Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions

2025-07-18

AI Summary

Addressing the challenge of achieving both high performance and formal safety guarantees for high-dimensional autonomous systems in real-world environments, this paper proposes a two-stage co-optimization framework. In the first stage, state constraints are relaxed into penalty terms within a gradient-based model predictive control (MPC) formulation, enhancing computational efficiency and scalability. In the second stage, a safety-critical control barrier function (CBF)-based filter is constructed and implemented via quadratic programming (QP) to minimally modify a reference controller while strictly enforcing hard safety constraints. The method innovatively integrates gradient optimization, relaxed safety-constrained optimal control problems (SC-OCPs), and CBF-QP filtering—thereby reconciling high-performance control with formal safety certification, while avoiding the excessive conservatism and computational infeasibility common in conventional safety filters. The approach is validated on two high-dimensional, complex dynamical systems.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time, they can become overly conservative when the nominal policy lacks safety awareness. Conversely, solving State-Constrained Optimal Control Problems (SC-OCPs) via dynamic programming offers formal guarantees but is intractable in high-dimensional systems. In this work, we propose a novel two-stage framework that combines gradient-based Model Predictive Control (MPC) with CBF-based safety filtering for co-optimizing safety and performance. In the first stage, we relax safety constraints as penalties in the cost function, enabling fast optimization via gradient-based methods. This step improves scalability and avoids feasibility issues associated with hard constraints. In the second stage, we modify the resulting controller using a CBF-based Quadratic Program (CBF-QP), which enforces hard safety constraints with minimal deviation from the reference. Our approach yields controllers that are both performant and provably safe. We validate the proposed framework on two case studies, showcasing its ability to synthesize scalable, safe, and high-performance controllers for complex, high-dimensional autonomous systems.

Problem

• Ensuring safety and performance in autonomous systems
• Overcoming conservatism in Control Barrier Functions (CBFs)
• Solving high-dimensional State-Constrained Optimal Control Problems (SC-OCPs)

Innovation

• Combines gradient-based MPC with CBF safety filtering
• Relaxes safety constraints as cost penalties initially
• Enforces hard safety via CBF-QP with minimal deviation