Computation of optimal actuator locations for nonlinear controllers in transport-reaction processes

Abstract This paper proposes a methodology for the computation of optimal locations of point actuators for nonlinear feedback controllers in transport-reaction processes described by a broad class of quasi-linear parabolic partial differential equations (PDE). Initially, Galerkin's method is employed to derive finite-dimensional approximations of the PDE system which are used for the synthesis of stabilizing nonlinear state feedback controllers via geometric techniques. Then, the optimal location problem is formulated as the one of minimizing a meaningful cost functional that includes penalty on the response of the closed-loop system and the control action and is solved by using standard unconstrained optimization techniques. It is established that the solution to this problem, which is obtained on the basis of the closed-loop finite-dimensional system, is near-optimal for the closed-loop infinite-dimensional system. The proposed methodology is successfully applied to a typical diffusion-reaction process.