Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems

TL;DR

This paper discusses flexible control Lyapunov functions (CLFs) that adaptively optimize stability parameters in real-time, reducing conservativeness and enhancing control of fast, constrained mechatronic systems in aerospace and automotive fields.

Contribution

It introduces a novel flexible CLF framework that allows online optimization of stability parameters, improving control performance for high-speed, constrained systems.

Findings

Flexible CLFs significantly reduce conservativeness compared to classical CLFs.

They enable stabilization of nonlinear systems with sampling periods below one millisecond.

Potential applications include aerospace and automotive control systems.

Abstract

The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly reduced compared to classical CLFs, which makes \emph{flexible CLFs} more suitable for stabilization of constrained discrete-time nonlinear systems and real-time control. The purpose of this overview is to highlight the potential of flexible CLFs for real-time control of fast mechatronic systems, with sampling periods below one millisecond, which are widely employed in aerospace and automotive applications.