Designing observer-based controllers for PDE systems: A heat-conducting rod with point observation and boundary control

In this paper, we propose a method to synthesize infinite-dimensional observer-based controllers for partial-differential systems. To illustrate the approach, we use a one-dimensional model of heat conduction with point observation and boundary control. Our method uses Sum-of-Squares optimization to solve linear operator inequalities in an infinite-dimensional Hilbert space. We use the semigroup framework and an operator version of the separation theorem and the Lyapunov inequality. We implement our method using SOSTOOLS and SeDuMi. We simulate the effects of our controller using Matlab.