Linear quadratic optimal boundary control of a diffusion-convection-reaction system

Linear quadratic optimal boundary control of a diffusion-convection-reaction system

In this work, the boundary control of a distributed parameter system (DPS) modeled by parabolic partial differential equations with spatially varying coefficients is studied. An infinite dimensional state space setting is formulated and an exact transformation of the boundary actuation is realized to obtain an evolutionary model. The evolutionary model is used for subsequent linear quadratic re...

Optimal Linear Quadratic Control

Linear Quadratic Optimal Control

In previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the feedback gain to achieve this is unique (as long as the system is controllable). For multi-input systems, the feedback gain is not unique, so there is additional design freedom. How does one utilize this...

Optimal Boundary Control of Reaction-Diffusion PDEs via Weak Variations

This paper derives linear quadratic regulator (LQR) results for boundary controlled parabolic partial differential equations (PDEs) via weak-variations. Research on optimal control of PDEs has a rich 40-year history. This body of knowledge relies heavily on operator and semigroup theory. Our research distinguishes itself by deriving existing LQR results from a more accessible set of mathematics...

Optimal Boundary Control & Estimation of Diffusion-Reaction PDEs

This paper considers the optimal control and optimal estimation problems for a class of linear parabolic diffusion-reaction partial differential equations (PDEs) with actuators and sensors at the boundaries. Diffusion-reaction PDEs with boundary actuation and sensing arise in a multitude of relevant physical systems (e.g. magneto-hydrodynamic flows, chemical reactors, and electrochemical conver...