Observer-based sliding mode control of Markov jump systems with random sensor delays and partly unknown transition rates

ABSTRACT In this paper, the sliding mode control problem of Markov jump systems (MJSs) with unmeasured state, partly unknown transition rates and random sensor delays is probed. In the practical engineering control, the exact information of transition rates is hard to obtain and the measurement channel is supposed to subject to random sensor delay. Design a Luenberger observer to estimate the unmeasured system state, and an integral sliding mode surface is constructed to ensure the exponential stability of MJSs. A sliding mode controller based on estimator is proposed to drive the system state onto the sliding mode surface and render the sliding mode dynamics exponentially mean-square stable with H∞ performance index. Finally, simulation results are provided to illustrate the effectiveness of the proposed results.

[1]  Zidong Wang,et al.  Distributed H∞ state estimation with stochastic parameters and nonlinearities through sensor networks: The finite-horizon case , 2012, Autom..

[2]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

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

[4]  Fuwen Yang,et al.  Observer-based networked control for continuous-time systems with random sensor delays , 2009, Autom..

[5]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[6]  Lu Bai,et al.  Observer‐based adaptive control for stochastic nonstrict‐feedback systems with unknown backlash‐like hysteresis , 2017 .

[7]  Guang-Hong Yang,et al.  Event-triggered fuzzy control for nonlinear networked control systems , 2017, Fuzzy Sets Syst..

[8]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[9]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[10]  Huijun Gao,et al.  Distributed Filtering for a Class of Time-Varying Systems Over Sensor Networks With Quantization Errors and Successive Packet Dropouts , 2012, IEEE Transactions on Signal Processing.

[11]  Qi Zhou,et al.  Robust control of uncertain semi-Markovian jump systems using sliding mode control method , 2016, Appl. Math. Comput..

[12]  Xingyu Wang,et al.  Sliding mode control design for uncertain delay systems with partial actuator degradation , 2009, Int. J. Syst. Sci..

[13]  Ligang Wu,et al.  Observer-based adaptive sliding mode control for nonlinear Markovian jump systems , 2016, Autom..

[14]  Leonid M. Fridman,et al.  Sliding Mode Identification and Control for Linear Uncertain Stochastic Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[15]  Daniel W. C. Ho,et al.  Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance , 2015, Autom..

[16]  Lijie Wang,et al.  Adaptive Fuzzy Control of Nonlinear Systems With Unmodeled Dynamics and Input Saturation Using Small-Gain Approach , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[17]  Yugang Niu,et al.  Robust Filtering Design for Stochastic System With Mode-Dependent Output Quantization , 2010, IEEE Transactions on Signal Processing.

[18]  Yuanqing Xia,et al.  Networked Data Fusion With Packet Losses and Variable Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Yugang Niu,et al.  Design of Sliding Mode Control Subject to Packet Losses , 2010, IEEE Transactions on Automatic Control.

[20]  Renquan Lu,et al.  A New Design of Model Predictive Tracking Control for Networked Control System Under Random Packet Loss and Uncertainties , 2016, IEEE Transactions on Industrial Electronics.

[21]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[22]  Fuwen Yang,et al.  H∞ filtering for nonlinear networked systems with randomly occurring distributed delays, missing measurements and sensor saturation , 2016, Inf. Sci..

[23]  Fuwen Yang,et al.  $H_{\infty }$ Fault Detection for Networked Mechanical Spring-Mass Systems With Incomplete Information , 2016, IEEE Transactions on Industrial Electronics.

[24]  S. Hassan HosseinNia,et al.  Design of second order sliding mode and sliding mode algorithms: a practical insight to DC-DC buck converter , 2017, IEEE/CAA Journal of Automatica Sinica.

[25]  Michael V. Basin,et al.  Sliding mode filter design for nonlinear polynomial systems with unmeasured states , 2012, Inf. Sci..

[26]  Dong Yue,et al.  Stabilization of Systems With Probabilistic Interval Input Delays and Its Applications to Networked Control Systems , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[27]  Yuanqing Xia,et al.  Output feedback delay compensation control for networked control systems with random delays , 2014, Inf. Sci..

[28]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[29]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[30]  Michael V. Basin,et al.  Sliding Mode Controller Design for Stochastic Polynomial Systems With Unmeasured States , 2014, IEEE Transactions on Industrial Electronics.

[31]  Jie Zhang,et al.  Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices , 2011, Autom..

[32]  Peng Shi,et al.  Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation , 2017, Fuzzy Sets Syst..

[33]  Zhiqiang Cao,et al.  Sliding mode control of MIMO Markovian jump systems , 2016, Autom..

[34]  Yuxin Zhao,et al.  Sliding mode control of continuous-time Markovian jump systems with digital data transmission , 2017, Autom..

[35]  Peng Shi,et al.  Adaptive Sliding-Mode Control of Markov Jump Nonlinear Systems With Actuator Faults , 2017, IEEE Transactions on Automatic Control.

[36]  Peng Shi,et al.  Robust Estimation for Neural Networks With Randomly Occurring Distributed Delays and Markovian Jump Coupling , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[38]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[39]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[40]  Peng Shi,et al.  Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems , 2006, Autom..

[41]  Keith J. Burnham,et al.  On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters , 2002, IEEE Trans. Autom. Control..

[42]  Abdesselem Boulkroune,et al.  Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay , 2017, IEEE Transactions on Fuzzy Systems.

[43]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[44]  Yuanqing Xia,et al.  Robust sliding-mode control for uncertain time-delay systems: an LMI approach , 2003, IEEE Trans. Autom. Control..

[45]  Vadim I. Utkin,et al.  Sliding mode control design principles and applications to electric drives , 1993, IEEE Trans. Ind. Electron..

[46]  Qing-Long Han,et al.  Distributed event-triggered H1 filtering over sensor networks with communication delays , 2014 .

[47]  Ming Yue,et al.  Neural network based terminal sliding mode control for WMRs affected by an augmented ground friction with slippage effect , 2017, IEEE/CAA Journal of Automatica Sinica.

[48]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[49]  Shihua Li,et al.  Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Mismatched Term , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[50]  Daniel W. C. Ho,et al.  Robust observer design for Itô stochastic time-delay systems via sliding mode control , 2006, Syst. Control. Lett..

[51]  Renquan Lu,et al.  Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[52]  Nan Xiao,et al.  Stabilization of Markov jump linear systems using quantized state feedback , 2010, Autom..

[53]  Peng Shi,et al.  Fault-Tolerant Sliding-Mode-Observer Synthesis of Markovian Jump Systems Using Quantized Measurements , 2015, IEEE Transactions on Industrial Electronics.

[54]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.