Mouradi. "Uncertainty analysis of single- and multiple-size-class frazil ice models." Cryosphere 17, no. 4 (April 14, 2023): 1645–74. http://dx.doi.org/10.5194/tc-17-1645-2023.

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Abstract. The formation of frazil ice in supercooled waters has been extensively studied, both experimentally and numerically, in recent years. Numerical models, with varying degrees of complexity, have been proposed; these are often based on many parameters, the values of which are uncertain and difficult to estimate. In this paper, an uncertainty analysis of two mathematical models that simulate supercooling and frazil ice formation is carried out within a probabilistic framework. The two main goals are (i) to provide quantitative insight into the relative importance of contributing uncertain parameters, to help identify parameters for optimal calibration, and (ii) to compare the output scatter of frazil ice models with single and multiple crystal size classes. The derivation of single- and multi-class models is presented in light of recent work, their numerical resolution is discussed, and a list of the main uncertain parameters is proposed. An uncertainty analysis is then carried out in three steps. Parameter uncertainty is first quantified, based on recent field, laboratory and numerical studies. Uncertainties are then propagated through the models using Monte Carlo simulations. Finally, the relative influence of uncertain parameters on the output time series – i.e., the total frazil volume fraction and water temperature – is assessed by means of Sobol indices. The influence of input parameters on the long-term asymptote as well as short-term transient evolution of the systems is discussed, depending on whether gravitational removal is included or not in the models.

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Jeetendra, R., and Vernold Vivin. "Stability analysis of uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties via augmented Lyapunov functional." Filomat 26, no. 6 (2012): 1179–88. http://dx.doi.org/10.2298/fil1206179j.

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In this work, the problem of delay-dependent stability for uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties is addressed. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing an augmented Lyapunov functional, a new delay interval-dependent stability criterion for the system is obtained in terms of Linear Matrix Inequalities (LMIs). Comparisons are made through numerical examples and less conservatism results are reported.

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Guan, Xinping, Yichang Liu, Cailian Chen, and Peng Shi. "Observer-based robust H∞, control for uncertain time-delay systems." ANZIAM Journal 44, no. 4 (April 2003): 625–34. http://dx.doi.org/10.1017/s1446181100012980.

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AbstractIn this paper, we present a method for the construction of a robust observer-based H∞ controller for an uncertain time-delay system. Cases of both single and multiple delays are considered. The parameter uncertainties are time-varying and norm-bounded. Observer and controller are designed to be such that the uncertain system is stable and a disturbance attenuation is guaranteed, regardless of the uncertainties. It has been shown that the above problem can be solved in terms of two linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the effectiveness of the proposed techniques.

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Chen, Shinn-Horng. "Robust Kalman-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems with Nonlinear Actuators." Journal of Vibration and Control 9, no. 6 (June 2003): 623–44. http://dx.doi.org/10.1177/1077546303009006001.

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Abstract:

In this paper, we present a time-domain control methodology, called the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method. Using this method, we treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high-frequency unmodeled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise), noise uncertainties and actuator nonlinearities. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, actuator nonlinearities and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF control methodology is that it can make the controlled closed-loop system have both good robustness at high frequencies and good performance at low frequencies. Besides, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system avoid the possibilities of instability induced by both spillover and time-varying parameter perturbations. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply-supported flexible beam and of a flexible rotor system.

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Chanthorn, Pharunyou, Grienggrai Rajchakit, Jenjira Thipcha, Chanikan Emharuethai, Ramalingam Sriraman, Chee Peng Lim, and Raja Ramachandran. "Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties." Mathematics 8, no. 5 (May 8, 2020): 742. http://dx.doi.org/10.3390/math8050742.

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In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.