Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints

Finite time control issue for a quite comprehensive class of system model, that is, Markov jump repeated scalar nonlinear systems (MJRSNSs) has been addressed.An asynchronous controller is first proposed in MJRSNSs, which has less conservatism than mode-dependent when the partly available mode information is encountered.The input constraints associated with physical limitations in some practical applications have been fully considered, which make our model more realistic. This paper is concerned with the problem of finite-time H ∞ control for Markov jump repeated scalar nonlinear systems (MJRSNSs) with input constraints. The jumps between MJRSNSs and desired mode-dependent controllers are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the different degrees of asynchronous jumps between MJRSNSs and controllers. With the aid of Lyapunov-Krasovskii methodology, some H ∞ performance criteria for the MJRSNSs are proposed. Based on these criteria, sufficient conditions on the existence of the desired controllers are established, and then the gains of the controllers can be obtained by solving a convex optimization problem. Finally, an example is presented to illustrate the effectiveness of our method.

[1]  Shouming Zhong,et al.  Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching , 2015, Int. J. Syst. Sci..

[2]  Eduardo D. Sontag,et al.  State observability in recurrent neural networks , 1994 .

[3]  Dan Ye,et al.  Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions , 2013, Fuzzy Sets Syst..

[4]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[5]  Fei Liu,et al.  Finite-Time $H_{\infty}$ Fuzzy Control of Nonlinear Jump Systems With Time Delays Via Dynamic Observer-Based State Feedback , 2012, IEEE Transactions on Fuzzy Systems.

[6]  Guoliang Wang,et al.  Stabilization of discrete‐time singular Markovian jump repeated vector nonlinear systems , 2016 .

[7]  Fang Wang,et al.  Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty , 2014 .

[8]  Shan Ma,et al.  Robust decentralized stabilization of Markovian jump large-scale systems: A neighboring mode dependent control approach , 2013, Autom..

[9]  Guanghui Wen,et al.  Distributed finite-time tracking control for multi-agent systems: An observer-based approach , 2013, Syst. Control. Lett..

[10]  Shihua Li,et al.  Finite-time tracking control of multiple nonholonomic mobile robots , 2012, J. Frankl. Inst..

[11]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[12]  Dan Zhang,et al.  Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback , 2012 .

[13]  Francesco Amato,et al.  Finite-Time Stability and Control , 2013 .

[14]  Seong-Young Ko,et al.  Trajectory following for a flexible probe with state/input constraints: An approach based on model predictive control , 2012, Robotics Auton. Syst..

[15]  Zhihong Man,et al.  Finite-time stability and instability of stochastic nonlinear systems , 2011, Autom..

[16]  Wei Xing Zheng,et al.  L2-L∞ filtering for stochastic Markovian jump delay systems with nonlinear perturbations , 2015, Signal Process..

[17]  Ju H. Park,et al.  Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network , 2012, 2012 12th International Conference on Control, Automation and Systems.

[18]  Ju H. Park,et al.  Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities , 2015, Appl. Math. Comput..

[19]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[20]  Randal W. Beard,et al.  Fixed Wing UAV Path Following in Wind With Input Constraints , 2014, IEEE Transactions on Control Systems Technology.

[21]  Guoliang Wang.  Partially mode-dependent design of H∞ filter for stochastic Markovian jump systems with mode-dependent time delays☆ , 2011 .

[22]  Huijun Gao,et al.  H∞ Fuzzy Control for Systems With Repeated Scalar Nonlinearities and Random Packet Losses , 2009, IEEE Trans. Fuzzy Syst..

[23]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[24]  Ligang Wu,et al.  Filter design for Markovian jump repeated scalar nonlinear systems , 2014, J. Frankl. Inst..

[25]  Guanghui Wen,et al.  Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances , 2013, Int. J. Control.

[26]  Hao Shen,et al.  Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts , 2014 .

[27]  Yun-Chung Chu,et al.  Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities , 1999, IEEE Trans. Autom. Control..

[28]  Huijun Gao,et al.  Induced l/sub 2/ and generalized H/sub 2/ filtering for systems with repeated scalar nonlinearities , 2005, IEEE Transactions on Signal Processing.

[29]  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.

[30]  Ligang Wu,et al.  Output Feedback Control of Markovian Jump Repeated Scalar Nonlinear Systems , 2014 .

[31]  Yueying Wang,et al.  Exponential $H_{\infty}$ Filtering for Singular Markovian Jump Systems With Mixed Mode-Dependent Time-Varying Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Dan Zhang,et al.  Finite-time H∞ control for discrete-time genetic regulatory networks with random delays and partly unknown transition probabilities , 2013, J. Frankl. Inst..

[33]  Yun-Chung Chu,et al.  Stabilization and performance synthesis for systems with repeated scalar nonlinearities , 1999, IEEE Trans. Autom. Control..