• English
  • Deutsch
  • Log In
    Password Login
    Research Outputs
    Fundings & Projects
    Researchers
    Institutes
    Statistics
Repository logo
Fraunhofer-Gesellschaft
  1. Home
  2. Fraunhofer-Gesellschaft
  3. Artikel
  4. Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids
 
  • Details
  • Full
Options
2017
Journal Article
Title

Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids

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 semi-discrete 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 semi-discrete system. Besides a low dimensional semi-discretization it is important to solve the HJB equation efficiently to address the curse of dimensionality. We propose to apply a semi-Lagrangian 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.
Author(s)
Garcke, J.
Kröner, A.
Journal
Journal of scientific computing  
Open Access
DOI
10.1007/s10915-016-0240-7
Language
English
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI  
  • Cookie settings
  • Imprint
  • Privacy policy
  • Api
  • Contact
© 2024