Reciprocal relationships in the linear optimal-control problem

Concepts of generalised flux and thermodynamic forces, and particularly the Onsager¿Casimir reciprocal relationships characterising the phenomenological equations for general irreversible-flow processes, are shown to exist analogously in the formulation of the linear optimal-control and estimation problems. Characteristics of the energy function used in the Lagrange and Hamiltonian representation of a system reacting with an environment are discussed, and the condition of zero dissipation in the formulation of the optimal-control problem defining the combined solution of the state and adjoint variables is illustrated.