Risk-sensitive control of Markov jump linear systems: Caveats and difficulties

Jun Moon, Tamer Başar

Research output: Contribution to journalArticlepeer-review


In this technical note, we revisit the risk-sensitive optimal control problem for Markov jump linear systems (MJLSs). We first demonstrate the inherent difficulty in solving the risk-sensitive optimal control problem even if the system is linear and the cost function is quadratic. This is due to the nonlinear nature of the coupled set of Hamilton-Jacobi-Bellman (HJB) equations, stemming from the presence of the jump process. It thus follows that the standard quadratic form of the value function with a set of coupled Riccati differential equations cannot be a candidate solution to the coupled HJB equations. We subsequently show that there is no equivalence relationship between the problems of risk-sensitive control and H control of MJLSs, which are shown to be equivalent in the absence of any jumps. Finally, we show that there does not exist a large deviation limit as well as a risk-neutral limit of the risk-sensitive optimal control problem due to the presence of a nonlinear coupling term in the HJB equations.

Original languageEnglish (US)
Pages (from-to)462-467
Number of pages6
JournalInternational Journal of Control, Automation and Systems
Issue number1
StatePublished - Feb 1 2017


  • Markov jump linear systems
  • risk-sensitive control
  • stochastic zero-sum differential games

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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