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- In this paper we introduce a new method to solve fixed-delay optimalcontrol problems which exploits numerical homotopy procedures. It is known thatsolving this kind of problems via indirect methods is complex andcomputationally demanding because their implementation is faced with twodifficulties: the extremal equations are of mixed type, and besides, theshooting method has to be carefully initialized. Here, starting from thesolution of the non-delayed version of the optimal control problem, the delayis introduced by numerical homotopy methods. Convergence results, which ensurethe effectiveness of the whole procedure, are provided. The numericalefficiency is illustrated on an example.

Solving Optimal Control Problems for Delayed Control-Affine Systems with Quadratic Cost by Numerical Continuation