Reinforcement learning-based adaptive optimal output feedback control for nonlinear systems with output quantization

In this research, a novel adaptive optimal control approach is proposed for nonlinear systems under output quantization. In order to achieve the optimized control, the reinforcement learning algorithm of the identifier-actor-critic architecture is implemented based on fuzzy logic systems. The identifier, critic, and actor are used for estimating unknown dynamics, assessing system performance, and carrying out control actions, respectively. Firstly, the updating laws of critics and actors are derived by using the negative gradient of a simple positive function generated by the partial derivatives of the Hamilton Jacobi Bellman equation. At the same time, the design has the ability to eliminate the persistence excitation that is necessary for the majority of current optimal controls. Secondly, the command filtering technique is employed to avoid direct differentiation of virtual control signals. This is necessary because the virtual control signals become discontinuous and non-differentiable under output quantization. Thirdly, the boundedness of the quantization errors is illustrated in Lemma 3 by establishing the relationships between the quantized signals and the unquantized signals. Based on this lemma, it is ensured that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). Finally, the proposed method's effectiveness is validated through two simulations.