Optimal discrete processes, nonlinear in time intervals: theory and selected applications
In the present paper we investigate the Hamiltonian based
optimization algorithms for inherently discrete processes, i.e. those in which state changes at the process stage are finite and may be large. Their mathematical models (difference equations) refer either for processes which are discrete by nature or are obtained from continuous (differential) models by suitable discretization. We show that, when discrete time intervals are linear in the discrete model, the optimal discrete process is described by a Hamiltonian of Pontryagin’s type which is constant along the discrete path. However, for models with nonlinear time intervals, the constancy of the optimal discrete Hamiltonian is lost and, instead, an extra difference equation constitutes a model component describing the change of the Hamiltonian. Selected applications of the obtained algorithms in evaporation and drying operations are presented, which involve models with linear and nonlinear time intervals.
CYBERNETICS AND PHYSICS, VOL. 1, No. 2, 2012, 120-127.