Iterative aggregation method for constrained optimal control problems (Q1196834)

A two-level interactive method, based on decomposition-coordination and aggregation-disaggregation ideas, is proposed for the solution of constrained large-scale optimal control problems. The method is intended for problems where the main difficulty is the large number of controls and hard control constraints. The typical example of such a problem is the dynamically resource allocation system, where a large number of relatively simple individual subsystems gathered by control (resource) constraints exist. The optimal control problem is formulated in \(n\)-dimensional Euclidean space and converted to a concave programming problem in Hilbert space, such that the saddle point and the Kuhn-Tucker theorems hold. The aggregated problem is formulated and necessary and sufficient conditions for the disaggregated control to be an optimal control of the original problem are established by using the Kuhn-Tucker conditions applied to the aggregated and the original problems and their duals. The linearly constrained optimal control problem is also considered as a special case. Two numerical examples, a theoretical one and the optimal control of a vertical oven having 12 heating zones, are presented with sufficient final results in order to demonstrate the efficiency of the method.