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Filtering and Control for Wide Bandwidth Noise Driven Systems

机译：宽带噪声驱动系统的滤波与控制

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Much of modern stochastic control theory uses ideal white noise driven models (Ito equations). If the observed data is corrupted by noise, then the noise is usually assumed to be 'white Gaussian'. Typically, if the underlying models are linear, one uses a Kalman-Bucy filter to get an estimate of the state, and then bases the control on this estimate. In practice, the noises are rarely 'white', and the reference signals and the systems are only approximations in some sense to a diffusion. Never-the-less, owing to lack of viable alternatives, one still uses the Kalman-Bucy filter, etc. Then the estimates are not optimal and, indeed, might be quite far from being optimal. Similarly for the corresponding control. (examples are given to illustrate this.) The sense in which the estimates and/or control is useful need to be examined in order to justify the use of the commonly used procedure. The issue is much deeper than mere 'robustness' in the usual sense, since basic questions of interpretation of the results are involved. The paper deals with these questions. For the filtering problem where the signal is a 'near' Gauss-Markov process and the observation noise wide band, it is shown that the usual method is 'nearly optimal' with respect to a class of alternative data processors. This alternative class is rather natural and includes the data processors which one would normally want to use.

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