Muneomi Sagara

Numerical solution of stochastic Nash games with state-dependent noise for weakly coupled large-scale systems

Abstract This paper discusses the infinite horizon stochastic Nash games with state-dependent noise. After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross-coupled stochastic algebraic Riccati equations (CSAREs), a new algorithm that combines Newton’s method with two fixed point algorithms for solving the CSAREs is derived. As a result, it is shown that the proposed algorithm attains quadratic convergence and the reduced-order computations for sufficiently small parameter e . As another important feature, the high-order approximate strategy that is based on the iterative solutions is proposed. Using such strategy, the degradation of the cost functional is investigated. Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided.

Efficient Numerical Computations of Soft Constrained Nash Strategy for Weakly Coupled Large-Scale Systems

In this paper, a high-order soft constrained Nash strategy for weakly coupled large-scale systems is investigated. In order to solve the cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) corresponding to strategy, the iterative algorithm on the basis of the Newton’s method is first applied. Second, the recursive algorithm for solving the CSAREs is also established to reduce the amount of algebraic computation as compared with the Newton’s method. Using these iterative solutions, a highorder soft-constrained Nash strategy is designed. As a result, it is proved that the proposed high-order approximate equilibrium strategies achieve better performance. Finally, in order to demonstrate the efficiency of the algorithm, a numerical example is given.

Recursive Computation of Static Output Feedback Stochastic Nash Games for Weakly-Coupled Large-Scale Systems

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 e. Finally, in order to demonstrate the efficiency of the proposed algorithm, numerical example is given.

Stochastic Nash games with state-dependent noise

This paper discusses the infinite horizon stochastic Nash games with state-dependent noise. First, stochastic Nash games are formulated by applying the results of stochastic linear quadratic control problems. Second, in order to obtain the Nash strategy, cross-coupled stochastic algebraic Riccati equations (CSAREs) are derived. Moreover, the algorithm that is based on the Newtons method is considered for solving the CSAREs. In order to demonstrate the efficiency of the proposed algorithms, computational examples are provided.

Numerical computation of linear quadratic control problem for singularly perturbed stochastic systems

In this paper, linear quadratic control with state-dependent noise for singularly perturbed stochastic systems (SPSS) is addressed. After establishing the asymptotic structure of the stochastic algebraic Riccati equation (SARE), a new iterative algorithm that combine the Newtons 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 both attained. As another important feature, a high-order state feedback controller by means of the obtained iterative solution is given and the degradation of the cost performance is investigated for the stochastic case for the first time. Finally, in order to demonstrate the efficiency of the proposed algorithm, numerical example is given for practical megawatt-frequency control problem.