Comparison of Various Noise Filtering Techniques in Strongly Nonlinear Adaptive Control

Abstract

In control applications the use of observed noisy and sometimes incomplete sets of observations makes a general problem arise that traditionally is tackled by the use of various Kalman filters. The main point behind these filters is to provide some “optimized” output based on the assumption that the measurement noises are of Gaussian nature and that the subsequent measurements of the same variables are statistically independent. The original concept was developed for linear system model, the later variants were extended to tackle nonlinear models, too, since the nonlinearities make the observation and filtering problems even more significant than in the case of linear systems. The Fixed Point Operation-based adaptive controllers are especially noise-sensitive since they need the feedback of higher order derivative errors feedback than the usual Resolved Acceleration Rate controllers. For supporting them simpler noise filtering techniques were developed than the Kalman filters since no filter optimization issues were considered by them. In the resent submission the operation of various noise filtering methods are compared with each other in this special control applied for the strongly nonlinear van der Pol oscillator. The simulations confirm that instead of the use of complicated Kalman filter the simpler ones seem to be applicable as well.