Control of constrained linear systems using fast sampling rates

Abstract This paper addresses the problem of optimal control of constrained linear systems when fast sampling rates are utilised. We show that there exists a well-defined limit as the sampling rate increases. An immediate consequence of this result is the existence of a finite sampling period such that the achieved performance is arbitrarily close to the limiting performance.

[1]  S. Lang.  Real and Functional Analysis , 1983 .

[2]  Graham C. Goodwin,et al.  Constrained Control and Estimation , 2005 .

[3]  Mark Cannon,et al.  Infinite horizon predictive control of constrained continuous-time linear systems , 2000, Autom..

[4]  James B. Rawlings,et al.  Constrained linear quadratic regulation , 1998, IEEE Trans. Autom. Control..

[5]  Daniel E. Miller,et al.  Simultaneous stabilization with near optimal LQR performance , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[6]  B. Kouvaritakis,et al.  Efficient active set optimization in triple mode MPC , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[7]  C. Panne.  Methods for Linear and Quadratic Programming , 1975 .

[8]  Manfred Morari,et al.  LQ control for constrained continuous-time systems: an approach based on singular value decomposition , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[9]  Richard B. Vinter,et al.  Optimal Control , 2000 .

[10]  M. Naumović.  Sampling in Digital Signal Processing and Control , 2001 .

[11]  Mario Sznaier,et al.  Suboptimal control of linear systems with state and control inequality constraints , 1987, 26th IEEE Conference on Decision and Control.

[12]  Manfred Morari,et al.  Contractive model predictive control for constrained nonlinear systems , 2000, IEEE Trans. Autom. Control..

[13]  Astrom.  Computer Controlled Systems , 1990 .

[14]  J. Rawlings,et al.  The stability of constrained receding horizon control , 1993, IEEE Trans. Autom. Control..

[15]  Bruce H. Krogh,et al.  Stability-constrained model predictive control , 2001, IEEE Trans. Autom. Control..

[16]  D. Chmielewski,et al.  On constrained infinite-time linear quadratic optimal control , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[17]  L. Berkovitz.  Optimal Control Theory , 1974 .

[18]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

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

[20]  Graham C. Goodwin,et al.  Digital control and estimation : a unified approach , 1990 .

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