Viscosity solutions of two classes of coupled hamilton-jacobi-bellman equations

Xiao Mingqing, Başar Tamer

Research output: Contribution to journalArticlepeer-review


This paper studies viscosity solutions of two sets of linearly coupled Hamilton-Jacobi-Bellman (HJB) equations (one for finite horizon and the other one for infinite horizon) which arise in the optimal control of nonlinear piecewise deterministic systems where the controls could be unbounded. The controls enter through the system dynamics as well as the transitions for the underlying Markov chain process, and are allowed to depend on both the continuous state and the current state of the Markov chain. The paper establishes the existence and uniqueness of viscosity solutions for these two sets of HJB equations, whose Hamiltonian structures are different from the standard ones.

Original languageEnglish (US)
Pages (from-to)519-543
Number of pages25
JournalJournal of Inequalities and Applications
Issue number5
StatePublished - 2001


  • And phrases: viscosity solutions
  • Coupled hamilton-jacobi-bellman equations
  • Piecewise deterministic systems

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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