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Quick Updates for the Perturbed Static Output Feedback Control Problem in Linear Systems

Published 30 Jul 2023 in eess.SY, cs.SY, and math.OC | (2307.16178v4)

Abstract: This paper introduces a method for efficiently updating a nominal stabilizing static output feedback (SOF) controller in perturbed linear systems. As operating points and state-space matrices change in dynamic systems, accommodating updates to the SOF controller are necessary. Traditional methods address such changes by re-solving for the updated SOF gain, which is often \textit{(i)} computationally expensive due to the NP-hard nature of the problem or \textit{(ii)} infeasible due the limitations of its semidefinite programming relaxations. To overcome this, we leverage the concept of \textit{minimum destabilizing real perturbation} to formulate a norm minimization problem that yields fast, reliable controller updates. This approach accommodates a variety of known perturbations, including abrupt changes, model inaccuracies, and equilibrium-dependent linearizations. We also introduce geometric metrics to quantify the proximity to instability and rigorously define stability-guaranteed regions. Extensive numerical simulations validate the efficiency and robustness of the proposed method. We demonstrate the results on the SOF control of mutlti-machine power networks with changing operating points, and demonstrate that the computed quick updates produce comparable solutions to the SOF ones, while requiring orders of magnitude less time.

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