Optimal control duality and the Douglas-Rachford algorithm
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Date
2024
Authors
Burachik, R.S.
Caldwell, B.I.
Kaya, C.Y.
Moursi, W.M.
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SIAM Journal of Control and Optimization, 2024; 62(1):680-698
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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 two example optimal control problems.
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Copyright 2024 Society for Industrial and Applied Mathematics
Access Condition Notes: Accepted manuscript available open access