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

Riccardo Bonalli (1, 2) , Bruno Hérissé (1) , Emmanuel Trélat (2)

1 ONERA - The French Aerospace Lab [Palaiseau]
2 LJLL - Laboratoire Jacques-Louis Lions

— 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.

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Riccardo Bonalli, Bruno Hérissé, Emmanuel Trélat. Solving Optimal Control Problems for Delayed Control-Affine Systems with Quadratic Cost by Numerical Continuation. American Control Conference, May 2017, Seattle, United States. ⟨hal-01490437⟩