Algorithm for the minimum-effort problem

Give a consistent set of linear equations in unknown variables, a minimum-effort solution is defined to be a solution of that set of equations whose maximum component\´s magnitude is the smallest possible. An algorithmic procedure for obtaining a minimum-effort solution is developed. Its development is based on the duality principle from functional analysis. Possible applications of such an algorithm for typical digital control problems is presented in the introductory section. In such situations, it is frequently desirable to effect a given control task while using minimum control amplitude.