Minimax optimal control of uncertain systems with structured uncertainty

This paper considers a minimax control problem for an uncertain system containing structured uncertainties. The uncertainties in this system are assumed to satisfy a certain integral quadratic constraint. For a given initial condition, the minimax optimal controller is constructed by solving a parameter-dependent Riccati equation of the game type. This controller leads to a closed-loop uncertain system which is absolutely stable.

[1]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[2]  D. Bertsekas,et al.  Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems , 1973 .

[3]  Uri Shaked,et al.  Minimax design for a class of linear quadratic problems with parameter uncertainty , 1974 .

[4]  G. Leitmann.  Guaranteed Asymptotic Stability for Some Linear Systems With Bounded Uncertainties , 1979 .

[5]  B. Barmish.  Stabilization of uncertain systems via linear control , 1983 .

[6]  Ian R. Petersen,et al.  A riccati equation approach to the stabilization of uncertain linear systems , 1986, Autom..

[7]  Ian R. Petersen,et al.  Linear quadratic differential games with cheap control , 1986 .

[8]  V. Yakubovich.  Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part , 1988 .

[9]  D. Bernstein,et al.  The optimal projection equations with Petersen-Hollot bounds: robust stability and performance via fixed-order dynamic compensation for systems with structured real-valued parameter uncertainty , 1988 .

[10]  M. James,et al.  Stabilization of uncertain systems with norm bounded uncertainty-a control , 1989 .

[11]  J. Doyle,et al.  Quadratic stability with real and complex perturbations , 1990 .

[12]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

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

[14]  Tamer Basar,et al.  H∞-Optimal Control and Related , 1991 .

[15]  Isaac Kaminer,et al.  Mixed H2/H∞ control for discrete-time systems via convex optimization , 1992, American Control Conference.

[16]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .

[17]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[18]  V. Yakubovich.  Nonconvex optimization problem: the infinite-horizon linear-quadratic control problem with quadratic constraints , 1992 .

[19]  Ian R. Petersen,et al.  Optimal Guaranteed Cost Control of Uncertain Linear System , 1992, 1992 American Control Conference.

[20]  Bernard Friedland,et al.  An Observer-Based Design of a Controller for Spring-Coupled Cars , 1992, 1992 American Control Conference.

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