SMS-Based Optimal Control of Completely Unknown Nonlinear Systems With Unknown Actuator Saturation

Abstract

A data-driven optimal control scheme integrating sliding mode surfaces (SMSs) and neural networks (NNs) is proposed for continuous-time nonlinear systems with fully unknown dynamics and actuator saturation. In existing methods, partial system knowledge is typically required, and computationally intensive actor-critic structures are employed. Three contributions are introduced to overcome these limitations. First, a data-driven model is constructed from a recurrent neural network (RNN) with an adaptive compensation term, by which the unknown dynamics are accurately reconstructed without prior model information. Second, an adaptive feedforward compensator based on a backpropagation neural network (BNN) is designed to counteract actuator saturation; no known saturation bounds are assumed. Finally, the conventional actor-critic architecture is replaced by a dedicated critic neural network (CNN) that incorporates SMS information to approximate the Hamilton-Jacobi-Bellman (HJB) equation solution, thereby simplifying the control structure and reducing online computation while preserving performance. By the proposed scheme, restrictive modeling and saturation assumptions are relaxed, and responsiveness and robustness are enhanced through inherent SMS properties. A Lyapunov-based analysis proves that all closed-loop signals remain uniformly ultimately bounded. Numerical simulations and robotic arm experiments confirm the strategy's effectiveness and practical feasibility under simultaneous model uncertainty and actuator saturation.