Safety-Aware Performance Boosting for Constrained Nonlinear Systems

TL;DR

This paper introduces a control architecture combining a performance-boosting controller with a predictive safety filter, enabling safe, complex behaviors in constrained nonlinear systems while guaranteeing stability and expanding safe trajectory sets.

Contribution

It proposes a novel integrated control framework that guarantees stability and safety, and allows for trajectory set expansion beyond traditional predictive safety filters.

Findings

The architecture guarantees closed-loop stability and safety.

It strictly expands the set of safe, stable trajectories.

Demonstrated on a constrained inverted pendulum with obstacle.

Abstract

We study a control architecture for nonlinear constrained systems that integrates a performance-boosting (PB) controller with a scheduled Predictive Safety Filter (PSF). The PSF acts as a pre-stabilizing base controller that enforces state and input constraints. The PB controller, parameterized as a causal operator, influences the PSF in two ways: it proposes a performance input to be filtered, and it provides a scheduling signal to adjust the filter's Lyapunov-decrease rate. We prove two main results: (i) Stability by design: any controller adhering to this parametrization maintains closed-loop stability of the pre-stabilized system and inherits PSF safety. (ii) Trajectory-set expansion: the architecture strictly expands the set of safe, stable trajectories achievable by controllers combined with conventional PSFs, which rely on a pre-defined Lyapunov decrease rate to ensure stability. This scheduling allows the PB controller to safely execute complex behaviors, such as transient detours, that are provably unattainable by standard PSF formulations. We demonstrate this expanded capability on a constrained inverted pendulum task with a moving obstacle.