Coupled State-Dependent Riccati Equation Control for Continuous Time Nonlinear Mechatronics Systems

This paper considers a novel coupled state-dependent Riccati equation (SDRE) approach for systematically designing nonlinear quadratic regulator (NLQR) and H∞ control of mechatronics systems. The state-dependent feedback control solutions can be obtained by solving a pair of coupled SDREs, guaranteeing nonlinear quadratic optimality with inherent stability property in combination with robust L2 type of disturbance reduction. The derivation of this control strategy is based on Nash's game theory. Both finite and infinite horizon control problems are discussed. An under-actuated robotic system, Furuta rotary pendulum, is used to examine the effectiveness and robustness of this novel nonlinear control approach.

[1]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[2]  D. Bernstein,et al.  LQG control with an H/sup infinity / performance bound: a Riccati equation approach , 1989 .

[3]  Xin Wang,et al.  Robust and resilient state dependent control of continuous-time nonlinear systems with general performance criteria , 2010, 49th IEEE Conference on Decision and Control (CDC).

[4]  P. Khargonekar,et al.  Mixed H/sub 2//H/sub infinity / control: a convex optimization approach , 1991 .

[5]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[6]  Mayra Antonio-Cruz,et al.  Linear State Feedback Regulation of a Furuta Pendulum: Design Based on Differential Flatness and Root Locus , 2016, IEEE Access.

[7]  C. Scherer.  Multiobjective H/sub 2//H/sub /spl infin// control , 1995 .

[8]  Jacob Hostettler,et al.  Sliding mode control of a permanent magnet synchronous generator for variable speed wind energy conversion systems , 2015 .

[9]  Carsten W. Scherer,et al.  Multiobjective H2/H∞ control , 1995, IEEE Trans. Autom. Control..

[10]  Wei Lin,et al.  Dissipativity, L/sub 2/-gain and H/sub /spl infin// control for discrete-time nonlinear systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[11]  K. Glover,et al.  Minimum entropy H ∞ control , 1990 .

[12]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[13]  J. Cloutier.  State-dependent Riccati equation techniques: an overview , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[14]  A. Schaft.  Nonlinear State Space H ∞ Control Theory , 1993 .

[15]  C. Byrnes,et al.  H∞-control of discrete-time nonlinear systems , 1996, IEEE Trans. Autom. Control..

[16]  Xin Wang,et al.  H2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach , 2011 .

[17]  Xiang Chen,et al.  Multiobjective \boldmathHt/Hf Control Design , 2001, SIAM J. Control. Optim..

[18]  Gang Tao,et al.  Adaptive Control Design and Analysis , 2003 .

[19]  K. Glover,et al.  A state space approach to H-infinity optimal control , 1989 .

[20]  Wei Lin,et al.  Mixed H 2/H ∞ control via state feedback for nonlinear systems , 1996 .

[21]  K. Glover,et al.  Mixed 𝓗2 and 𝓗∞ performance objectives. II. Optimal control , 1994, IEEE Trans. Autom. Control..

[22]  A. Isidori.  Nonlinear Control Systems , 1985 .

[23]  Tayfun Çimen,et al.  State-Dependent Riccati Equation (SDRE) Control: A Survey , 2008 .

[24]  Huijun Gao,et al.  Finite-Time Stabilization for Vehicle Active Suspension Systems With Hard Constraints , 2015, IEEE Transactions on Intelligent Transportation Systems.

[25]  Masaki Izutsu,et al.  Swing-up of Furuta Pendulum by Nonlinear Sliding Mode Control , 2008 .

[26]  Wei-Min Lu,et al.  Nonlinear optimal control: alternatives to Hamilton-Jacobi equation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[27]  Kemin Zhou,et al.  Mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// performance objectives. II. Optimal control , 1994 .

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

[29]  M.D.S. Aliyu.  Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations , 2011 .

[30]  M. Grimble,et al.  Optimized discrete-time state dependent Riccati equation regulator , 2005, Proceedings of the 2005, American Control Conference, 2005..

[31]  Huijun Gao,et al.  Disturbance Observer-Based Adaptive Tracking Control With Actuator Saturation and Its Application , 2016, IEEE Transactions on Automation Science and Engineering.

[32]  B. Anderson,et al.  A Nash game approach to mixed H/sub 2//H/sub /spl infin// control , 1994 .

[33]  Pablo A. Iglesias,et al.  Discrete time H ∞ controllers satisfying a minimum entropy criterion , 1990 .

[34]  Huijun Gao,et al.  Filter-Based Adaptive Vibration Control for Active Vehicle Suspensions With Electrohydraulic Actuators , 2016, IEEE Transactions on Vehicular Technology.

[35]  Wei Lin,et al.  discrete-time nonlinear H∞ control with measurement feedback , 1995, Autom..

[36]  Edwin E. Yaz,et al.  Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria , 2011 .