Game Theory Approach to Stochastic H2/H∞ Control of Markov Jump Singular Systems

Game Approach for H∞ Robust Control Strategy to Follow the Production in the Singularly Perturbed Bilinear Dynamic Input‐Output Systems

“…Therefore, it is necessary to study the nonlinear input-output problems. Chander and Tokao studied the nonlinear input-output model as the form of [13] ( ) = ( ) ( ) + [ ( + 1) − ( )] + ( ) , (1) where ( ) is the nonlinear functions of the output addition to its wide existence and applications, the bilinear system also has good approximation properties. Tie et al pointed out that the bilinear system could approximate any nonlinear system theoretically, and the accuracy was much higher than traditional linear approximation [14].…”

“…According to the basic method of robust control designing based on the noncooperative differential game theory, we can regard the control strategy designer as one player, that is, Player 1, and the stochastic disturbance as another player. Consequently, the robust control problem is converted into a problem of two players' game, that is, when anticipating the possible disturbance, how Player 1 should design his strategy to achieve the equilibrium with Player 2 and optimize his goal at the same time [13]. So models (7) and (8) ], = […”

Pareto Optimal Control for Uncertain Markov Jump Linear Stochastic Systems

“…By applying the well-known guaranteed cost control principle [7], the conditions, wherein the stochastic system is exponentially meansquare stable (EMSS) and has a cost bound, are given by the stochastic algebraic Riccati inequality (SARI). In contrast to the existing control strategy [3,4,5,6], it is more difficult for dynamic games to attain their equilibrium due to the complexity of the calculation of their cost bound. Hence, this research is a non-trivial extension of the existing results.…”

“…Nash games and the related 2 / ∞ control for a class of linear stochastic systems with Markovian jump parameters, both in finite-time and infinite-time horizon, have been studied [5]. In [6], the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its applications have been studied extensively. Even though fruitful results have been obtained in these studies, there is no discussion on robust dynamic games taking into account unmodeled deterministic uncertainties and external disturbances.…”