Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems

Abstract

Abstract In this article, robust static output feedback (SOF) Nash games for a class of uncertain Markovian jump linear stochastic systems (UMJLSSs) are investigated, in which each player may have access to local/private SOF information. It is proved that the robust SOF Nash strategy set can be obtained by minimizing the upper bounds of the cost functions based on a guaranteed cost control mechanism. By using the Karush–Kuhn–Tucker (KKT) condition, the necessary conditions for the existence of the robust SOF Nash strategy set are established in terms of the solvability conditions of nonlinear simultaneous algebraic equations (NSAEs). A heuristic algorithm is developed to solve the NSAEs. Particularly, it is shown that the robust convergence of the heuristic algorithm is guaranteed by combining the Krasnoselskii–Mann (KM) iterative algorithm with a new convergence condition. Finally, a simple practical example is presented to show the reliability and usefulness of the proposed algorithm.

Keywords

• Optimisation techniques
• Interpolation and function approximation (numerical analysis)
• Linear algebra (numerical analysis)
• Algebra
• Mathematical analysis
• Game theory