Time suboptimal feedback control of systems described by linear parabolic partial differential equations

Feedback control for systems described by linear parabolic partial differential equations is considered from a time suboptimal point of view. A scalar quadratic function representing the deviation from a desired distribution is first formulated, and the rate of approach to the target is maximized by minimizing this quadratic function at each time step. An orthogonal collocation technique enables an accurate low-order lumped parameter model to be constructed. A direct search optimization can then be used to obtain the optimal quadratic function and, subsequently, the optimal feedback gain matrix for control. The resulting control applied to a diffusion process takes the system to the target rapidly and in a stable manner.