A Scheduling Algorithm for Constrained Control Systems: An Approach Based on a Parameter Dependent Lyapunov Function

We propose a gain-scheduling control algorithm for locally stabilizing a discrete-time linear system with input saturation. The proposed control law has a structure that a high-gain control law and a low-gain control law are interpolated by using a single scheduling parameter. The closed-loop stability is guaranteed by using a parameter dependent Lyapunov function (PDLF). The scheduling parameter is computed on-line by solving a convex optimization problem with LMI constraints.

[1]  D. Bernstein,et al.  A chronological bibliography on saturating actuators , 1995 .

[2]  Ali Saberi,et al.  Editorial (Special issue on control problems with constraints) , 1999 .

[3]  Frédéric Grognard,et al.  Improving the performance of low-gain designs for bounded control of linear systems , 2002, Autom..

[4]  Masami Saeki,et al.  An LMI based scheduling algorithm for constrained stabilization problems , 2008, Syst. Control. Lett..

[5]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[6]  Zongli Lin.  Global Control of Linear Systems with Saturating Actuators , 1998, Autom..

[7]  A. Teel.  Linear systems with input nonlinearities: Global stabilization by scheduling a family of H∞-type controllers , 1995 .

[8]  Ali Saberi,et al.  On simultaneous global external and global internal stabilization of critically unstable linear systems with saturating actuators , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[9]  A. Megretski,et al.  L 2 Bibo Output Feedback Stabilization With Saturated Control , 1996 .

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

[11]  P. Apkarian,et al.  Parametrized linear matrix inequalities for nonlinear discrete H/sub /spl infin// control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

[13]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2003, Autom..

[14]  Richard M. Murray,et al.  Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation , 1998 .

[15]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[16]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[17]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[18]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[19]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[20]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..