Optimal control problems on stratified domains

Alberto Bressan, Yunho Hong

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

We consider a class of optimal control problems defined on a stratified domain. Namely, we assume that the state space ℝN admits a stratification as a disjoint union of finitely many embedded submanifolds Mi. The dynamics of the system and the cost function are Lipschitz continuous restricted to each submanifold. We provide conditions which guarantee the existence of an optimal solution, and study sufficient conditions for optimality. These are obtained by proving a uniqueness result for solutions to a corresponding Hamilton-Jacobi equation with discontinuous coefficients, describing the value function. Our results are motivated by various applications, such as minimum time problems with discontinuous dynamics, and optimization problems constrained to a bounded domain, in the presence of an additional overflow cost at the boundary.

Original languageEnglish (US)
Pages (from-to)313-331
Number of pages19
JournalNetworks and Heterogeneous Media
Volume2
Issue number2
StatePublished - Dec 1 2007

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Submanifolds
Optimal Control Problem
Discontinuous Coefficients
Overflow
Hamilton-Jacobi Equation
Dynamic Problem
Stratification
Value Function
Cost functions
Lipschitz
Cost Function
Bounded Domain
Optimality
Disjoint
State Space
Union
Uniqueness
Optimal Solution
Optimization Problem
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

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Optimal control problems on stratified domains. / Bressan, Alberto; Hong, Yunho.

In: Networks and Heterogeneous Media, Vol. 2, No. 2, 01.12.2007, p. 313-331.

Research output: Contribution to journalArticle

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