Centralized and decentralized control schemes for Gauss-Poisson processes

Gauss-Poisson processes are defined as jump processes with jump times according to a Poisson process and Gaussian jump size. Filtering and prediction recursive schemes are obtained and used in the derivation of optimal control schemes. Dynamic programming sufficient conditions are given for both centralized and delayed information sharing decentralized schemes. For the linear quadratic model, we derive explicit solutions for the optimal control.