Optimal Boundary Control of Reaction-Diffusion PDEs via Weak Variations

This paper derives linear quadratic regulator (LQR) results for boundary controlled parabolic partial differential equa-tions (PDEs) via weak-variations. Research on optimal con-trol of PDEs has a rich 40-year history. This body of knowl-edge relies heavily on operator and semigroup theory. Our research distinguishes itself by deriving existing LQR results from a more accessible set of mathematics, namely weak-variational concepts. Ultimately, the LQR controller is com-puted from a Riccati PDE that must be derived for each PDE model under consideration. Nonetheless, a Riccati PDE is a significantly simpler object to solve than an operator Ric-cati equation, which characterizes most existing results. To this end, our research provides an elegant and accessible method for practicing engineers who study physical systems described by PDEs. Simulation examples, closed-loop sta-bility analyses, comparisons to alternative control methods, and extensions to other models are also included