Fuzzy actor–critic learning-based interpretable control and stability-informed guarantee with error mapping for discrete-time nonlinear system

This paper focuses on the issues of fuzzy actor–critic learning architecture, including insufficient interpretability, lack of stability guarantee, and neglect of historical error information. A novel actor–critic learning architecture based on interval type-2 Takagi–Sugeno-Kang fuzzy neural networks (ISAC-IT2-TSK-FNN) is proposed, comprising an interpretable IT2-TSK fuzzy actor (IT2-TSK-FA) and a stability-informed IT2-TSK fuzzy critic (IT2-TSK-FC). In the structure learning of interpretable IT2-TSK-FA, this paper proposes a fuzzy set classification and aggregation method, which reduces the number of fuzzy rules and the complexity of the model. For parameter learning, a value function that concurrently considers control performance and interpretability is designed. To enhance the transparency of fuzzy set partitioning, this paper proposes an iteration-based adaptive learning rate adjustment method. In the parameter learning of stability-informed IT2-TSK-FC, the Lyapunov theorem is introduced. The constraint on the learning rate is derived based on the Lyapunov stability condition to ensure the stability of the control system. Additionally, a weighted historical error mapping method is proposed, which improves the sensitivity of stability-informed IT2-TSK-FC to error changes, enhancing the control strategy evaluation capability. Finally, an algorithm is designed to implement the learning process of the ISAC-IT2-TSK-FNN architecture, with simulation results validating its effectiveness and robustness in various control tasks and under conditions with noise and disturbance.