JournalsifbVol. 8, No. 3pp. 281–300

Static PDEs for time-dependent control problems

  • Alexander Vladimirsky

    Cornell University, Ithaca, United States
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Abstract

We consider two different non-autonomous anisotropic time-optimal control problems. For the min-time-from-boundary problem, we show that the value function is recovered as a viscosity solution of a static Hamilton-Jacobi-Bellman partial differential equation\\ H(u(\x),u(\x),\x)=1.H\left(\nabla u(\x), u(\x), \x \right) = 1. We demonstrate that the space-marching Ordered Upwind Methods (introduced in \cite{SethVlad2} for the autonomous control) can be extended to this non-autonomous case. We illustrate this approach with several numerical experiments. For the min-time-to-boundary problem, where no reduction to a static PDE is possible, we show how the space-marching methods can be efficiently used to approximate individual level sets of the time-dependent value function.

Cite this article

Alexander Vladimirsky, Static PDEs for time-dependent control problems. Interfaces Free Bound. 8 (2006), no. 3, pp. 281–300

DOI 10.4171/IFB/144