Frequency-domain adaptive control with design constraints

We show how the frequency-domain LMS algorithm can be used in adaptive controllers to minimize the variance of an error signal, while including design constraints. We also showed how the frequency-domain LMS can be modified and used in an internal model controller, to implement an adaptive controller which track changes in the disturbance, while maintaining robust stability to changes in the plant. Other constraints can also be included, and the approach can similarly be used in feedforward control. Since the adaptive solution to the constrained problem is based on a penalty function and the steepest descent method, other iterative solution methods can be considered which might improve the relatively slow convergence rate of the steepest descent method, and the computation load involved with the penalty function