A new formulation of state constraint problems for first-order PDES

Hitoshi Ishii*, Shigeaki Koike

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Citations (Scopus)


The first-order Hamilton-Jacobi-Bellman equation associated with the state constraint problem for optimal control is studied. Instead of the boundary condition which Soner introduced, a new and appropriate boundary condition for the PDE is proposed. The uniqueness and Lipschitz continuity of viscosity solutions for the boundary value problem are obtained.

Original languageEnglish
Pages (from-to)554-571
Number of pages18
JournalSIAM Journal on Control and Optimization
Issue number2
Publication statusPublished - 1996 Mar
Externally publishedYes


  • Comparison principle
  • State constraint problem
  • Viscosity solution

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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