Title :
A discrete maximum principle for solving optimal control problems
Author :
Guibout, Vincent ; Bloch, Anthony
Author_Institution :
Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA
Abstract :
We develop a discrete maximum principle that yields discrete necessary conditions for optimality. These conditions are in agreement with the usual conditions obtained from the Pontryagin maximum principle and define symplectic algorithms that solve the optimal control problem. We show that our approach allows one to recover most of the classical symplectic algorithms and can be enhanced so that the discrete necessary conditions define symplectic-energy conserving algorithms. Finally we illustrate its use with an example of a sub-Riemannian optimal control problem.
Keywords :
maximum principle; Pontryagin maximum principle; discrete maximum principle; sub-Riemannian optimal control problem; symplectic-energy conserving algorithms; Aerodynamics; Boundary value problems; Cost function; Couplings; Differential equations; Mathematics; Nonlinear equations; Optimal control; Partial differential equations; Performance analysis;
Conference_Titel :
Decision and Control, 2004. CDC. 43rd IEEE Conference on
Print_ISBN :
0-7803-8682-5
DOI :
10.1109/CDC.2004.1430309