Reduced order distributed boundary control of thermal transients in microsystems

We study the problem of regulation of thermal transients in a microsystem using empirical eigenfunctions. Proper orthogonal decomposition (POD) is applied to an ensemble of data to obtain the dominant structures, called empirical eigenfunctions, that characterize the dynamics of the process. These eigenfunctions are the most efficient basis for capturing the dynamics of an infinite dimensional process with a finite number of modes. In contrast to published approaches, we propose a new receding horizon boundary control scheme using the empirical eigenfunctions in a constrained optimization procedure to track a desired spatiotemporal profile. Finite element method (FEM) simulations of heat transfer are provided and used in order to implement and test the performance of the controller.