Optimal Parameter Adaptation for Safety-Critical Control via Safe Barrier Bayesian Optimization

TL;DR

The paper tackles the challenge of safely improving performance in safety-critical control by integrating control barrier functions (CBFs) with Safe Barrier Bayesian Optimization (SB2O). It provides a principled, model-agnostic framework that categorizes configurable parameters, enforces feasibility via barrier-based acquisition, and delivers theoretical safety and suboptimality guarantees. The CBF-SB2O framework is validated on swing-up cart-pole and high-fidelity adaptive cruise control tasks, where it outperforms baselines in both safety and optimization efficiency. This approach enables efficient, safe parameter tuning for complex safety-critical systems in scenarios where objective and constraint functions are black-box and expensive to evaluate.

Abstract

Safety is of paramount importance in control systems to avoid costly risks and catastrophic damages. The control barrier function (CBF) method, a promising solution for safety-critical control, poses a new challenge of enhancing control performance due to its direct modification of original control design and the introduction of uncalibrated parameters. In this work, we shed light on the crucial role of configurable parameters in the CBF method for performance enhancement with a systematical categorization. Based on that, we propose a novel framework combining the CBF method with Bayesian optimization (BO) to optimize the safe control performance. Considering feasibility/safety-critical constraints, we develop a safe version of BO using the barrier-based interior method to efficiently search for promising feasible configurable parameters. Furthermore, we provide theoretical criteria of our framework regarding safety and optimality. An essential advantage of our framework lies in that it can work in model-agnostic environments, leaving sufficient flexibility in designing objective and constraint functions. Finally, simulation experiments on swing-up control and high-fidelity adaptive cruise control are conducted to demonstrate the effectiveness of our framework.

Figures (8)

• Figure 1: An overview of the CBF-SB2O framework for SC2Ts.
• Figure 2: A safe tracking control task with three different configurations. (Left) The moving trajectories with different $\mathbf{z}_i$. (Right) the LQR performance ($Q=I$ and $R=2I$) and the response time $t_i = \inf_{t>t_0} \{\left\Vert x(t)-x_d\right\Vert \leq 0.1\}$.
• Figure 3: An example of optimal control for linear systems via vanilla BO (optimal LQR) and SB2O (safe LQR). The search space is $[-5, -0.001]^2$. The best solution for optimal LQR is $[-1.0, -1.732]$ (same as the solution to the Riccati equation), and the one for safe LQR is $[-1.004, -2.324]$. (Left) The mean and variance of best observations during search with $5$ repetitive experiments. (Right) Trajectories of system state with different gains.
• Figure 4: The physical structure of a 2-D cart-pole system.
• Figure 5: Preliminary test on the swing up control using an unsafe nominal controller with $[k_E,k_p,k_d]=[0.3,0.8,1.0]$. We manually set the CBF parameters as $[\alpha,\mu] = [1.0, 1.0]$, with LQR performance $25.74$. After $40$ function evaluations by CBF-SB2O, we have $[\alpha,\mu] = [0.3, 7.7]$, with performance $22.44$. (Left) Trajectories of position of systems with different controllers. (Right) Trajectories of angle under different controllers.