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Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes

Hongxuan Wang, Xiaocong Li, Lihao Zheng, Adrish Bhaumik, Prahlad Vadakkepat

TL;DR

Hardware experiments on a permanent magnet synchronous motor demonstrate that, compared to baseline safe Bayesian optimization algorithms, SafeCtrlBO attains the best overall performance while ensuring safety.

Abstract

Controller tuning and optimization have been among the most fundamental problems in robotics and mechatronic systems. The traditional methodology is usually model-based, but its performance heavily relies on an accurate mathematical system model. In control applications with complex dynamics, obtaining a precise model is often challenging, leading us towards a data-driven approach. While various researchers have explored the optimization of a single controller, it remains a challenge to obtain the optimal controller parameters safely and efficiently when multiple controllers are involved. In this paper, we propose SafeCtrlBO to optimize multiple controllers simultaneously and safely. We simplify the exploration process in safe Bayesian optimization, reducing computational effort without sacrificing expansion capability. Additionally, we use additive kernels to enhance the efficiency of Gaussian process updates for unknown functions. Hardware experimental results on a permanent magnet synchronous motor (PMSM) demonstrate that compared to existing safe Bayesian optimization algorithms, SafeCtrlBO can obtain optimal parameters more efficiently while ensuring safety.

Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes

TL;DR

Hardware experiments on a permanent magnet synchronous motor demonstrate that, compared to baseline safe Bayesian optimization algorithms, SafeCtrlBO attains the best overall performance while ensuring safety.

Abstract

Controller tuning and optimization have been among the most fundamental problems in robotics and mechatronic systems. The traditional methodology is usually model-based, but its performance heavily relies on an accurate mathematical system model. In control applications with complex dynamics, obtaining a precise model is often challenging, leading us towards a data-driven approach. While various researchers have explored the optimization of a single controller, it remains a challenge to obtain the optimal controller parameters safely and efficiently when multiple controllers are involved. In this paper, we propose SafeCtrlBO to optimize multiple controllers simultaneously and safely. We simplify the exploration process in safe Bayesian optimization, reducing computational effort without sacrificing expansion capability. Additionally, we use additive kernels to enhance the efficiency of Gaussian process updates for unknown functions. Hardware experimental results on a permanent magnet synchronous motor (PMSM) demonstrate that compared to existing safe Bayesian optimization algorithms, SafeCtrlBO can obtain optimal parameters more efficiently while ensuring safety.
Paper Structure (29 sections, 13 theorems, 100 equations, 8 figures, 1 table, 1 algorithm)

This paper contains 29 sections, 13 theorems, 100 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work.
  3. Our contributions.
  4. Problem Statement
  5. Safe Bayesian Optimization
  6. SafeCtrlBO
  7. Additive Gaussian Kernels
  8. Acquisition Functions
  9. Theoretical Results
  10. Empirical Study
  11. Simulations on Synthetic Benchmark Functions
  12. Results.
  13. Hardware Experiments on A SpeedGoat Real-Time Machine
  14. Results.
  15. Conclusion
  16. ...and 14 more sections

Key Result

Theorem 4.1

When the outermost region $O_n$ is sufficiently large, within $O_n$, the point with maximum predictive uncertainty $\sigma_n^2(\textbf{a})$ lies on the safe boundary $\mathcal{B}_n$.

Figures (8)

  • Figure 1: A block diagram for a 2-layer cascade system. The dark grey blocks represent controllers, and the light grey blocks represent plants.
  • Figure 2: Optimization for synthetic benchmark functions.
  • Figure 3: Hardware experimental setup.
  • Figure 4: Hardware experiment results.
  • Figure 5: A simplified block diagram for PMSM FOC loops. The dark grey blocks represent controllers, and the light grey blocks represent plants.
  • ...and 3 more figures

Theorems & Definitions (28)

  • Theorem 4.1
  • Definition 5.1
  • Definition 5.2
  • Theorem 5.1
  • Theorem 5.2
  • Lemma D.1
  • proof
  • Theorem D.1
  • proof
  • Theorem D.2
  • ...and 18 more