Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation

In this paper, a set invariance analysis and gain scheduling control design approach is proposed for the polytopic linear parameter-varying systems subject to actuator saturation. A set invariance condition is first established. By utilizing this set invariance condition, the design of a time-invariant state feedback law is formulated and solved as an optimization problem with LMI constraints. A gain-scheduling controller is then designed to further improve the closed-loop performance. Numerical examples are presented to demonstrate the effectiveness of the proposed analysis and design method.

[1]  ApkarianPierre,et al.  Self-scheduled H control of linear parameter-varying systems , 1995 .

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

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

[4]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[5]  A. Packard,et al.  LQG control design for LPV systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[6]  Zongli Lin,et al.  Low gain feedback , 1999 .

[7]  A. Packard Gain scheduling via linear fractional transformations , 1994 .

[8]  Fen Wu,et al.  Induced L2‐norm control for LPV systems with bounded parameter variation rates , 1996 .

[9]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[10]  Michael Athans,et al.  Analysis of gain scheduled control for nonlinear plants , 1990 .

[11]  Wilson J. Rugh,et al.  Analytical Framework for Gain Scheduling , 1990, 1990 American Control Conference.

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

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

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

[15]  Stephen P. Boyd,et al.  Analysis of linear systems with saturation using convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).