Feedback control for Partial Differential Equations
Feedback control for Partial Differential Equations
Expositor: Alessandro Alla
Instituição: PUC-Rio
Data e Horário: 20/03/2018 | 17h:30min
Resumo: The dynamic programming (DP) approach provides a synthesis of optimal feedback controls for many nonlinear optimal control problems. However, once we adopt this approach and compute the value function via the numerical approximation of Hamilton-Jacobi-Bellman (HJB) equation there are two major difficulties: the solutions of an HJB equation are in general non-smooth and the approximation in high dimension ​requires huge memory allocations​.
In this talk, I will start describing the Linear Quadratic Regulator (LQR) case for infinite horizon problems and then, switching to nonlinear evolutive Partial Differential Equations (PDEs). The discretization of a PDE leads ​to ​a very large system of ODEs and therefore model order reduction, e.g Proper Orthogonal Decomposition (POD), ​​is crucial in order to reduce the complexity of the problem. Finally, I ​will ​discuss some numerical tests ​will illustrate the effectiveness of the method.