Application of optimal boundary control to reaction-diffusion system with time-varying spatial domain

This paper considers the optimal boundary control of a parabolic partial differential equation (PDE) with time-varying spatial domain which is coupled to a second order ordinary differential equation (ODE) describing the time evolution of the domain boundary. The infinite-dimensional state space representation of the PDE yields a linear non autonomous evolution system with an operator which generates a two-parameter semigroup with analytic expression provided in this work. The nonautonomous evolution system is trans formed into an extended system which enables the optimal boundary control problem to be considered. The optimal control law of the extended system is determined and numerical results of the closed-loop feedback system are provided.