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arXiv · 2303.06527

Optimal Control Duality and the Douglas-Rachford Algorithm

Regina S. Burachik·Bethany I Caldwell·C. Yalçın Kaya·Walaa M. Moursi
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Abstract

We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas-Rachford (DR) algorithm. We obtain an expression for the fixed point of the DR operator as applied to solving the optimal control problem, which in turn devises a certificate of optimality that can be employed for numerical verification. The fixed point and the optimality check are illustrated in an example optimal control problem.

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Regina S. Burachik, Bethany I Caldwell, C. Yalçın Kaya, Walaa M. Moursi. 2023-03-12. Optimal Control Duality and the Douglas-Rachford Algorithm. https://arxiv.org/abs/2303.06527

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