The control Engineer is often confronted with the task of designing controllers for noisy systems whose parameter variation is so severe that classical or state space based controllers cannot handle it. This problem provides the material of Adaptive Control Theory. There are several aspects to Adaptive Control Theory. The first is to produce algorithms that will estimate varying parameters in real time and then use these estimates to modify the controller settings. The next is to study the behavior and performance of such algorithms. This involves questions of global stability, robustness to model error (parasitics) and performance (e.g. output power and control signal power). The major thrust of this research concerns issues related to performance analysis of Adaptive algorithms, namely; convergence, misadjustment and excess lag. The latter two have yet to be investigated for Stochastic Adaptive Control. To do this, some new premises are needed. The premise of parameter convergence is no longer relevant, instead the almost sure behavior of performance indices must be directly analyzed. Finally, it is possible to do approximate sensitivity calculations for Adaptive Controllers. It is expected that this research will yield a better understanding of stochastic adaptive control and eventually to better control algorithms.
