Optimization of Distributed Feedback Controllers for a Nonlinear Parabolic Integro-differential Equation
Monday, March 14, 2016 - 12:00pm - 12:30pm
A nonlocal Pyragas type feedback controller is considered for a parabolic partial differential equation with cubic reaction term. The main goal is to find an optimal kernel in the controller such that the solution of the associated parabolic integro-differential equation is close to a desired spatio-temporal pattern. This leads to a nonlinear optimal control problem with the feedback kernel taken as control function. The well-posedness of the problem and necessary optimality conditions are discussed. Special emphasis is laid on the approximation of time-periodic target functions. The oscillatory behavior of solutions to the parabolic integro-differential equation is discussed. This is joint work with Peter Nestler and Eckehard Schöll.