Adaptive Safety-Critical Control for Nonlinear Systems with Parametric Uncertainties Using Control Barrier Functions and Adaptive Laws

Kernkonzepte

This paper presents a novel approach that combines control barrier functions and adaptive laws to generate a safe controller for nonlinear systems with parametric uncertainties in both drift terms and control-input matrices.

Zusammenfassung

The paper proposes an adaptive control barrier function (aCBF) approach to ensure the safety of control-affine systems with parametric uncertainties. The key highlights are:

1. The method combines control barrier functions (CBFs) and adaptive laws to generate a safe controller through a nonlinear program (NLP) with an explicitly given closed-form solution.

2. The proposed approach verifies the non-emptiness of the admissible control set independently of online parameter estimations, which can ensure that the safe controller is singularity-free. This is in contrast to existing aCBF methods where the CBF condition relies on estimated parameters.

3. A data-driven algorithm is developed to improve the performance of the proposed controller by tightening the bounds of the unknown parameters.

4. The effectiveness of the control scheme is demonstrated through numerical simulations.

Statistiken

There exist known functions 𝑓_u(x), 𝑓_u(x) such that 𝑓_u(x) ≤ 𝑓_u(x) ≤ 𝑓_u(x).
There exist known vectors 𝜃_i, 𝜃_i and 𝜆_i, 𝜆_i such that 𝜃_i ≤ 𝜃_i ≤ 𝜃_i and 𝜆_i ≤ 𝜆_i ≤ 𝜆_i for all i ∈ [n].
There exist constants 𝑏_1, ..., 𝑏_n > 0 such that |𝑔_i(x) + 𝜆_i^⊤𝜓_i(x)| ≥ 𝑏_i for any i ∈ [n] and any x ∈ C.

Zitate

"The main challenge of stabilizing such a system using adaptive controllers arises from the so-called "loss of controllability" problem; that is, although the system is controllable, the identification model may lose its controllability at some points in time, owing to parameter adaptations."
"To the best of our knowledge, the singularity-free aCBF-based safe controller is not yet developed in the literature, though relevant stabilizing adaptive control schemes have been proposed."

Wichtige Erkenntnisse aus

Adaptive Safety-Critical Control for a Class of Nonlinear Systems with Parametric Uncertainties: A Control Barrier Function Approach

by Yujie Wang,X... um arxiv.org 04-16-2024

https://arxiv.org/pdf/2302.08601.pdf

Tiefere Fragen

How can the proposed aCBF-NLP-based control design be extended to handle systems with more general forms of parametric uncertainties beyond the diagonal structures considered in this work

The proposed aCBF-NLP-based control design can be extended to handle systems with more general forms of parametric uncertainties by modifying the CBF condition and the adaptive laws to accommodate the new structures. In the case where the parametric uncertainties in 𝑔 and 𝑔𝜆 are not diagonal, the CBF condition can be reformulated to include these non-diagonal terms. This extension would involve adjusting the terms in the CBF condition and the adaptive laws to account for the new structure of the uncertainties. By appropriately defining the new CBF condition and updating the adaptive laws to estimate the parameters associated with the non-diagonal uncertainties, the aCBF-NLP-based control design can be effectively applied to systems with more general forms of parametric uncertainties.

What are the potential limitations or drawbacks of the data-driven approach used to tighten the parameter bounds, and how can it be further improved

The data-driven approach used to tighten the parameter bounds may have limitations in terms of computational complexity and the accuracy of the parameter estimates. One potential drawback is the reliance on historical data for parameter estimation, which may not always capture the full range of variations in the system. Additionally, the conservatism of the tightened parameter bounds could lead to overly restrictive control policies, limiting the system's performance. To improve the data-driven approach, techniques such as incorporating real-time data feedback, enhancing the learning algorithms for parameter estimation, and refining the uncertainty modeling could be implemented. By refining the data-driven algorithms and incorporating more sophisticated machine learning methods, the accuracy and efficiency of the parameter estimation process can be enhanced, leading to more effective tightening of the parameter bounds.

Can the aCBF-NLP-based control framework be applied to safety-critical control problems in other domains beyond robotics and aerospace, such as in the context of smart grids or transportation networks

The aCBF-NLP-based control framework can be applied to safety-critical control problems in various domains beyond robotics and aerospace, including smart grids and transportation networks. In the context of smart grids, where the control of power distribution and energy management systems is crucial, the aCBF-NLP approach can be utilized to ensure the safe operation of the grid under uncertain conditions. By modeling the uncertainties in the grid parameters and applying the aCBF-NLP control design, the stability and reliability of the smart grid can be enhanced. Similarly, in transportation networks, such as autonomous vehicle control or traffic management systems, the aCBF-NLP framework can be employed to address safety-critical control challenges. By adapting the control barrier functions to the specific dynamics of transportation systems and integrating adaptive laws for parameter estimation, the aCBF-NLP approach can contribute to enhancing the safety and efficiency of transportation operations. The flexibility and adaptability of the aCBF-NLP framework make it a versatile tool for addressing safety-critical control problems in a wide range of domains.