Taylor Expansions for the Hamilton-Jacobi-Bellman Equation associated to optimal control of Fokker-Planck Equations.
Speaker : Prof. Karl Kunisch (Johann Radon Institute for Computational and Applied Mathematics RICAM Linz, and University of Graz (Austria)).
Feedback control strategies for the Fokker-Planck equation that speed up convergence to the stationary distributions are investigated. At first, projected Riccati and Lyapunov equation techniques are investigated and their numerical performance is illustrated. Subsequently, polynomial approximations of the associated
value function are characterized in terms of multilinear forms, which can be obtained as solutions to generalized Lyapunov equations with recursively defined right-hand sides. They form the basis for defining new feedback laws. Their approximation properties are investigated analytically and their performance compared Riccati based laws is investigated numerically.
This is joint work with T. Breiten and L. Pfeiffer.