Applications of modern optimal control theory to environmental control of confined spaces and life support systems: Part 3—optimal control of systems in which state variables have equality constraints at the final process time

Abstract

The basic form of Pontryagin's maximum principle is extended to cover optimal problems with equality constraints imposed on the final state variables. The necessary conditions for optimum control policy are developed and are applied to two concrete examples. The dynamic behavior of the life support system consisting of an air-conditioned cabin (the system proper) subject to an impulse heat disturbance and a heat exchanger (the control element) is again studied. The first example considers the optimal control policy for a system having a heat exchanger with a negligibly small time constant. The square form of the final condition of the state variable is considered as an equality constraint. The second example considers the optimal policy of a system where the flow of air in the cabin is characterized by the two completely stirred tanks-in-series (2 CST's-in-series) model. The time constant of the heat exchanger is not neglected, that is, the response of the heat exchanger is not instantaneous. The squares of the final conditions of the state variables are again considered as equality constraints.