  - In this paper we introduce a new method to solve fixed-delay optimal
control problems which exploits numerical homotopy procedures. It is known that
solving this kind of problems via indirect methods is complex and
computationally demanding because their implementation is faced with two
difficulties: the extremal equations are of mixed type, and besides, the
shooting method has to be carefully initialized. Here, starting from the
solution of the non-delayed version of the optimal control problem, the delay
is introduced by numerical homotopy methods. Convergence results, which ensure
the effectiveness of the whole procedure, are provided. The numerical
efficiency is illustrated on an example.
