Hierarchical control and decomposition of decentralized linear stochastic systems

The contents of this thesis can be separated into two distinct divisions. The first is concerned with the development of a general theory of decomposition algorithms for optimization problems. The second develops an application of the methodology of the decomposition theory to a decentralized linear stochastic control problem. An indirect approach to the development of the theory of decomposition of optimization problems is taken. It is assumed that a set of necessary conditions for the optimization can be expressed in the form of a system of nonlinear equations. It is this system of equations which is decomposed. The result is a constructive approach for the decomposition of optimization problems which includes most hierarchical algorithms proposed to date. Because the approach is indirect, the convergence analysis is local in nature. Also, the formulation admits the development and analysis of multiple decompositions (and hence multilevel hierarchies). The theory of decomposition is applied to a linear stochastic optimal control problem with information flow constraints. The particular problem formulation considered is the interconnected system problem where the