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arXiv · 2304.05037

A structure exploiting SDP solver for robust controller synthesis

Dennis Gramlich·Tobias Holicki·Carsten W. Scherer·Christian Ebenbauer
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Abstract

In this paper, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP Lemma and they play a crucial role in e.g. robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require $O(n^6)$ arithmetic operations per Newton step to solve this class of problems, where $n$ is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to $O(n^3)$. However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this paper, we show how to include such constraints in structure exploiting KYP-SDP solvers.

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Dennis Gramlich, Tobias Holicki, Carsten W. Scherer, Christian Ebenbauer. 2023-04-11. A structure exploiting SDP solver for robust controller synthesis. https://arxiv.org/abs/2304.05037

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