Adaptive parameter identification and state estimation with partial state information and bounded disturbances (original) (raw)
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International Journal of Robust and Nonlinear Control, 2010
This paper develops an adaptive state estimator design methodology for nonlinear systems with unknown nonlinearities and persistently bounded disturbances. In the proposed estimation scheme, the boundary layer strategy in variable structure techniques is utilized to design a continuous state estimator such that the undesirable chattering phenomenon is avoided; and the adaptive bounding technique is used for online estimation of the unknown bounding parameter. The existence condition of the adaptive estimators is provided in terms of linear matrix inequality (LMI). Since the orthogonal projection of the state estimation error onto the null space of the linear measurement distribution matrix is used in the derivation process, the update law of bounding parameter estimate is represented in terms of the available measurement error. The proposed estimator can ensure that the state estimation error is uniformly ultimately bounded (UUB) with an ultimate bound. Furthermore, using the existing LMI optimization technique, a suboptimal adaptive state estimator can be obtained in the sense of minimizing an upper bound of the peak gains in the ultimate bound. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method. the total state vector can seldom be measured and the number of outputs is much less than the number of states. In addition, the process measurements are often corrupted by experimental error, and the process itself is subject to external disturbance. Without some consideration of these problems in the total control system design, the measurements used for feedback control will often be inadequate for acceptable control system performance. Thus, the state estimation problem has been studied extensively over the past decades. A large number of powerful results on state estimation are available for linear or nonlinear systems, such as the well-known Kalman filtering and H ∞ filtering methods
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The design of unknown-input decoupled observers and filters requires the assumption of an existence condition in the literature. This paper addresses an unknown input filtering problem where the existence condition is not satisfied. Instead of designing a traditional unknown input decoupled filter, a Double-Model Adaptive Estimation approach is extended to solve the unknown input filtering problem. It is proved that the state and the unknown inputs can be estimated and decoupled using the extended Double-Model Adaptive Estimation approach without satisfying the existence condition. Numerical examples are presented in which the performance of the proposed approach is compared to methods from literature.
Adaptive kalman filter for control of systems with unknown disturbances
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A canonical industrial filtering situation is considered whereby state estimates are required for feedback control purposes and parameter estimates are required because of an unknown and varying output disturbance. It is shown that the order of the extended Kalman filter may be reduced considerably by careful modelling. The disturbance is modelled using a modification to a technique proposed by Panuska. This modification allows parameters which can be assumed known to be removed from the state equations. This latter method may also be applied to simplifying the identification algorithms used in self-tuning systems.
State and unknown inputs estimation for a class of nonlinear systems
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Non-Asymptotic State Estimation for a Class of Linear Time-Varying Systems with Unknown Inputs
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In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulating functions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulating functions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.