An Algorithm of Interaction Coordination in Multilevel Control of Nonlinear Systems

Abstract

This paper proposes a coordination algorithm for a multilevel control of a large-scale dynamical system. The system considered consists of weakly interconnected nonlinear subsystems and the performance index is quadratic in states and controls. According to the variational principle, the optimal control is given by solving a nonlinear two-point boundary-value problem, of which analytical solution is generally impossible. The present technique is to solve the overall problem, first by solving decomposed problems of the subsystems, and secondly by coordinating interactions among the subsystems. Since each subsystem problem is a linear two-point boundary-value problem, it is relatively easy to solve. The present idea of coordination is to adjust directly the interaction variables by an iteration without using the conventional Lagrange multiplier. A sufficient condition for convergence of the iteration algorithm is presented in the paper. The algorithm is computationally simple and the convergence is quite rapid for the problem of weakly coupled systems with small nonlinearities. The effectiveness of the method is illustrated in two examples.