Control of LPV systems subject to state constraints and input saturation

This paper deals with the stabilization of state-constrained linear parameter-varying systems subject to parameter uncertainties and input saturation. Based on a class of parameter-dependent Lyapunov functions, and the set invariance, sufficient conditions for the stabilization problem of the linear parameter-varying systems are established in terms of parameterized linear matrix inequalities. Further, these conditions are converted into linear matrix inequalities by using a parameter relaxation technique. Finally, detailed simulation results are presented to illustrate the effectiveness of the proposed methodology.

[1]  Zongli Lin,et al.  Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  W. Xie.  H2 gain scheduled state feedback for LPV system with new LMI formulation , 2005 .

[3]  Yongming Li,et al.  Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function , 2014 .

[4]  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.

[5]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[6]  Zongli Lin,et al.  Saturation-based switching anti-windup design for linear systems with nested input saturation , 2014, Autom..

[7]  Peng Yan,et al.  On switching Hinfinity controllers for a class of linear parameter varying systems , 2007, Syst. Control. Lett..

[8]  Jakob Stoustrup,et al.  Fault‐tolerant control of discrete‐time LPV systems using virtual actuators and sensors , 2015 .

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

[10]  Karolos M. Grigoriadis,et al.  Anti-windup controller synthesis via linear parameter-varying control design methods , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[11]  Adolf Hermann Glattfelder,et al.  Control Systems with Input and Output Constraints , 2003 .

[12]  Jun Zhao,et al.  Parameter-dependent H∞ filter design for LPV systems and an autopilot application , 2012, Appl. Math. Comput..

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

[14]  Didier Henrion,et al.  Polynomial LPV synthesis applied to turbofan engines , 2010 .

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

[16]  Zongli Lin,et al.  Robust global stabilization of linear systems with input saturation via gain scheduling , 2010 .

[17]  Toshiharu Sugie,et al.  Output feedback model predictive control for LPV systems based on quasi-min-max algorithm , 2011, Autom..

[18]  PooGyeon Park,et al.  $\mathcal{H}_{2}$ state-feedback control for LPV systems with input saturation and matched disturbance , 2012 .

[19]  Dennis S. Bernstein,et al.  Benchmark Problems for Robust Control Design , 1991, 1991 American Control Conference.

[20]  Olivier Sename,et al.  Control design for LPV systems with input saturation and state constraints: An application to a semi-active suspension , 2011, IEEE Conference on Decision and Control and European Control Conference.

[21]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[22]  PooGyeon Park,et al.  LPV controller design for the nonlinear RTAC system , 2001 .

[23]  Ben S. Cazzolato,et al.  Linear-Parameter-Varying Control of an Improved Three-Degree-of-Freedom Aeroelastic Model , 2010 .

[24]  Yijing Wang,et al.  An Improved Set Invariance Analysis and Gain-Scheduled Control of LPV Systems subject to Actuator Saturation , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[25]  PooGyeon Park,et al.  State‐feedback disturbance attenuation for polytopic LPV systems with input saturation , 2009 .

[26]  Jun Zhao,et al.  Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function , 2013, Int. J. Syst. Sci..

[27]  Jun Zhao,et al.  Brief Paper - Output tracking control for a class of switched non-linear systems with partial state constraints , 2013 .

[28]  J Witte,et al.  Robust and LPV control of an AMB system , 2010, Proceedings of the 2010 American Control Conference.

[29]  Luca Zaccarian,et al.  Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance , 2008, Autom..

[30]  Tingshu Hu,et al.  Analysis of linear systems in the presence of actuator saturation and I-disturbances , 2004, Autom..

[31]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[32]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[33]  Wei Xie.  Multi-objective H2/L2 performance controller synthesis for LPV systems , 2008, WCICA 2008.

[34]  Karolos M. Grigoriadis,et al.  LPV Systems with parameter-varying time delays: analysis and control , 2001, Autom..

[35]  Xu Jin,et al.  Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems , 2016 .

[36]  Javad Mohammadpour,et al.  Control of linear parameter varying systems with applications , 2012 .

[37]  Ligang Wu,et al.  Nonfragile Output Tracking Control of Hypersonic Air-Breathing Vehicles With an LPV Model , 2013, IEEE/ASME Transactions on Mechatronics.

[38]  Guang-Ren Duan,et al.  Stabilization of linear systems with distributed input delay and input saturation , 2012, Autom..