Adaptive inverse control and filtering using wavelets

The Adaptive Inverse Control (AIC) scheme, and the Wavelet based Linear System Modeling and Adaptive Filtering scheme are integrated to form a Wavelet based Adaptive Inverse Control method. This new control and filtering method is applicable to a wide range of control and communication systems.; Wavelet based Adaptive Filtering using the wavelet Transform Least Mean Square (TLMS) method is studied and compared to TLMS algorithms that uses other than wavelet transforms such as the Discrete Fourier Transform, Discrete Cosine Transform, Discrete Hartley Transform, Walsh Hadamard Transform, among others. Different wavelets are used such as Daubechies, Haar, and Symmlets, with different subband decompositions. Comparisons are done by computation of the eigenvalue ratios of the maximum over the minimum eigenvalues of the normalized transformed input autocorrelation matrices using different transforms and coloring input signals. The eigenvalue ratio is known to give a good indication of the speed of convergence of the TLMS algorithm. Results were verified by running Monte Carlo type simulations utilizing all of the different TLMS methods. The simulation and theoretical results matched very well. From those two methods it was determined that in general the uniform subband decomposition of the wavelet TLMS algorithm gave the best results except for the few well known cases that are known to be optimal with other transforms such as the DCT with Markov inputs. In those few cases the wavelet TLMS still produced results that are close to the optimal methods.; Next the wavelet based AIC was implemented and researched. Many simulations were run using different plant models that are minimum and nonminimum phase, as well as different wavelet TLMS schemes, reference models, and colored stationary and nonstationary input signals. Comparisons are made here again between the different methods as well as to the non-transform AIC. Results showed better convergence speeds and stability bounds of the wavelet based AIC than others.; Finally, a disturbance canceling algorithm which is based on the AIC was also integrated with the wavelet TLMS and those results where very encouraging as well.