Concepts of General System Theory in the Linear Optimal Control Problem

Concepts of generalised flux and thermodynamic forces and particularly the Onsager-Casinir reciprocal relations 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 variable is illustrated. Concepts of energy in the general linear system based on quadratic functions are discussed with reference to an electromechanical system, and the solution of the optimal control problem with resulting cross-product weighting terms in the performance criterion is illustrated........