Approximate computation of storage functions for discrete-time systems using sum-of-squares techniques

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Pirkelmann, Simon ; Angeli, David ; Grüne, Lars:
Approximate computation of storage functions for discrete-time systems using sum-of-squares techniques.
Bayreuth , 2019 . - 9 S.

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Abstract

In this paper we present a method for automated verification of dissipativity by numerical means for discrete time systems with polynomial dynamics and stage cost. It relies on sum-of-squares techniques in order to compute storage functions that satisfy a dissipation inequality. The method can also be used to treat systems subject to constraints. Moreover, an Taylor approximation based extension to more general nonlinear stage costs is presented which enables the computation of approximate local storage functions.