Feedback control for reaction diffusion systems
Tobias Breiten and Karl Kunisch
Many problems of practical interest often cannot be modeled exactly but rather include uncertainties in form of noise or process disturbances. In this case, feedback-based, or closed-loop, control laws often are more robust than open loop controls. The optimal feedback law is known to be given in terms of the gradient of the value function satisfying the Hamilton-Jacobi-Bellman (HJB) equation. Due to the curse of dimensionality, solving the HJB equation however is tractable only for very limited examples. The development of suboptimal feedback laws is the focus of this project. A particular application of interest will be the monodomain and bidomain equations arising in electric cardiophysiology.
