Lyapunov theory based stable Markov game fuzzy control for non-linear systems

In this paper we propose a Lyapunov theory based Markov game fuzzy controller which is both safe and stable. We attempt to optimize a reinforcement learning (RL) based controller using Markov games, simultaneously hybridizing it with a Lyapunov theory based control for stability. Proposed technique generates in an RL based game theoretic, adaptive, self learning, optimal fuzzy controller which is both robust and has guaranteed stability. Proposed controller is an “annealed” hybrid of fuzzy Markov games and the Lyapunov theory based control. Fuzzy systems have been employed as generic function approximators for scaling the proposed approach to continuous state-action domains. We test our proposed controller on three benchmark non-linear control problems: (i) inverted pendulum, (ii) trajectory tracking of standard two-link robotic manipulator, and (iii) tracking control of a two link selective compliance assembly robotic arm (SCARA). Simulation results and comparative evaluation against baseline fuzzy Markov game based control showcases superiority and effectiveness of the proposed approach.