Minimum energy control of systems using -state controls

A recently developed decomposition algorithm of Meyer is applied to the problem of the minimum energy transfer of a linear time-invariant system from a given initial state to a compact, convex but otherwise arbitrary target set using -state controls. The problem is thus decomposed into a sequence of subproblems which differ from it only in that the target set is a hyperplane. An algorithm for the solution of the subproblem is developed. It has the important property that it converges if and only if a solution exists. The convergence does not depend on the customary "initial guess." When this algorithm is incorporated into the Meyer algorithm, the overall convergence likewise does not depend on an initial guess. This Property is useful for on-line computation. The method of solution also applies to a class of singular problems. As a by-product of the method of solution of the subproblem, an interesting property of the costate variable is obtained.