Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids
 Journal of scientific computing 70 (2017), Nr.1, S.128 ISSN: 08857474 ISSN: 15737691 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer SCAI () 
Abstract
An approach to solve finite time horizon suboptimal feedback control problems for partial differential equations is proposed by solving dynamic programming equations on adaptive sparse grids. A semidiscrete optimal control problem is introduced and the feedback control is derived from the corresponding value function. The value function can be characterized as the solution of an evolutionary HamiltonâJacobi Bellman (HJB) equation which is defined over a state space whose dimension is equal to the dimension of the underlying semidiscrete system. Besides a low dimensional semidiscretization it is important to solve the HJB equation efficiently to address the curse of dimensionality. We propose to apply a semiLagrangian scheme using spatially adaptive sparse grids. Sparse grids allow the discretization of the value functions in (higher) space dimensions since the curse of dimensionality of full grid methods arises to a much smaller extent.