Optimization of coupled non-linear systems†

Abstract

A coupling perturbation method is developed for near optimum design of non-linear systems. A scalar parameter ϵ is introduced in an nth-order system such that for ϵ ϵ = the system decouples into two (or more) independent low-order sub-systems. By the same procedure ϵ is introduced into the performance index. The near optimal control u¯ is defined as a truncated power series in ϵ. It is shown that each term of the above series can be sequentially obtained by separate sub-system calculations. Thus a considerable saving in computational effort is achieved Two examples are presented and the results compared with those obtained by conventional iterative methods. Applicability of the method to problems which cannot be solved by conventional methods is also discussed.