Performance and information pattern trade-offs in a consensus based distributed optimization method

In this paper, aspects of a consensus based distributed optimization method are studied. The method is applied to approximate the solution of a multi-variate Linear-Quadratic (LQ) optimal control problem via distributed decision makers. The decision makers are constrained in terms of the pattern of local computation and information exchange, as a mechanism for managing the corresponding overheads. Feasibility (i.e., constraints satisfaction by the approximated solutions), convergence, and optimality of the method are proved. Convergence to the solution of finite horizon LQ optimal control problem is illustrated for a system with six interacting linear time invariant subsystems. For this system, trade-offs between approximation error (i.e. performance loss relative to the optimal solution) and the patterns used to constrain information exchange and computation, are also illustrated.