A Parallel Homotopic Optimized Control Scheme of Uncertain Nonlinear Markov Jump Systems and Its Applications

This paper investigates the optimized control problem for nonlinear Markov jump systems with uncertain time-varying parameters. First, the Takagi-Sugeno fuzzy model is applied to describe the uncertain nonlinear Markov jump systems, where the identification of the uncertain time-varying parameters is reformulated as zero-sum game problems. Subsequently, the reinforcement learning-based scheme is employed to solve such zero-sum game problems and achieve optimization even when the system dynamics remain unknown. Afterward, a parallel homotopic scheme is first adopted for such systems. The assumption of an initial stabilizing gain in the policy iteration scheme may be removed in this scheme, naturally enhancing the generality of the developed method. Finally, the actual availability of the proposed parallel homotopic scheme is validated through a single-link robot arm and a series DC motor.