Multitime controlled linear PDE systems

摘要

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