### Abstract

We consider a class of optimal control problems defined on a stratified domain. Namely, we assume that the state space ℝ^{N} 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 language | English (US) |
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Pages (from-to) | 313-331 |

Number of pages | 19 |

Journal | Networks and Heterogeneous Media |

Volume | 2 |

Issue number | 2 |

State | Published - Dec 1 2007 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Networks and Heterogeneous Media*,

*2*(2), 313-331.

}

*Networks and Heterogeneous Media*, vol. 2, no. 2, pp. 313-331.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal control problems on stratified domains

AU - Bressan, Alberto

AU - Hong, Yunho

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=55849090281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55849090281&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:55849090281

VL - 2

SP - 313

EP - 331

JO - Networks and Heterogeneous Media

JF - Networks and Heterogeneous Media

SN - 1556-1801

IS - 2

ER -