Probability-based constrained MPC for structured uncertain systems with state and random input delays

This article is concerned with probability-based constrained model predictive control (MPC) for systems with both structured uncertainties and time delays, where a random input delay and multiple fixed state delays are included. The process of input delay is governed by a discrete-time finite-state Markov chain. By invoking an appropriate augmented state, the system is transformed into a standard structured uncertain time-delay Markov jump linear system (MJLS). For the resulting system, a multi-step feedback control law is utilised to minimise an upper bound on the expected value of performance objective. The proposed design has been proved to stabilise the closed-loop system in the mean square sense and to guarantee constraints on control inputs and system states. Finally, a numerical example is given to illustrate the proposed results.

[1]  Tongwen Chen,et al.  Model predictive control for networked control systems , 2009 .

[2]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[3]  Lihua Xie,et al.  Robust MPC for polytopic uncertain systems with time-varying delays , 2008, Int. J. Control.

[4]  Dewei Li,et al.  Constrained robust feedback model predictive control for uncertain systems with polytopic description , 2009, Int. J. Control.

[5]  Wu-Hua Chen,et al.  Delay-dependent stability and H∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays , 2004, Syst. Control. Lett..

[6]  Biao Huang,et al.  Constrained robust model predictive control for time-delay systems with polytopic description , 2007, Int. J. Control.

[7]  Oswaldo Luiz do Valle Costa,et al.  Constrained quadratic state feedback control of discrete-time Markovian jump linear systems , 1999, Autom..

[8]  Dewei Li,et al.  Robust model predictive control approach to time-delay systems with structured uncertainty , 2010, 2010 8th World Congress on Intelligent Control and Automation.

[9]  Wook Hyun Kwon,et al.  Robust Receding Horizon Control of Discrete-Time Markovian Jump Uncertain Systems , 2001 .

[10]  M. Fu.  Perturbation Analysis , 2007 .

[11]  Dewei Li,et al.  Constrained feedback robust model predictive control for polytopic uncertain systems with time delays , 2011, Int. J. Syst. Sci..

[12]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[13]  Wook Hyun Kwon,et al.  Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems , 2002, Autom..

[14]  Shiyin Qin,et al.  Stability analysis and controller design for networked control systems with random time delay , 2009, 2009 9th International Conference on Electronic Measurement & Instruments.

[15]  Guoping Lu,et al.  Stability analysis of networked control systems with Markov delay , 2005, 2005 International Conference on Control and Automation.

[16]  U. Ozguner,et al.  Stability of Linear Feedback Systems with Random Communication Delays , 1991, 1991 American Control Conference.

[17]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[18]  M. Kothare,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[19]  Laurent El Ghaoui,et al.  4. Linear Differential Inclusions , 1994 .

[20]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[21]  Frank Kozin,et al.  A survey of stability of stochastic systems , 1969, Autom..

[22]  Yu-Geng Xi,et al.  Design of Robust Model Predictive Control Based on Multi-step Control Set , 2009 .

[23]  Tongwen Chen,et al.  Network-based predictive control of multirate systems , 2010 .

[24]  Alberto Bemporad,et al.  Scenario-based model predictive control of stochastic constrained linear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[25]  PooGyeon Park,et al.  Constrained MPC algorithm for uncertain time-varying systems with state-delay , 2005, IEEE Trans. Autom. Control..

[26]  Yuguang Fang,et al.  Stochastic stability of jump linear systems , 2002, IEEE Trans. Autom. Control..

[27]  Yeung Sam Hung,et al.  Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case , 2010, Autom..