Optimization and Systems Theory Seminar

November 22, 11.00-12.00

Professor Hector Sussmann
Department of Mathematics,
Rutgers University,
New Brunswick,
USA.

A tale of two hamiltonians

We show how the evolution from the calculus of variations to optimal control theory would have been considerably speeded up if only Hamilton's equations had been written from the very beginning in a slightly different form, which would clearly have made a sense at the time. This would have allowed to do conjecture immediately the so-called Weierstrass side conditions, to see their relationship with the Hamiltonian formulation, to give a rigorous coordinate-free formulation of Hamilton's equations of motion for free and charged particles in special relativity, and to guess right away the general form of the Pontryagin maximum principle that was only discovered in the 1950's. This will be illustrated with very simple examples showing the superior power and the simplicity of the control-theoretic hamiltonian formulation.