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access icon free Robust incentive Stackelberg strategy for Markov jump linear stochastic systems via static output feedback

© The Institution of Engineering and Technology
Received 06/08/2019, Accepted 05/03/2020, Revised 06/11/2019, Published 06/03/2020

In this study, a robust static output feedback (SOF) incentive Stackelberg game for a Markov jump linear stochastic system governed by Itô differential equations with multiple leaders and multiple followers is investigated. The existence conditions for the SOF incentive Stackelberg strategies are derived in terms of the solvability of a set of higher-order cross-coupled stochastic algebraic Lyapunov type equations (CCSALTEs). A classical Lagrange multiplier technique is employed to solve the CCSALTEs; therefore, the solution of the bilinear matrix inequality, which is a common NP-hard problem when designing SOF strategies, is not required. A heuristic algorithm is developed based on the CCSALTEs. In particular, it is shown that a robust convergence is guaranteed by combining the Krasnoselskii–Mann iterative algorithm with a new convergence condition. The performance of the proposed algorithm is discussed and a simple practical example is provided to demonstrate the effectiveness of the proposed algorithm and the SOF incentive Stackelberg strategies.

Inspec keywords: linear systems; computational complexity; feedback; stochastic systems; iterative methods; linear matrix inequalities; game theory; robust control; differential equations; Lyapunov methods

Other keywords: NP-hard problem; SOF incentive Stackelberg strategies; robust static output feedback incentive Stackelberg game; higher-order cross-coupled stochastic algebraic Lyapunov type equations; CCSALTEs; bilinear matrix inequality; Markov jump linear stochastic system; robust incentive Stackelberg strategy; Krasnoselskii–Mann iterative algorithm; classical Lagrange multiplier technique; SOF strategies; Itô differential equations

Subjects: Control system analysis and synthesis methods; Computational complexity; Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Differential equations (numerical analysis); Stability in control theory; Time-varying control systems; Linear control systems; Game theory; Linear algebra (numerical analysis)

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