Constantin Udriste

Abstract:

Multitime optimal control theory has been recently used in economics. Here, we develop some ideas using the context of optimal control and differential geometry. Specifically, two problems are analysed: (i) multitime evolution of reproducible resources, and (ii) multitime evolution of non-reproducible resources. The technique is to associate each problem with proper functional (like multiple integral or curvilinear integral) and appropriate constraints (geometric PDEs like m-flows, Goursat-Darboux PDEs, parallelism PDEs, and specific isoperimetric constraints like integrals). When the Hamiltonian is linear affine in the control, we focus on bang-bang and singular optimal controls.