MPC as a Copilot: A Predictive Filter Framework with Safety and Stability Guarantees

TL;DR

This paper introduces PS2F, a predictive filter framework combining MPC and a secondary filter to ensure safety and stability in control systems, with theoretical guarantees and flexible operation modes.

Contribution

The paper presents a unified predictive filter architecture that guarantees safety and stability, integrating a nominal MPC with a secondary filter for goal-oriented control.

Findings

Guarantees recursive feasibility and asymptotic stability.

Enables smooth transition between safety and stability modes.

Demonstrates effectiveness through numerical experiments.

Abstract

Ensuring both safety and stability remains a fundamental challenge in learning-based control, where goal-oriented policies often neglect system constraints and closed-loop state convergence. To address this limitation, this paper introduces the Predictive Safety--Stability Filter (PS2F), a unified predictive filter framework that guarantees constraint satisfaction and asymptotic stability within a single architecture. The PS2F framework comprises two cascaded optimal control problems: a nominal model predictive control (MPC) layer that serves solely as a copilot, implicitly defining a Lyapunov function and generating safety- and stability-certified predicted trajectories, and a secondary filtering layer that adjusts external command to remain within a provably safe and stable region. This cascaded structure enables PS2F to inherit the theoretical guarantees of nominal MPC while accommodating goal-oriented external commands. Rigorous analysis establishes recursive feasibility and asymptotic stability of the closed-loop system without introducing additional conservatism beyond that associated with the nominal MPC. Furthermore, a time-varying parameterisation allows PS2F to transition smoothly between safety-prioritised and stability-oriented operation modes, providing a principled mechanism for balancing exploration and exploitation. The effectiveness of the proposed framework is demonstrated through comparative numerical experiments.