Risksensitive Control of Markov Jump Linear Systems: Caveats and Difficulties Jun Moon* and Tamer Basar
International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp.462467, 2017
Abstract : "In this technical note, we revisit the risksensitive optimal control problem for Markov jump linear
systems (MJLSs). We first demonstrate the inherent difficulty in solving the risksensitive 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 HamiltonJacobiBellman (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 risksensitive 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 riskneutral limit
of the risksensitive optimal control problem due to the presence of a nonlinear coupling term in the HJB equations."
Keyword :
Markov jump linear systems, risksensitive control, stochastic zerosum differential games.
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