Computing methods in optimization problems - Gradient methods for the optimization of dynamic system parameters by hybrid computation

Publisher Summary This chapter discusses the computer implementation of both continuous and discrete gradient methods for adjusting the parameters of a dynamic system so as to match a specified response function as closely as possible. Continuous parameter optimization is an appealing concept and a number of adaptive control schemes have been based on it. Also continuous parameter optimization algorithms are conceptually simple, but their convergence properties are difficult to determine. Subsequently, the convergence problems encountered in continuous parameter variation schemes may be largely circumvented by making use of a discrete iterative adjustment algorithm; when this is done, it becomes possible to determine the true gradient of a given criterion function as parameter changes are made only at discrete points in time. Continuous parameter adjustment is easily carried out by analog computation, while iterative adjustment seems to be best suited to a digital computer. A combination of digital decision and branching capabilities and analog solution speed is available in a hybrid computer. By monitoring the results of continuous parameter adjustment via analog-to-digital converters, the digital machine can assure stability in otherwise uncertain circumstances.