## Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 462-467 |

Number of pages | 6 |

Journal | International Journal of Control, Automation and Systems |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2017 |

## Keywords

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

## ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications