A Polynomial Approach to ℓ1 Optimal Control Problems

Abstract

In this paper, the scalar multi-block ℓ1-optimal control problem is considered. It is shown that it can be converted via polynomial equation techniques to an infinite dimensional linear programming (LP) problem. Finite dimensional sub/super approximations can be determined by considering two sequences of modified finite dimensional linear programming problems derived directly from the YJBK parameterization by exploiting the underlying algebraic structure. This approach induces the application of a consistent truncation strategy that leads to a redundancy-free constraint formulation and, as a consequence, to linear programming problems less affected by degeneracy. Further, more insight on the algebraic structure of the problem and on the achievement of exact rational solutions is provided, allowing the development of a simple and conceptually attractive theory.