Robust SOF Stackelberg game for stochastic LPV systems

摘要

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.