Adaptive Neural Network Optimal Backstepping Control of Strict Feedback Nonlinear Systems via Reinforcement Learning

In nonlinear control, barrier Lyapunov function is frequently utilized to handle state constraints; however, a feasibility condition for virtual signals often needs to be verified. In addition, when dealing with asymmetric state constraints, complex calculation is commonly involved. This article develops an adaptive neural network optimal backstepping control scheme for strict feedback nonlinear systems with input delay and asymmetric time-varying state constraints. To remove feasibility conditions, an asymmetric nonlinear state dependent function is introduced, and then the original system is transformed into an unconstrained one. Therefore, a direct method that does not require the usage of tracking error as an intermediate variable is provided to deal with state constraints. Simultaneously, a coordinate transformation with integral is proposed to tackle input delay. In the face of increasingly scarce resources, an optimal control strategy based on reinforcement learning is devised to optimize the interaction cost between agents or actors and the environment. According to the stability analysis, the developed scheme ensures that all signals in the closed-loop system remain bounded and all states do not exceed the constraint space. Ultimately, the effectiveness of the proposed strategy is verified through a simulation example.