Search

Decentralized optimization of distributed stochastic differential systems has been an active area of research for over half a century. Its formulation utilizing static team and person-by-person optimality criteria is well investigated. However, the results have not been generalized to nonlinear distributed stochastic differential systems possibly due to technical difficulties inherent with decentralized decision strategies. In this first part of the two-part paper, we derive team optimality and person-by-person optimality conditions for distributed stochastic differential systems with different information structures. The optimality conditions are given in terms of a Hamiltonian system of equations described by a system of coupled backward and forward stochastic differential equations and a conditional Hamiltonian, under both regular and relaxed strategies. Our methodology is based on the semi martingale representation theorem and variational methods. Throughout the presentation we discuss similarities to optimality conditions of centralized decision making., Comment: 39 pages, 1 figure Submitted to IEEE Transactions on Automatic Control

In this second part of our two-part paper, we invoke the stochastic maximum principle, conditional Hamiltonian and the coupled backward-forward stochastic differential equations of the first part [1] to derive team optimal decentralized strategies for distributed stochastic differential systems with noiseless information structures. We present examples of such team games of nonlinear as well as linear quadratic forms. In some cases we obtain closed form expressions of the optimal decentralized strategies. Through the examples, we illustrate the effect of information signaling among the decision makers in reducing the computational complexity of optimal decentralized decision strategies., Comment: 39 pages Submitted to IEEE Transaction on Automatic Control

The relation between nonanticipative Rate Distortion Function (RDF) and filtering theory is discussed on abstract spaces. The relation is established by imposing a realizability constraint on the reconstruction conditional distribution of the classical RDF. Existence of the extremum solution of the nonanticipative RDF is shown using weak$^*$-convergence on appropriate topology. The extremum reconstruction conditional distribution is derived in closed form, for the case of stationary processes. The realization of the reconstruction conditional distribution which achieves the infimum of the nonanticipative RDF is described. Finally, an example is presented to illustrate the concepts., Comment: 41 pages,5 figures, Provisionally Accepted Version of the manuscript submitted to IEEE Transactions on Automatic Control; Part of this work was presented in 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS '12)