Admissibility-Guided Backstepping via Recursive Constraint Propagation

Conventional backstepping typically decouples recursive controller synthesis from global feasibility analysis, obscuring inter-layer constraint coupling and yielding conservative a posteriori conditions. To address this, this paper develops an admissibility-guided backstepping framework for strict-feedback nonlinear systems. By treating prescribed performance constraints as admissible input specifications, the proposed framework recursively propagates predicted operating regions, reducing global feasibility verification to local invariance conditions. Under this framework, the filtering-error challenge in dynamic surface control (DSC) is recast as a constrained-subsystem invariance problem, solved via a newly introduced Jacobian-modulated filter under relaxed conditions. Moreover, the propagated invariant sets provide a priori compact domains for neural network (NN) approximation, eliminating the circular dependence between approximation validity and Lyapunov stability. Simulations demonstrate the effectiveness of the proposed framework.