Hybrid Game Strategy in Fuzzy Markov-Game-Based Control

This paper proposes a novel control approach that incorporates a hybrid game strategy in Markov-game-based fuzzy control. Specifically, we aim at designing a ldquosafe and universally consistentrdquo controller that exhibits an ability to maintain performance against large disturbance and environment variations. The proposed hybrid control is a convex combination (based on experiential information) of ldquoa variation of cautious fictitious playrdquo approach and the ldquominimaxrdquo control approach implemented on a fuzzy Markov game platform. We show analytical convergence of Markov-game-based control in the presence of bounded external disturbances, and extend the analysis to show convergence of the proposed Markov-game-based hybrid control approach. Controller simulation and comparison against baseline Markov game fuzzy control and fuzzy Q -learning control on a highly nonlinear two-link robot brings out the superiority of the approach in handling severe environment and disturbance variations over different desired trajectories. This paper illustrates the possibility of obtaining ldquouniversal consistency,rdquo i.e., reasonable performance against severe environment and disturbance variations, by hybridizing ldquocautious fictitious playrdquo with ldquominimaxrdquo approaches in Markov-game-based control.