Title :
Minimax control under a restriction on the moments of disturbance
Author :
Gusev, Sergei V.
Author_Institution :
Dept. of Math. & Mech., St. Petersburg State Univ., Russia
Abstract :
The discrete-time linear MIMO plant is considered, which is acted on by a stochastic disturbance. It is assumed that the disturbance is not known but belongs to the given class, which is specified by a restriction on the moments of disturbances. The cost function is the maximum of the closed-loop system controlled output variance over the class of disturbances. The problem is to construct the optimal linear stabilizing regulator. For the SISO plant the approach includes both H 2 and H∞ optimal controls as the special cases. The solution of the minimax control problem is obtained. The method proposed involves the solution of some auxiliary convex optimization problem and the solution of the model-matching problem. The criterion is obtained also to determine the worst case disturbance. The solution is based on the generalization of the Chebyshev-type inequalities
Keywords :
MIMO systems; closed loop systems; convex programming; discrete time systems; maximum principle; minimax techniques; multivariable control systems; stability; stochastic systems; Chebyshev-type inequalities; H∞ optimal control; H2 optimal control; SISO plant; auxiliary convex optimization problem; closed-loop system controlled output variance maximum; cost function; discrete-time linear MIMO plant; disturbance moments restriction; minimax control; model-matching problem; optimal linear stabilizing regulator; stochastic disturbance; worst case disturbance; Cost function; Hydrogen; MIMO; Minimax techniques; Noise generators; Optimal control; Optimization methods; Performance analysis; Regulators; Stochastic processes;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.480259
