OVERVIEW

Gradient-based algorithms are particularly suitable for performance measures that are either quadratic or at least unimodal. For some classes of problems [1] [3] the mathematical relation of the variable parameters to the performance measure is either unknown or is too complex to be useful. In yet other problems, constraints may be placed on the variable parameters of the adaptive controller with the result that the performance surface may no longer be unimodal. When the performance surface of interest is multimodal and contains saddlepoints, then any gradient-based algorithm must be used with caution. One way of approaching such problems is to employ a search algorithm. Algorithms belonging to this class have global search capabilities for both unimodal and multimodal performance surfaces and work for any computable performance measure [4] [11]. Until recently search algorithms were used only reluctantly, principally because little effort was made to use past information in guiding the search thereby resulting in slow convergence. Furthermore, search algorithms are not very powerful in unimodal applications. They do, however, have the advantage of being simple to implement in logical form, require little computation, are insensitive to discontinuities and exhibit a high degree of efficiency where little is known about the performance surface. The major types of search algorithms are systematic and random searches.

Systematic searches employ an exhaustive survey of the parameter space within the bounds of interest and therefore are easily capable of finding the global extremum of a multimodal performance measure. As a practical matter, however, this type of...