Lecturer: Emmanuel TRELAT, Université de Orleans, France Title: FINITE DIMENSIONAL OPTIMAL CONTROL: THEORY, APPLICATIONS, NUMERICAL IMPLEMENTATION Date and time: Mon, March 12, 2012, 09:00 – Fri, March 16, 2012, 11:00 Program: - Introduction to optimal control in finite dimension. Pontryagin Maximum Principle. Examples. (3 hours) - Numerical methods in optimal control: * concepts of direct and indirect methods, implementation on academic examples (with Matlab) (3h) * expert implementation of the shooting method on the optimal orbit transfer problem (with fortran / Matlab) (2h) * expert implementation of direct methods on the optimal downrange glider problem, with the use of automatic differentiation (AMPL) combined with optimization routines (IPOPT) (2h) References: [B] J.T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second Edition (Advances in Design and Control), SIAM, 2009. [LM] E.B. Lee, L. Markus, Foundations of optimal control theory, John Wiley, New York, 1967. [AMPL] R. Fourer, D.M. Gay, B.W. Kernighan, AMPL: A modeling language for mathematical programming, Duxbury Press, Brooks-Cole Publishing Company (1993). [P] L. Pontryagin, V. Boltyanskii, R. Gramkrelidze, E. Mischenko, The mathematical theory of optimal processes, Wiley Interscience, 1962. [T] E. Trélat, Contrôle optimal: théorie & applications (in french), Vuibert, 2005 (2nd Ed. 2008). [IPOPT] A. Wächter, L.T. Biegler, On the implementation of an interior-point filter line- search algorithm for large-scale nonlinear programming, Mathematical Programming 106 (2006), 25-57.