Multiscale optimal control of transport-reaction system with time varying spatial domain

This paper deals with the multi-scale optimal control of transport-reaction systems with the underlying dynamics governed by the second order rigid body dynamics, coupled with the parabolic partial differential equations (PDEs) with time-varying spatial domains, developed by considering the first principles dynamical equations for continuum mechanics. A functional theory is employed to explore the process model time-varying features, which lead to the characterization of the time varying spatial operator as a Riesz-spectral operator. This characterization facilitates the formulation of the optimal control problem where the infinite-dimensional system associated with the time-varying spatial operator is coupled with a finite-dimensional system describing the motion of the domain. The temperature control of the underlying transportreaction dynamics is realized through the optimal control law regulating the trajectory of the domain boundary coupled with the optimal heating input applied along the domain. The optimal control law associated with the domain´s boundary is obtained as a solution to the algebraic Riccati equation, while the optimal control law associated with the temperature regulation is obtained as a solution of a time-dependent Ricatti equation.