A structure exploiting SDP solver for robust controller synthesis

RWTH Publications (RWTH Aachen)

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.

Authors 4

1. Dennis Gramlich Aachen Intelligent Control Systems

   RWTH Aachen University · University of Stuttgart

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany

   Mathematical Systems Theory , University of Stuttgart , 70569 Stuttgart , Germany

2. Tobias Holicki Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany

3. Carsten W. Scherer Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany

4. Christian Ebenbauer Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany