IBLFs-Based Closed-Loop Dynamics Modeling and Neural Control for Time-Varying Full State Constrained Unknown Nonlinear Systems via Deterministic Learning

Learning is central to intelligent control, particularly in real-world scenarios with complex time-varying constraints. This paper proposes an adaptive neural network-based control method for unknown nonlinear systems subject to fully time-varying state constraints. Unlike conventional barrier Lyapunov functions (BLFs) methods, the proposed approach directly enforces state constraints through time-varying integral barrier Lyapunov functions (IBLFs). An adaptive neural controller is developed to ensure all system states remain within their prescribed time-varying bounds while achieving tracking convergence. However, the use of IBLF leads to a highly intricate closed-loop error subsystem and unknown system dynamics, posing challenges for theoretical learning analysis. To address this, we provide a rigorous proof of the closed-loop neural network (NN) learning process under IBLF constraints, ensuring accurate approximation of unknown dynamics. Furthermore, the learned constraint-related dynamics are encapsulated in constant NNs, enabling a knowledge-based learning controller. By addressing closed-loop learning under time-varying IBLF constraints, the proposed method achieves high-performance control and advances dynamic learning and control theory for constrained nonlinear systems.