Robust control for a class of state-constrained high-order switched nonlinear systems with unstable subsystems

ABSTRACT This paper addresses the issue of robust stabilisation for a class of state-constrained high-order switched nonlinear systems whose subsystems are allowed to be all unstabilizable. A novel robust control scheme is established based on effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions. Explicitly, a sufficient condition for robustly stabilising the resulting closed-loop system in a domain is presented, which meanwhile can also guarantee that the violation of the constraints does not happen. Moreover, in the switching law design, we do not require the connection of barrier Lyapunov functions for two adjacent subsystems, and even a certain amount of jump is also allowed. Finally, the effectiveness of the provided control strategy is demonstrated via a simulation example.

[1]  Jun Zhao,et al.  Adaptive control for a class of high-order switched nonlinearly parameterized systems , 2017 .

[2]  Peng Shi,et al.  Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time , 2009, IEEE Transactions on Automatic Control.

[3]  Qingyu Su,et al.  Stabilization of state‐constrained switched nonlinear systems in p‐normal form , 2014 .

[4]  Yasushi Hada,et al.  Constrained Model Predictive Control , 2006 .

[5]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[6]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[7]  Zongli Lin,et al.  Output Feedback Stabilization of Linear Systems With Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[8]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[9]  Wei Wang,et al.  Predictive control of nonlinear continuous networked control systems with large time-varying transmission delays and transmission protocols , 2016, Autom..

[10]  Jun Zhao,et al.  $H_{\infty}$ Control of Switched Nonlinear Systems in $p$-Normal Form Using Multiple Lyapunov Functions , 2012, IEEE Transactions on Automatic Control.

[11]  Guang-Hong Yang,et al.  Adaptive fuzzy fault tolerant tracking control for a class of uncertain switched nonlinear systems with output constraints , 2016, J. Frankl. Inst..

[12]  Wei Lin,et al.  Adaptive regulation of high-order lower-triangular systems : an adding a power integrator technique , 2000 .

[13]  Ying Tan,et al.  On Designing Event-Triggered Schemes for Networked Control Systems Subject to One-Step Packet Dropout , 2016, IEEE Transactions on Industrial Informatics.

[14]  Kenji Hirata,et al.  Reference Governor for Constrained Systems with Time-varying References , 2006, 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems.

[15]  Honghai Liu,et al.  Stabilization of Discrete‐time Switched Systems with State Constraints Based on Mode‐Dependent Average Dwell Time , 2017 .

[16]  Wei Wang,et al.  A PD-Like Protocol With a Time Delay to Average Consensus Control for Multi-Agent Systems Under an Arbitrarily Fast Switching Topology , 2017, IEEE Transactions on Cybernetics.

[17]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[18]  P. Kokotovic,et al.  Adaptive nonlinear design with controller-identifier separation and swapping , 1995, IEEE Trans. Autom. Control..

[19]  Shuzhi Sam Ge,et al.  Switched Linear Systems , 2005 .

[20]  Fuad E. Alsaadi,et al.  Distributed optimisation for multi-agent systems with the first-order integrals under Markovian switching topologies , 2017, Int. J. Syst. Sci..

[21]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[22]  Ligang Wu,et al.  Fault Detection Filtering for Nonhomogeneous Markovian Jump Systems via a Fuzzy Approach , 2018, IEEE Transactions on Fuzzy Systems.

[23]  Fen Wu,et al.  Analysis and control of switched linear systems via dwell-time min-switching , 2014, Syst. Control. Lett..

[24]  Liang Liu,et al.  Robust Adaptive State Constraint Control for Uncertain Switched High-Order Nonlinear Systems , 2017, IEEE Transactions on Industrial Electronics.

[25]  Jun Fu,et al.  Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers , 2015, Autom..

[26]  Yu Zhang,et al.  Impulsive Control of Discrete Systems With Time Delay , 2009, IEEE Transactions on Automatic Control.

[27]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

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

[29]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[30]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[31]  Kenji Hirata,et al.  Reference Governor for Constrained Systems with Time-varying References , 2006, MFI.

[32]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[33]  Peng Shi,et al.  Input-to-State Stability for Nonlinear Systems With Large Delay Periods Based on Switching Techniques , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[34]  Shaocheng Tong,et al.  Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems , 2017, Autom..

[35]  Uri Shaked,et al.  Robust State-Dependent Switching of Linear Systems With Dwell Time , 2013, IEEE Transactions on Automatic Control.

[36]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

[37]  Peter Kuster,et al.  Nonlinear And Adaptive Control Design , 2016 .

[38]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

[39]  Jun Zhao,et al.  On stability, L 2 -gain and H 8 control for switched systems , 2008 .

[40]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[41]  Jie Lian,et al.  Sampled-Data Control of Switched Linear Systems With Application to an F-18 Aircraft , 2017, IEEE Transactions on Industrial Electronics.

[42]  Shaocheng Tong,et al.  Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints , 2016, Autom..

[43]  Keng Peng Tee,et al.  Control of nonlinear systems with time-varying output constraints , 2009, 2009 IEEE International Conference on Control and Automation.

[44]  Wei Wang,et al.  Adaptive Tracking Control for a Class of Stochastic Uncertain Nonlinear Systems With Input Saturation , 2017, IEEE Transactions on Automatic Control.

[45]  Guangdeng Zong,et al.  Command Filter-Based Adaptive Neural Tracking Controller Design for Uncertain Switched Nonlinear Output-Constrained Systems , 2017, IEEE Transactions on Cybernetics.

[46]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[47]  Xudong Zhao,et al.  A new control method for state-constrained nonlinear switched systems with application to chemical process , 2015, Int. J. Control.

[48]  Yanhui Ding,et al.  OPTIMAL SWITCHING TIME CONTROL OF DISCRETE-TIME SWITCHED AUTONOMOUS SYSTEMS , 2015 .

[49]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.