Adaptive-Slack Prescribed-Performance Control: Achieving Safe Trajectory Tracking in Cluttered Environments via Reinforcement Learning.

Achieving high-precision trajectory tracking while ensuring collision avoidance presents a fundamental conflict for autonomous systems operating in cluttered environments. Traditional prescribed-performance control (PPC) imposes rigid shrinking funnels that may become infeasible during avoidance maneuvers, whereas soft penalty-based avoidance may sacrifice tracking recovery. To resolve this dilemma, this article proposes an adaptive-slack Hamilton-Jacobi-Bellman (HJB)-based integral reinforcement learning (IRL) framework with an explicit control-barrier-function quadratic-programming (CBF-QP) safety layer. The adaptive boundary component relaxes the PPC envelope according to the geometric clearance demand and contracts after the avoidance demand disappears. A time-varying HJB formulation is used to generate a nominal performance-oriented controller for the unknown nonlinear system, while the CBF-QP minimally modifies this nominal input to guarantee forward invariance of the safe set. The resulting architecture separates nominal optimal tracking, performance-envelope feasibility, and CBF-certified physical safety. Comparative simulations demonstrate the different failure modes of rigid PPC and soft avoidance, and show that the proposed strategy recovers high-precision tracking after safety-critical maneuvers.