An Algorithm for Interaction Coordination in Multilevel Control of Nonlinear Systems
Yoshikazu Nishikawa, Nobuo Sannomiya, Takeo Ojika · Transactions of the Society of Instrument and Control Engineers · 1974
This paper proposes a coordination algorithm for 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 an analytical solution is generally impossible.The present technique is to solve the overall problem, first by solving decomposed problems of the subsystems, and second 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 the interaction variables directly 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 an example.