Feedback control on Nash equilibrium for discrete-time stochastic systems with Markovian jumps: Finite-horizon case

Nonzero-sum Stochastic Differential Gamefor Discrete-Time Markovian jump Linearsystem with incomplete transition rates

“…Remark 4 Compared to [23], the result in Theorem 3 is supplementary and practical because [23] investigated the Nash equilibrium in finite time, while this work considers the guaranteed cost Nash equilibrium in infinite time. Regarding the transition probabilities with complete transition descriptions, in [23] the solution of differential game involves four-coupled generalized difference Riccati equations [23], [20], [35], requiring an iterative algorithm [36] to solve these equations. However, this method is no longer suitable for solving optimization problems (47) that satisfy both BMIs and matrix inequalities.…”

“…The essence of the game relationship is to fully consider the gains and losses of all players and stabilize to a balanced state. However, due to assuming that B 2i = 0, C 1i = 0, the problem of guaranteed cost differential game of [23] and [15] is single-player control game. In this case, the control gains for one player are independent of the other players, and the solutions become simpler.…”

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

“…Thus, based on the strong Markov property, applying homogeneity in (25) and introducing it in (24), we arrive at…”

“…By introducing stochastic exact observability and stochastic exact detectability, the optimal strategies (Nash equilibrium strategies) and the optimal cost values have been given. In [25], we have considered LQ differential games in finite horizon for discrete-time stochastic systems with Markovian jump parameters and multiplicative noise. Furthermore, a suboptimal solution of the LQ differential games is proposed based on a convex optimization approach.…”

RobustH∞Fuzzy Control for Nonlinear Discrete-Time Stochastic Systems with Markovian Jump and Parametric Uncertainties

“…The class of systems may represent a large variety of processes including those in the production systems, fault-tolerant systems, communication systems, and economic systems [15]. In the past two decades, many important issues of MJSS were researched extensively, such as the controllability and observability [16], stability and stabilization (see [17][18][19][20][21][22]), 2 [23] and ∞ performance [24][25][26][27], and robustness [28,29]. To the best of our knowledge, despite these efforts, very few results are available for the control design for nonlinear MJSS.…”