Learning-Based Scaling Scheme for Markov Jump Systems and Its Application in Operational Amplifier Circuit

This brief addresses the optimization problem for Markov jump systems (MJSs) with unknown dynamics via a novel scaling-based reinforcement learning scheme. First, by employing subsystem transformation, the optimal controller design problem for MJSs is reformulated into solving a set of parallel and decoupled algebraic Riccati equations (DAREs). Traditional learning schemes for solving these equations either require initially admissible control policies or suffer from slow convergence. To overcome these limitations, a novel scaling-based reinforcement learning algorithm is proposed. Several notable advantages are exhibited by the proposed algorithm: it eliminates the need for system dynamics during the learning process, achieves faster convergence, and relaxes the requirement for an initially admissible control policy. The effectiveness of the proposed scheme is rigorously proven through a mathematical induction method. Finally, the feasibility of the proposed scheme is verified using an operational amplifier circuit example, and its superiority is demonstrated through a series of comparative simulations.