A successive approximation method for non-linear distributed-parameter control systems†

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Abstract
A successive approximation algorithm based on the second-order expansion of the performance index is developed for a general class of non-linear distributed-parameter systems with non-linear functional boundary conditions. Necessary conditions and sufficient conditions for convergence, which are independent of the system dynamics, are satisfied and are readily tested for a wider class of control problems than those of the standard second-variation algorithm. Two non-linear examples, one with a distributed control and one with a spatially independent control, provide a comparison of the computational efficiencies of both second-order methods. Because of the absence of the system adjoint equations in the present technique the time required per iteration is less than that of the standard algorithm with very little sacrifice in the rate of convergence.