Noise Sensitivity Reduction of the Fixed Point Iteration-based Adaptive Control

In various control application areas, at least some approximate dynamic model of the physical systems under control are available. Though these models are not precise enough for serving as the exclusive basis for realizing satisfactory control, the information they convey is valuable for developing a model-based control that can be improved by either adaptive or robust modifications. The traditional model-based adaptive approaches for strongly nonlinear systems’ control use Lyapunov’s second method that normally requires full state estimation. To evade this problem an alternative solution was elaborated for digital controllers based on Stefan Banach’s Fixed Point Iteration-based approach. In contrast to the “Resolved Acceleration Rate Controllers” of mechanical systems that feedback only integrated, proportional and first time-derivatives of the observed motion, like the “Acceleration Feedback Controllers”, this method utilizes the observed second time-derivatives that makes its original version noise-sensitive, especially if the observed noisy signals are numerically differentiated. To reduce this effect at first the “continuous version” of the originally discrete method is introduced then it is numerically investigated by the use of subsequent drastic signal smoother in the control of a drastically nonlinear system. As a result, the relevant application area of this improved method can be outlined.