Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems

Mircea Lazar
(Eindhoven University of Technology, NL)

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 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.

In Manuela Bujorianu and Michael Fisher: Proceedings FM-09 Workshop on Formal Methods for Aerospace (FMA 2009), Eindhoven, The Netherlands, 3rd November 2009, Electronic Proceedings in Theoretical Computer Science 20, pp. 76–79.
Published: 28th March 2010.

ArXived at: https://dx.doi.org/10.4204/EPTCS.20.8 bibtex PDF

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