Set Membership Estimation Theory Method And Its Application

The thesis aims to study the set-membership estimation theory. The issues of parameter set identification, state bounding estimation and learning algorithm of neural network are discussed in details based on the framework of unknown but bounded noise system. It includes the following research works.In least-square method with noise bounds, the relationship between outer bounding ellipsoid set and least-square algorithm is analyzed and interpreted. Further, a novel solution to the general set-membership identification called bounding ellipsoidal self-adaptive constrained least-square algorithm is presented based on summarizing the optimal bounding ellipsoid algorithms in existence. The proposed approach updates the estimates selectively depending on whether the observed data contain sufficient new information and can ensure that the worst-case estimation error is bounded and non-increasing. Theory analysis and simulation results indicate that the final convergent region provided by this algorithm is relatively small with sparse updates.In linear system state bounding estimation with ellipsoidal set description of uncertainty, a recursive state bounding estimation algorithm using ellipsoidal sets to describe the state uncertainties and to bound the process and observation noises is proposed. The algorithm optimizes stage of time updating according to the minimum-volume and minimum-trace bounding ellipsoid and measurement updating according to minimum-radius bounding ellipsoid. Simulation results and performance comparisons with traditional set-membership algorithm and Kalman filter show its usefulness. Furthermore, We extend the algorithm to parameter set estimation of time-varying system. It is shown that the algorithm is guaranteed to contain the true parameter in the parameter set.In nonlinear system state bounding estimation, an extended optimal bounding ellipsoid (EOBE) state estimation algorithm is presented. As in the EKF, the EOBE linearizes the state equations about the current state estimation. Unlike the EKF, the EOBE does not neglect the linearization errors. Rather, the linearization errors are considered as part of bounded noise. Theory analysis shows that the state estimationerror is bounded and non-divergent in the case of sufficiently small initial estimation error and noise terms. The algorithm not only reduces the computation, but also enhances the accuracy.We take into account the learning algorithm of neural network based on the above research work. A multilayered neural network is a nonlinear system having a layered structure, and its learning algorithm is regarded as parameter estimation for such a nonlinear system. In this paper, a new real-time learning algorithm for a multilayered neural network is derived from the EOBE. It is shown that the use of the EOBE results in better accuracy and fast learning than conventional learning algorithms.