Min-max sliding-mode control for multimodel linear time varying systems

Abstract

An original linear time-varying system with unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system with a complete knowledge leads to a linear multi-model system with known bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed min-max sliding-mode control strategy gives an optimal robust sliding-surface design algorithm, which is reduced to a solution of an equivalent linear quadratic problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. An illustrative numerical example is presented. Min-max, optimality, sliding-mode control. . He conducts research in sliding-mode control with applications to reusable launch vehicle control, aircraft reconfigurable flight control systems, missile control systems, an autonomous conventional, and nuclear reactor systems of electric power supply. He published over 120 technical papers. Carlos Jiménez Gallegos was born in 1975 at San Luis Potosí, México. He received the Bc.Sc. degree in electronic engineering and the Ms.Sc. degree from the University of San Luis Potosí, México, in 1999 and 2000, respectively. He is currently working toward the D.Sci. degree in robust and min-max multimodal optimization at the same university. His research interests include robust control of nonlinear dynamical systems, optimal control, and game theory. Index Terms-

Numerical method for weights adjustment in minimax multi‐model LQ‐control

“…This numerical method practically makes workable the realization of the robust optimal control suggested in [7,8] and complements the results given in [12][13][14].…”

Decomposition of the min-max multi-model problem via integral sliding mode

“…In view of this concept, the original system model is replaced by a finite set of dynamic models such that each model describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded unmatched disturbances. In Reference [6] the authors developed the concept of min-max sliding mode control design for linear time variant multi-model system. This control design technique has the following disadvantages:…”

Integral HOSM Semiglobal Controller for Finite-Time Exact Compensation of Unmatched Perturbations

“…establishes the finite-time-stable r-sliding mode 0 with the transient time (12). The equality (t; x(t)) = (t 0 t 0 ; 0 !…”