Reciprocity and duality in control programming problems

Abstract A general control programming problem of minimizing a “primal” functional subject to differential and inequality constraints, is transformed into a reciprocal form where the extremal curve is unchanged, but the roles of the state and adjoint variables are interchanged. Conditions are given for this stationary extremal to maximise the reciprocal functional, thus generating a “dual” problem. Applications are made to error estimation of approximate control schemes.