Stackelberg strategy for discrete-time stochastic system and its application to weakly coupled systems

In this paper, infinite-horizon Stackelberg strategy for discrete-time stochastic system is investigated. A necessary condition for the existence of the strategy set is established via a set of cross-coupled stochastic algebraic Lyapunov and Riccati equations (CSALREs). As another important contribution, weakly coupled large-scale stochastic discrete-time systems are considered. After establishing an asymptotic structure with positive definiteness for CSALREs solutions, parameter independent strategy set is established. Moreover, degradation of cost via the proposed strategy set is also derived. Finally, the equivalence between the parameter independent linear quadratic (LQ) controls and the proposed approximate reduced-order Stackelberg strategy set is proved for ε = 0. A numerical example is provided to demonstrate the efficiency of the obtained results.