Optimization of large-scale systems using gradient-type interaction prediction approach

Abstract

In this paper, a new decomposition–coordination framework is presented for two-level optimal control of large-scale nonlinear systems. In the proposed approach, decomposition is performed by defining an interaction vector, while coordination is based on a new interaction prediction approach. In the first level, sub-problems are solved for nonlinear dynamics using a gradient method, while in the second level, the coordination is done using the gradient of coordination errors. This is in contrast to the conventional gradient-type coordination schemes, where they use the gradient of Lagrangian function. It is shown that the proposed decomposition–coordination framework considerably reduces the number of iterations. Moreover, compared to the substitution-type coordination approaches which are well known for their fast convergence rates and limited convergence regions, the proposed approach is robust with respect to parameters’ variation in addition to its good convergence rate. The robustness and the convergence rate of the proposed approach in compare to the costate prediction method are shown through simulations of a benchmark problem. The results are also compared to the ones obtained using centralized approach.