Multitime controlled linear PDE systems

TL;DR

This paper advances the theory of multitime controlled linear PDE systems by establishing new controllability and reachability results, with implications for engineering, economics, and biology.

Contribution

It provides new conditions for controllability, reachability, and solution existence in multitime PDE systems, extending recent multitime optimal control theory.

Findings

Refined controllability and reachability criteria.

Derived conditions for solution existence and integrability.

Introduced new concepts like multitime fundamental matrix and controllability gramians.

Abstract

We derive new results regarding the controllability and the reachability of multitime controlled linear PDE systems of first order. These systems describe some important multitime evolution in engineering, economics and biology. Some of them come from evolution PDEs of superior order. The original results include a refinement and a supplement of multitime optimal control theory, developed in some recent papers by the second author. They refer to the complete integrability conditions, conditions for the existence of solutions, path independent curvilinear integrals, the multitime fundamental matrix, multitime adjoint Cauchy problems, control space, controllability and reachability of phases, controllability gramian, reachability gramian, controllability matrix, counter-examples and commentaries.