Optimality: Multipliers

Abstract

As described in the introduction to Chapter 8, an alternative approach to optimal control relies upon Lagrange multipliers in order to link static optimization problems. In this chapter, we provide a brief introduction to several selected topics in variational, or multiplier-based, optimal control, namely: minimization of Lagrangians (and the associated Hamiltonian formalism) for open input-value sets, the basic result in the classical Calculus of Variations seen as a special case, some remarks on numerical techniques, and the Pontryagin Minimum (or Maximum, depending on conventions) Principle for arbitrary control-value sets but free final state. The area of nonlinear optimal control is very broad, and technically subtle, and, for a more in-depth study, the reader should consult the extensive literature that exists on the subject.