Optimal Decentralized Control for Markov Jump Linear Systems with Asymmetric One-Step Delayed Information Sharing

This paper addresses the issue of optimal control for Markov Jump Linear Systems with asymmetric one-step delayed information sharing characteristics. We assume two models, each involving two participants. In the first model, there is no communication in one direction while there is a delay in the other. In the second model, both directions have communication, but one direction has a delay. Both models possess a partially nested information structure, which implies the existence of linear optimal control laws. Utilizing summary statistics, we derive analytical solutions for the optimal control laws. We also tackle the problem of output feedback control when system observations are corrupted by noise. This paper introduces, for the first time, the combination of Markov Jump Linear Systems with asymmetric one-step delayed information.