A Convex Approach to Output Feedback Control of Parabolic PDEs Using Sum-of-Squares

In this paper we use optimization-based methods to design output-feedback controllers for a class of one-dimensional parabolic partial differential equations. The output may be distributed or pointmeasurements. The input may be distributed or boundary actuation. We use Lyapunov operators, duality, and the Luenberger observer framework to reformulate the synthesis problem as a convex optimization problem expressed as a set of Linear-Operator-Inequalities (LOIs). We then show how feasibility of these LOIs may be tested using Semidefinite Programming (SDP) and the Sum-of-Squares methodology.