Lukas Munser | Searcharxiv

arXiv2021

Synthesis of Lyapunov Functions using Formal Verification

Recent employments of SMT solvers within the Lyapunov function synthesis provided effective tools for automated construction of Lyapunov functions alongside with sound computer-assisted certificates. The main benefit of the suggested approach is the formal correctness and elimination of the numerical uncertainty. In the present work, we extend the SMT-based synthesis approach for wider classes of continuous and discrete-time systems. Additionally, we address constructions of Lyapunov functions for state-dependent switching systems. We illustrate our approach by means of various examples from the control systems literature.

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arXiv2020

Prototypical Description and Controller Design for a Set of Systems Using v-gap Based Clustering

We present an approach to design stabilizing controllers for a set of linear systems without restrictions regarding their modeling order. To this end, the systems are treated as abstract objects in the space of the $ν$-gap metric. Via a cluster analysis the set of systems is split into v-gap similar clusters which are treated separately. For this purpose we provide an algorithm that constructs an explicit prototype system by generalizing the information of a given set of systems. Applying this algorithm to each cluster a set of prototype systems is obtained. Given these prototypes we design controllers in such a way that all systems assigned to a cluster will be stabilized by a corresponding controller. The approach is demonstrated for a set of 80 linear systems.

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