Safe Control of Arbitrary Nonlinear Systems using Dynamic Extension

TL;DR

This paper introduces a novel, energy-function-based method for safely controlling complex nonlinear systems by dynamically extending control-affine frameworks, ensuring safety and performance with computational efficiency.

Contribution

It proposes an optimal algorithm for safe control of extended systems, combining energy function extension and hyperparameter optimization, applicable to a wide range of nonlinear systems.

Findings

Guarantees safety through forward invariance of the safe set.

Ensures bounded tracking error and smoother trajectories.

Demonstrates computational efficiency in numerical validations.

Abstract

Safe control for control-affine systems has been extensively studied. However, due to the complexity of system dynamics, it is challenging and time-consuming to apply these methods directly to non-control-affine systems, which cover a large group of dynamic systems, such as UAVs and systems with data-driven Neural Network Dynamic Models (NNDMs). Although all dynamic systems can be written in control-affine forms through dynamic extension, it remains unclear how to optimally design a computationally efficient algorithm to safely control the extended system. This paper addresses this challenge by proposing an optimal approach to synthesize safe control for the extended system under the framework of energy-function-based safe control. The proposed method first extends the energy function and then performs hyperparameter optimization to maximize performance while guaranteeing safety. It has been theoretically proved that our method guarantees safety (forward invariance of the safe set) and performance (bounded tracking error and smoother trajectories). It has been numerically validated that the proposed method is computationally efficient for non-control-affine systems.