Disturbance attenuation via state feedback for systems with a saturation nonlinearity in the control channel

We study the problem of disturbance attenuation via state feedback for asymptotically stable systems with a saturation nonlinearity in the control channel. The disturbance is assumed to be bounded, with the bound known. This amounts to adding a saturation nonlinearity in the disturbance channel. A sufficient condition is derived in terms of algebraic matrix inequalities, which are much simpler to solve than the general Hamilton-Jacobi-Isaacs partial differential inequality. A suboptimal control law is given based on the solution to the Riccati inequalities. The computational complexity of solving the optimal controller is similar to that of liner H∝ controller design.

[1]  J. W. Helton,et al.  Piecewise Riccati equations and the bounded real lemma , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[2]  Eduardo D. Sontag,et al.  Remarks on finite gain stabilizability of linear systems subject to input saturation , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[3]  J. Helton,et al.  H∞ control for nonlinear systems with output feedback , 1993, IEEE Trans. Autom. Control..

[4]  Zigang Pan.  H∞-Optimal Control for Singularly Perturbed Systems , 1992 .

[5]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[6]  A. Saberi,et al.  Semi-global stabilization of linear discrete-time systems subject to input saturation via linear feedback-an ARE-based approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[7]  J. Helton,et al.  H∞ control for nonlinear systems with output feedback , 1993, IEEE Trans. Autom. Control..

[8]  A. Isidori,et al.  H∞ control via measurement feedback for general nonlinear systems , 1995, IEEE Trans. Autom. Control..

[9]  W. Zhan,et al.  H∞ Control for Systems with Sector Bound Nonlinearities , 1995 .

[10]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

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

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

[13]  Katsuhisa Furuta,et al.  Nonlinear H∞ Control via Measurement Feedback in Robotic Systems , 1998 .

[14]  P. S. Bauer.  Dissipative Dynamical Systems: I. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[15]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[16]  Tamer Basar,et al.  H∞-optimal control for singularly perturbed systems part i: perfect state measurements , 1993, 1992 American Control Conference.

[17]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

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