Linear Quadratic Control Problem of Systems With Markov Jumps in Reverse Time and Observation With Anticipation of the Jumps

This article studies the linear-quadratic optimal control of linear systems with jump parameters driven by a Markov chain in reverse-time, anticipative observation of the jump variable, and exogenous inputs. This type of problem appears, for example, when a system with Markov jumps interacts with a first-in last-out queue, as illustrated in different contexts in this article. The solution is given in terms of precomputable, coupled Riccati equations, and the number of variables depends on the information structure, making it easier to compute and implement when more information is available. Numerical experiments illustrate applications and indicate that the optimal controller outperforms other controllers.