An example of the application of dynamic programming to the design of optimal control programs

The paper suggests a method for applying dynamic programming techniques to the design of optimal control programs. A step-by-step description of the method is given as it was applied to the problem of determining an optimal startup sequence for a satellite power plant. In the present case the criterion of optimality is the amount of auxiliary energy required for the startup of the power plant in orbit. A phase space is defined in terms of pertinent power plant variables; the solution is then obtained by treating the problem as aa N -stage decision problem consisting of selecting a sequence of phase space points such that the path so traced between the point representing the initial state of the plant and the point representing the final, operating state satisfies the criterion of optimality. Numerical calculations were performed with the aid of the digital code described in the Appendix. The results of this parametric study indicate possible energy savings up to 25 per cent. The paper is self-contained in the sense that very little if any contact with reactor technology or dynamic programming is required by the reader.