Fig. 3. Comparison of optimum and truncated Gaussian nondimensional power density functions. 5. CONCLUDING REMARKS The analysis as presented here leads to very simple formulas for many of the main unknowns, and as such enables a designer to see and understand the effects of parameter changes very quickly. When the cost function is made more complex or additional restrictions on the variables are introduced, naturally the results become more complicated and more computing time is required. However, unless the changes are very considerable, the results obtained in this paper do not seem to be altered to any great extent. One of the main factors that permits such concise results to be derived is, of course, the fact that the differential equations of the system can be explicitly integrated. In most optimal control problems of which we are aware, this simplification is not possible. It is worth pointing out that the results obtained are essentially applicable to any pair of antennas with an associated penalty function of the same general type as our cost function C. For example, transmission of power between two mountain tops should be amenable to the type of analysis carried out here. REFERENCES 1. P.E. Glaser, Power from the Sun: Its Future, Science, 162, (3856), 857-861, 1968. 2. J.W. Goodman, Introduction to Fourier Optics, McGraw-Hill Book Company, New York, 1968, p. 60. 3. G. Moyer and H. Hinz, Minimum Cost Transmitter-Receiver Antenna Pairs, Research Department Memorandum RM-690, Grumman Aerospace Corporation, Bethpage, New York, September 1979.
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