This paper investigates open-loop Stackelberg games for a class of stochastic systems with multiple players. First, the necessary conditions for the existence of an open-loop Stackelberg strategy set are established using the stochastic maximum principle. Such conditions can be represented as solvability conditions for cross-coupled forward-backward stochastic differential equations (CFBSDEs). Second, in order to obtain the open-loop strategy set, a computational algorithm based on a four-step scheme is developed. A numerical example is then demonstrated to show the validity of the proposed method.

The application of neural networks to the state-feedback guaranteed cost control problem of discrete-time system that has uncertainty in both state and input matrices is investigated. Based on the Linear Matrix Inequality (LMI) design, a class of a state feedback controller is newly established, and sufficient conditions for the existence of guaranteed cost controller are derived. The novel contribution is that the neurocontroller is substituted for the additive gain perturbations. It is newly shown that although the neurocontroller is included in the discrete-time uncertain system, the robust stability for the closed-loop system and the reduction of the cost are attained.

This paper discusses the infinite horizon static output feedback stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems. In order to construct the strategy, the conditions for the existence of equilibria have been derived from the solutions of the sets of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of CSAREs, recursive algorithm for solving CSAREs is derived. As a result, it is shown that the proposed algorithm attains the reduced-order computations and the reduction of the CPU time. As another important contribution, the uniqueness of the strategy set is proved for the sufficiently small parameter ε. Finally, in order to demonstrate the efficiency of the proposed algorithm, numerical example is given.

This paper addresses linear quadratic control with state-dependent noise for singularly perturbed stochastic systems (SPSS). First, the asymptotic structure of the stochastic algebraic Riccati equation (SARE) is established for two cases. Second, a new iterative algorithm that combines Newton's method with the fixed point algorithm is established. As a result, the quadratic convergence and the reduced-order computation in the same dimension of the subsystem are attained. As another important feature, a high-order state feedback controller that uses the obtained iterative solution is given and the degradation of the cost performance is investigated for the stochastic case for the first time. Furthermore, the parameter independent controller is also given in case the singular perturbation is unknown. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example is given for the practical megawatt-frequency control problem.

In this paper, the H2/H∞ control problem for a class of stochastic discrete-time linear systems with state-, control-, and external-disturbance-dependent noise or (x, u, v)-dependent noise involving multiple decision makers is investigated. It is shown that the conditions for the existence of a strategy are given by the solvability of cross-coupled stochastic algebraic Riccati equations (CSAREs). Some algorithms for solving these equations are discussed. Moreover, weakly-coupled large-scale stochastic systems are considered as an important application, and some illustrative examples are provided to demonstrate the effectiveness of the proposed decision strategies.

In this paper, an infinite-horizon team-optimal incentive Stackelberg strategy is investigated for a class of stochastic linear systems with many non-cooperative leaders and one follower. An incentive structure is adopted which allows for the leader's team-optimal Nash solution. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati equations (CCSAREs). In order to demonstrate the effectiveness of the proposed strategy, a numerical example is solved.

In this letter, a computational approach for solving cross-coupled algebraic Riccati equations (CAREs) is investigated. The main purpose of this letter is to propose a new algorithm that combines Newton's method with a gradient-based iterative (GI) algorithm for solving CAREs. In particular, it is noteworthy that both a quadratic convergence under an appropriate initial condition and reduction in dimensions for matrix computation are both achieved. A numerical example is provided to demonstrate the efficiency of this proposed algorithm.