A Synthesis Technique for Certain Time Optimum Controllers

The synthesis of optimum controllers is a topic of considerable current interest. Whereas many solutions to problems of optimization are available there are relatively few proposals in the literature for closed-loop, optimum system construction. This paper proposes that (a) the constancy property, associated with the Pontriagin Hamiltonian for linear, time-invariant plants, be used to determine the initial conditions necessary for the adjoint equation with time-optimum problems and (b) proposes a closed-loop configuration that utilizes this approach. The operation of the proposed system is discussed, its limitations arc stated and the stability is indicated in a special case.