Identification For Multirate Multiple-input Systems

Multirate systems abundantly exist in actual areas, such as communication, chemical pro-cess and biomedical systems. Multirate systems have two or more sampling and updating rates.The mathematical description of multirate systems is more complicated than that of conven-tional discrete-time systems. Thus, the identification of multirate systems has been attractedmore and more attention. In this dissertation, based on the multi-innovation identification the-ory, the auxiliary model identification idea, the hierarchical identification principle, the leastsquares identification principle and the gradient search principle, the identification of multi-rate multiple-input systems has been stuied. The numerical examples are given to test thee?ectiveness of the proposed algorithms. The main contributions of this dissertation are asfollows:1. The identification problem of multiple-input multiple-output systems is studied. By meansof the multi-innovation identification theory, introducing an innovation length and ex-panding a single innovation vector into an multi-innovation matrix, the multi-innovationstochastic gradient algorithm is derived. Using the Martingale convergence theorem, theconvergence properties of the multi-innovation stochastic gradient algorithm are analyzed.2. The identification problem of error equation multirate systems is studied. In order toimprove the convergence speed and enhance the estimates accuracy of algorithms, from theviewpoint of multi-innovation, introducing an innovation length and expanding the singlescalar to an multi-innovation vector, the multi-innovation stochastic gradient algorithm isproposed. The convergence properties of the proposed algorithm are analyzed by usingthe Martingale convergence theorem. Since the state-space model of mulrirate systemsobtained by using the discretization technique has a high demension and a large numberof parameters needed to be identified, this case leads to a large conputational load for thealgorithms. For reducing the computational load, by using the hierarchical identificationprinciple, the hierarchical least squares algorithm is presented.3. The identification problem of output error multirate systems is considered. Combiningthe auxiliary model identification idea and the multi-innovation identification theory, themulti-innovation stochastic gradient based auxiliary model algorithm is derived. By usingthe auxiliary model identification idea, the least squres based auxiliary model algorithm ispresented. Using the Martingale convergence theorem, the convergence properties of theleast squres based auxiliary model algorithm are analyzed. 4. The identification problem of multirate systems with sub-models is considered. Based on theauxiliary model iedntification idea, the auxiliary sub-models are set up. The least squaresbased auxiliary sub-models algortihm is proposed. Compared with the least squares basedauxiliary model algortihm, the proposed algorithm has less parameters needed to identifiedand less computational load.5. The identification problem of Box-Jenkins multirate systems is considered. Combining theauxiliary model iedntification idea and the multi-innovation identification theory, the auxil-iary model multi-innovation generalized extended stochastic gradient algorithm is proposed.The auxiliary model multi-innovation generalized extended stochastic gradient algorithmrepeatedly uses the multirate input-ouput data. Thus, compared with the auxiliary modelgeneralized extended stochastic gradient algorithm, it has faster convergence speed andbetter parameter estimates accuaracy. The auxiliary model multi-innovation generalizedextended stochastic gradient algorithm does not compute the covariance matrix. Com-pared with the auxiliary model generalized extended least squares algorithm, it has lesscomputational load.