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Neural Robust Optimal Tracking Control for Nonlinear State-Constrained Systems with Input Saturation and External Disturbances

Yuzhu Huang, Zhaoyan Zhang, Shuo Zhao

Applied Intelligence(2025)

Hebei University

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Abstract
This paper addresses the challenging problem of designing robust optimal tracking control for a class of nonlinear uncertain systems subjected to full-state constraints, input saturation and external disturbances. First, by leveraging neural network identification and nonlinear disturbance observation techniques, we develop a composite observer framework that enables the decoupling and simultaneous estimation of both uncertain dynamics and lumped disturbances. Second, to tackle the issue of input saturation in control design, a smooth approximation function is introduced in conjunction with an auxiliary variable to mitigate its adverse effects on system performance. Third, a novel barrier-type cost function, derived from barrier Lyapunov functions (BLFs), is proposed. This cost function incorporates both the tracking error and its derivative, effectively overcoming the unbounded nature of the traditional input quadratic cost function in tracking control over an infinite time horizon. Moreover, unlike typical actor-critic paradigms, the critic-only adaptive dynamic programming (ADP) algorithm with the novel barrier-type cost function is employed for each subsystem to determine the optimal virtual and actual controls, which together with the disturbance compensation signals constitute the corresponding robust optimal control schemes. Using Lyapunov’s direct method, it is proven that all closed-loop signals are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin without transgressing any state constraints. Finally, the effectiveness of the proposed approach is further validated through simulation results.
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Key words
Neural network,Composite observer,Adaptive dynamic programming,Full state constraints,Input saturation
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