A note on guaranteed cost control for nonlinear stochastic systems with input saturation and mixed time‐delays

ThisIn the system under investigation, the control input is subject to the saturation constraint, and both discrete and distributed time‐delays are taken into consideration. The objective of the addressed problem is to design a state feedback controller such that the resulting closed‐loop system is asymptotically stable in probability and an upper bound is guaranteed on a prespecified quadratic cost function. Sufficient conditions are established for the existence of the desired guaranteed cost control strategy in terms of the solvability of certain Hamilton–Jacobi inequalities. Simulation results demonstrate the correctness and applicability of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.

[1]  Jianliang Wang,et al.  Reliable guaranteed cost control for uncertain nonlinear systems , 2000, IEEE Trans. Autom. Control..

[2]  Yonggang Chen,et al.  Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays , 2015, J. Frankl. Inst..

[3]  Yugang Niu,et al.  Finite-time sliding mode control synthesis under explicit output constraint , 2016, Autom..

[4]  A. Klimek,et al.  Fuzzy Adaptive Transmission-Line Differential Relay Immune to CT Saturation , 2012, IEEE Transactions on Power Delivery.

[5]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[6]  Bor-Sen Chen,et al.  Some Remarks on General Nonlinear Stochastic $H_{\infty }$ Control With State, Control, and Disturbance-Dependent Noise , 2014, IEEE Transactions on Automatic Control.

[7]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[8]  Ali Saberi,et al.  Semiglobal stabilization of linear discrete-time systems subject to input saturation, via linear feedback-an ARE-based approach , 1996, IEEE Trans. Autom. Control..

[9]  Guangming Zhuang,et al.  Fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation , 2016, Int. J. Syst. Sci..

[10]  Peng Shi,et al.  Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems , 2009, J. Frankl. Inst..

[11]  Huajing Fang,et al.  Robust non-fragile H∞ state estimation for discrete-time genetic regulatory networks with Markov jump delays and uncertain transition probabilities , 2015, Neurocomputing.

[12]  L. Keel,et al.  Robust Stability and Stabilization of a Class of Nonlinear Itô-Type Stochastic Systems via Linear Matrix Inequalities , 2013 .

[13]  Zidong Wang,et al.  A game theory approach to mixed H2/H∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities , 2011, Syst. Control. Lett..

[14]  Weihai Zhang,et al.  State Feedback HINFINITY Control for a Class of Nonlinear Stochastic Systems , 2006, SIAM J. Control. Optim..

[15]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[16]  Marek T. Malinowski,et al.  Itô type stochastic fuzzy differential equations with delay , 2012, Syst. Control. Lett..

[17]  Shuai Liu,et al.  Error-constrained reliable tracking control for discrete time-varying systems subject to quantization effects , 2016, Neurocomputing.

[18]  Yugang Niu,et al.  Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation , 2013, Autom..

[19]  Oswaldo Luiz V. Costa,et al.  Stochastic stabilization and induced l2-gain for discrete-time Markov jump Lur'e systems with control saturation , 2014, Autom..

[20]  Jürgen Adamy,et al.  On stabilizing linear systems with input saturation via soft variable structure control laws , 2016, Syst. Control. Lett..

[21]  Hiroaki Mukaidani.  The guaranteed cost control for uncertain nonlinear large-scale stochastic systems via state and static output feedback , 2009 .

[22]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[23]  Fuad E. Alsaadi,et al.  A new framework for output feedback controller design for a class of discrete-time stochastic nonlinear system with quantization and missing measurement , 2016, Int. J. Gen. Syst..

[24]  Yurong Liu,et al.  Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays , 2016, Neurocomputing.

[25]  Zidong Wang,et al.  Variance‐constrained state estimation for networked multi‐rate systems with measurement quantization and probabilistic sensor failures , 2016 .

[26]  Fuad E. Alsaadi,et al.  Robust filtering for a class of nonlinear stochastic systems with probability constraints , 2016, Autom. Remote. Control..

[27]  Fuad E. Alsaadi,et al.  Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays , 2016, Neurocomputing.

[28]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[29]  Allison W. Albrecht,et al.  Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions , 1999 .

[30]  Gang Feng,et al.  Nonlinear Stochastic $H_2/H_\infty$ Control with $(x,u,v)$-Dependent Noise: Infinite Horizon Case , 2008, IEEE Transactions on Automatic Control.

[31]  M. J. Anabtawi,et al.  Practical stability of nonlinear stochastic hybrid parabolic systems of Itô-type: Vector Lyapunov functions approach , 2011 .

[32]  Yonggang Chen,et al.  Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback , 2015, Autom..

[33]  Shuai Liu,et al.  Extended Kalman filtering for stochastic nonlinear systems with randomly occurring cyber attacks , 2016, Neurocomputing.

[34]  Donghua Zhou,et al.  Event-Based $H_{\infty}$ Consensus Control of Multi-Agent Systems With Relative Output Feedback: The Finite-Horizon Case , 2015, IEEE Transactions on Automatic Control.

[35]  M. D. S. Aliyu,et al.  A transformation approach for solving the Hamilton-Jacobi-Bellman equation in H2 deterministic and stochastic optimal control of affine nonlinear systems , 2003, Autom..

[36]  Diana Keller,et al.  Optimal Control of a Nonlinear Stochastic Schrödinger Equation , 2015, J. Optim. Theory Appl..

[37]  Fuwen Yang,et al.  Set-membership filtering for systems with sensor saturation , 2009, Autom..

[38]  Zidong Wang,et al.  Event-based state estimation for a class of complex networks with time-varying delays: A comparison principle approach , 2017 .

[39]  Quanyan Zhu,et al.  Resilient control in the presence of DoS attack: Switched system approach , 2015 .

[40]  Prashant Mhaskar,et al.  Lyapunov-based model predictive control of stochastic nonlinear systems , 2012, Autom..

[41]  Zidong Wang,et al.  Variance-constrained state estimation for networked multi-rate systems with measurement quantization and probabilistic sensor failures , 2016 .

[42]  Yurong Liu,et al.  Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects , 2016, Neurocomputing.

[43]  Fuad E. Alsaadi,et al.  H∞ and I2-I∞ finite-horizon filtering with randomly occurring gain variations and quantization effects , 2017, Appl. Math. Comput..

[44]  Ulrich G. Haussmann.  Generalized Solutions of the Hamilton-Jacobi Equation of Stochastic Control , 1994 .