Singular L-Q problems and the dirac-bergmann theory of constraints

Abstract

We apply Dirac’s theory of constraints to singular linear-quadratic optimal control problems and compare the results with our previous characterization of the “generalized optimal solutions” for this class of problems. The generalized optimal control(s) for a singular L-Q problem is the sum of a real-analytic function with a distribution of order r concentrated at the extremes of the time interval and the corresponding trajectory is the sum of an analytic function with a distribution of order (r − 1). The Dirac’s approach provides an alternative method to find the continuous term of the generalized optimal solution(s) by solving a set of equations involving Poisson brackets but omits the distributional term. We show how the Dirac-Bergmann approach can be modified to allow for the distributional terms.

This work is part of the author PhD project at the University of Aveiro, under supervision of A. Sarychev