Sliding mode optimal control for linear systems

Abstract This paper addresses the optimal control problem for a linear system with respect to a Bolza–Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional linear feedback control fails to provide a causal solution. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQ regulator that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode control.

[1]  Yuanqing Xia,et al.  Observer-based sliding mode control for a class of discrete systems via delta operator approach , 2010, J. Frankl. Inst..

[2]  Zehui Mao,et al.  Observer based fault-tolerant control for a class of nonlinear networked control systems , 2010, J. Frankl. Inst..

[3]  Alessandro Pisano,et al.  Fault diagnosis for the vertical three-tank system via high-order sliding-mode observation , 2010, J. Frankl. Inst..

[4]  Michael Basin,et al.  Optimal and robust integral sliding mode filter design for systems with continuous and delayed measurements , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[6]  Engin Yaz,et al.  Sliding-Mode Adaptive Observer Approach to Chaotic Synchronization , 2000 .

[7]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  Y. Shtessel,et al.  Output feedback tracking in causal nonminimum-phase nonlinear systems using HOSM techniques , 2008, 2008 International Workshop on Variable Structure Systems.

[9]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[10]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

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

[12]  Yuri B. Shtessel,et al.  Higher order sliding modes , 2008 .

[13]  Michael Basin,et al.  Integral sliding mode design for robust filtering and control of linear stochastic time‐delay systems , 2005 .

[14]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[15]  Yuri B. Shtessel,et al.  Robust adaptive tracking with an additional plant identifier for a class of nonlinear systems , 2010, J. Frankl. Inst..

[16]  Antonella Ferrara,et al.  Sliding mode regulator as solution to optimal control problem , 2008, 2008 47th IEEE Conference on Decision and Control.

[17]  Hamid Reza Karimi,et al.  A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations , 2010, J. Frankl. Inst..

[18]  Igor Boiko.  Frequency domain precision analysis and design of sliding mode observers , 2010, J. Frankl. Inst..

[19]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[20]  Sarah K. Spurgeon,et al.  Sliding mode observers: a survey , 2008, Int. J. Syst. Sci..

[21]  Antonella Ferrara,et al.  On second order sliding mode controllers , 1998 .

[22]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[23]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[24]  Katsuhisa Furuta,et al.  VS-CONTROL WITH TIME-VARYING SLIDING SECTOR — DESIGN AND APPLICATION TO PENDULUM — , 2008 .

[25]  Antonella Ferrara,et al.  Sliding mode optimal regulator for a bolza-meyer criterion with non-quadratic state energy terms , 2009, 2009 American Control Conference.

[26]  Michael V. Basin,et al.  Optimal control for linear systems with multiple time delays in control input , 2006, IEEE Transactions on Automatic Control.

[27]  Leonid M. Fridman,et al.  Analysis and design of integral sliding manifolds for systems with unmatched perturbations , 2006, IEEE Transactions on Automatic Control.

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

[29]  Leonid M. Fridman,et al.  Analysis of Chattering in Systems With Second-Order Sliding Modes , 2007, IEEE Transactions on Automatic Control.

[30]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .