Guaranteed recursive nonlinear state bounding using interval analysis. (English) Zbl 1006.93067
Summary: The problem considered here is state estimation in the presence of unknown but bounded state perturbations and measurement noise. In this context, most available results are for linear models, and the purpose of the present paper is to deal with the nonlinear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the perturbation and noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first estimator for which this claim can be made. The precision of the set estimate can be improved, at the cost of more computation. Theoretical properties of the estimator are studied, and computer implementation receives special attention. A simple, illustrative example is treated.
MSC:
| 93E10 | Estimation and detection in stochastic control theory |
| 93C55 | Discrete-time control/observation systems |
| 93C10 | Nonlinear systems in control theory |
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