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DOI: 10.23952/cot.2025.47
Received October 30, 2023; Accepted May 6, 2024; Published online October 19, 2025
Abstract. In this paper, the finite horizon linear quadratic regulator (LQR) problem for switched linear differential algebraic equations is studied. It is shown that for switched DAEs with a switching signal that induces locally finitely many switches, the problem can be solved by recursively solving several LQR problems for non-switched DAE. First, it is shown how to solve the non-switched problems for index-1 DAEs followed by an extension of the results to higher index DAEs. The resulting optimal control can be computed based on the solution of a Riccati differential equation expressed in terms of the differential system matrices. The paper concludes with the extension of the results to the LQR problem for general switched DAEs.
How to Cite this Article:
P. Wijnbergen, S. Trenn, Impulse-free linear quadratic optimal control of switched differential algebraic equations, Commun. Optim. Theory 2025 (2025) 47.