Robust SOF Stackelberg game for stochastic LPV systems

Abstract

A robust static output feedback (SOF) Stackelberg game with multiple followers in stochastic linear parameter varying (LPV) systems is investigated. The conditions for the existence of a robust SOF Stackelberg strategy set under H∞ constraints are established by the cross-coupled matrix inequality (CCMI). To determine this strategy set, the optimization problems corresponding to the relevant cost bounds are defined, and their solution sets are derived using the Karush-Kuhn-Tucker conditions. The results show that the robust SOF Stackelberg strategy set can be obtained by solving higher-order cross-coupled matrix equations (CCMEs). Because CCMEs are complex and difficult to solve numerically, a heuristic algorithm is developed by combining the CCMEs with the CCMIs. The convergence property is proven using the Krasnoselskii-Mann (KM) iteration algorithm. Finally, two numerical examples are solved to demonstrate the reliability and usefulness of the proposed heuristic algorithm.

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