Optimal control of a 2D diffusion–advection process with a team of mobile actuators under jointly optimal guidance

This paper describes an optimization framework to control a distributed parameter system (DPS) using team of mobile actuators. The simultaneously seeks optimal the DPS and guidance actuators such that cost function associated with both is minimized subject dynamics each. incurred from controlling linear–quadratic, which transformed into equivalent form as quadratic term operator-valued Riccati equation. reduces problem seeking only for because can be recovered once obtained. We establish conditions existence solution proposed problem. Since computing requires approximation, we also convergence exact approximate solution. That is, when evaluating these two solutions by original function, difference becomes arbitrarily small approximation gets finer. Two numerical examples demonstrate performance obtained approach.