Pontryagin's maximum principle for optimal control of a non-well-posed parabolic differential equation involving a state constraint

Abstract

In this paper, we study Pontryagin's maximum principle for some optimal control problems governed by a non-well-posed parabolic differential equation. A new penalty functional is applied to derive Pontryagin's maximum principle and an application for this system is given.

On the Chernous'ko Time-Optimal Problem for the Equation of Heat Conductivity in a Rod

“…Despite 70 years of development, the solution of concrete non-trivial examples of time-optimal control still needs considerable effort [2,4,19]. The problem becomes even more difficult when a control system is described by a partial differential equation [11,24,25,34], particularly, for the heat conductivity equation [12,22,26,29,35,36]. In [1], the correctness of parabolic equations for heat propagation is discussed and for that purpose, a parabolic equation with time delay is considered.…”