Error estimates for the Euler discretization of an optimal control problem with first-order state constraints

Joseph Frederic Bonnans (1, 2) , Adriano Festa (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
3 RICAM - Johann Radon Institute for Computational and Applied Mathematics

We study the error introduced in the solution of an optimal control problem with first order state constraints, for which the trajectories are approximated with a classical Euler scheme. We obtain order one approximation results in the L ∞ norm (as opposed to the order 2/3 obtained in the literature). We assume either a strong second order optimality condition, or a weaker one in the case where the state constraint is scalar, satisfies some hypotheses for junction points, and the time step is constant. Our technique is based on some homotopy path of discrete optimal control problems that we study using perturbation analysis of nonlinear programming problems.

Mots clés: Nonlinear systems; State constraints; Optimal control; Rate of convergence; Euler discretization

Domaines: Optimisation et contrôle [math.OC]

Joseph Frederic Bonnans, Adriano Festa. Error estimates for the Euler discretization of an optimal control problem with first-order state constraints. SIAM Journal on Numerical Analysis, 2017, 55 (2), pp.445--471. ⟨hal-01093229v2⟩