A Convex Approach to Output Feedback Control of Parabolic PDEs Using Sum-of-Squares
It provides a convex framework for output-feedback control of parabolic PDEs, addressing a known bottleneck in non-convex synthesis for infinite-dimensional systems.
This paper presents a convex optimization approach using sum-of-squares to design output-feedback controllers for 1D parabolic PDEs with various input/output configurations, reformulating the synthesis problem as Linear-Operator-Inequalities solvable via SDP.
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 point-measurements. 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.