Synthesizing Safety in Infinite-Horizon Optimal Control for Disturbed High-Relative-Degree Systems via Barrier-Regulating Auxiliary Variables

TL;DR

This paper introduces a novel safety-aware optimal control framework for nonlinear systems that enhances safety guarantees and reduces local trapping by embedding barrier functions and adaptive excitation in an extended state space.

Contribution

It develops a barrier-Lyapunov function-based approach with adaptive excitation and high-order safe set construction for disturbed high-relative-degree systems, improving safety and performance.

Findings

Reduced local trapping in safety filters

Enhanced safety-performance trade-offs demonstrated in simulations

Safe operation maintained under disturbances with online learning

Abstract

Optimal stabilization of safety-critical nonlinear systems requires balancing long-term performance and strict safety constraints. Existing quadratic-programming-based control barrier function (CBF) safety filters are point-wise and may exhibit myopic behavior and local trapping when the safeguarding action conflicts with the nominal optimal control. This paper develops a safety-aware infinite-horizon optimal control framework by embedding a barrier-Lyapunov function (BLF)-based safeguarding action into the system dynamics and introducing a barrier-regulating auxiliary variable, thereby reformulating the original constrained problem as an unconstrained one on an extended state space. To mitigate local trapping, we introduce an adaptive alignment-conditioned tangential excitation orthogonal to the safety direction, with activation adaptively modulated by the degree of directional alignment between the nominal and safeguarding controllers, and incorporate it as an admissible $\mathcal{L}2$ disturbance in an $H\infty$ formulation. For high-relative-degree systems under disturbances, we further augment the recursive high-order safe-set construction with barrier compensation terms to obtain a high-order BLF and formulate an adversarial disturbance attenuation problem, which is approximately solved via safe-exploration-enhanced online critic learning. Simulations demonstrate reduced local trapping, improved safety--performance trade-offs, and safe operation under disturbances.