Discrete-time JLQG with dependently controlled jump probabilities

Abstract

Jump linear quadratic Gaussian (JLQG) model is well studied due to its wide applications. The existing studies on JLQG model with controlled jump probabilities usually impose an assumption that jump probabilities are independent and separately controlled. However, in some practical systems, their jump probabilities may not be independent of each other. In this paper, we study JLQG model with dependently controlled jump probabilities and formulate it as a two-level control problem. We propose an approach to calculate its performance gradient with respect to jump probabilities and develop a gradient-based optimization algorithm. We present an application of manufacturing system to illustrate the main results of this paper.