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In this study, the author discusses a Pareto strategy implemented via state and static output feedback for a class of weakly coupled large-scale discrete-time stochastic systems with state- and control-dependent noise. The asymptotic structure along with the uniqueness and positive semi-definiteness of the solutions of cross-coupled non-linear matrix equations (CNMEs) is newly established via the implicit function theorem. The main contribution of this study is the proposal of a parameter-independent local state and static output feedback Pareto strategy. Moreover, a computational approach for solving the CNMEs is also considered if the information about the small parameter is available. Particularly, a new iterative algorithm based on the linear matrix inequality is established to design a Pareto strategy. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided for practical aircraft control problems. [ABSTRACT FROM AUTHOR]

In this study, the authors investigate the infinite-horizon linear quadratic control involving state- and control-dependent noise in weakly coupled large-scale systems. In contrast to the existing results, they allow the control and state weighting matrices in the cost function to be indefinite. After establishing an asymptotic structure for the solutions of the stochastic algebraic Riccati equation (SARE), a weak coupling parameter-independent control is provided. Moreover, by solving the reduced-order linear matrix inequality (LMI), they can easily obtain the proposed control without using any numerical algorithms. As a result, although the small positive weak coupling parameter that connects the other subsystems is very small or unknown, it is possible to compute the desired controller. Finally, the extension of the result of the study to the static output feedback control problem is discussed by considering the Lagrange multiplier method. [ABSTRACT FROM AUTHOR]

In this paper, N-player linear quadratic differential games that are sign-indefinite for infinite horizon weakly coupled large-scale systems are discussed. After establishing the asymptotic structure and local uniqueness of the solution for cross-coupled sign-indefinite algebraic Riccati equations (CSARE), a new algorithm for solving CSARE is provided. It is shown that the proposed algorithm attains linear convergence. Moreover, in order to reduce the computational workspace, the recursive algorithm is combined. Finally, a high-order approximation strategy based on the proposed iterative solutions is described. As a result, it was recently proved that the numerical strategy achieves a high-order approximation of the equilibrium value. As another important feature, when the small parameters are unknown, a parameter-independent strategy is developed. [ABSTRACT FROM AUTHOR]

In this paper, the optimal Kalman filtering problem for multiparameter singularly perturbed systems is considered. In order to obtain the filter gain, the solution of the multiparameter algebraic Riccati equations (MAREs) is needed. The main contributions in this paper are to propose a new recursive algorithm for solving the MARE and to establish sufficient conditions related to the convergence property of the proposed algorithm. Using the recursive algorithm, it is shown that the solution of the MARE converges to a positive semidefinite stabilizing solution with the rate of convergence of O (|μ| i ). Moreover, it is proved that the mean square error via the proposed high-order filter attain, the O (|μ| 2 i +1 ) approximation compared with the optimal filter. [ABSTRACT FROM AUTHOR]