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Adaptive Inverse Reinforcement Learning Optimal for Nonlinear System via Takagi–Sugeno Fuzzy Model
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DOI：10.1109/tfuzz.2026.3697370.png)
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Abstract
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Inverse reinforcement learning (RL) optimal control is under the framework of an expert learner, where the learner system can imitate expert system's trajectory and optimal solutions via an inverse RL algorithm and minimize the cost function; thus, it can deal with optimal control problems effectively. This article presents a fuzzy inverse RL optimal control approach for a nonlinear system with partially unknown dynamics. First, the controlled nonlinear system is modeled using a Takagi–Sugeno fuzzy system. Second, the fuzzy optimal controller and the worst case disturbance input are given via a zero-sum game. To imitate the expert system's demonstrated behavior and achieve optimization, an online adaptive inverse RL algorithm is developed. The presented algorithm consists of four synchronous neural networks (NNs): a critic NN, an actor NN, a rival NN, and a state-penalty NN, which are used to reconstruct the expert system's cost function, optimal controller, disturbance input, and state-penalty weight. Moreover, the tuning law of the critic NN is implemented using the experience replay technique, instead of the persistent excitation condition. It is proved that the proposed online adaptive inverse RL algorithm can learn the expert system's optimal solutions and imitate its behavior. In addition, the presented fuzzy inverse RL optimal control scheme ensures that the controlled fuzzy learner system is asymptotically stable and achieves a Nash equilibrium solution. Finally, a continuous stirring tank reactor system is provided to illustrate the feasibility and superiority of the developed algorithm.
Keywords:
Experience replay
expert-learner framework
inverse reinforcement learning (RL) algorithm
neural network (NN)
optimal control
Takagi–Sugeno (T–S) fuzzy systems
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