By Graham C Goodwin
Ideal for complicated undergraduate and graduate periods, this therapy includes components. the 1st part issues deterministic structures, overlaying types, parameter estimation, and adaptive prediction and regulate. the second one half examines stochastic structures, exploring optimum filtering and prediction, parameter estimation, adaptive filtering and prediction, and adaptive keep an eye on. huge appendices supply a precis of proper historical past fabric, making this quantity principally self-contained. Readers will locate that those theories, formulation, and functions are on the topic of numerous fields, together with biotechnology, aerospace engineering, machine sciences, and electric engineering.
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Additional resources for Adaptive filtering prediction and control
However, the reader should bear in mind the general comments made above so as to view these algorithms within their proper perspective. In the next section we introduce a particular class of on-line parameter estimation algorithms which are particularly attractive because of their simplicity. 2 ON-LINE ESTIMATION SCHEMES As we mentioned in the preceding section, on-line estimation schemes produce an updated parameter estimate within the time span between successive samples. Thus it is highly desirable that the algorithm be simple and easy to implement.
Note that we have not-said anything about 8(t)necessarily converging to 8,. In fact, we have not said that 8(t) converges to anything. However, the properties as given above are of great importance since they have been derived under extremely weak assumptions. For example, no restriction has been imposed on the nature of the data [in particular, $(t) need not necessarily be bounded]. Property (i) ensures that 8(t) is never further from 8, than 8(0) is. Property (ii) implies that the modeling error, e(t), when appropriately normalized is square summable.
The obvious criterion to use is one that can measure how well the final objective is achieved. For example, in a control problem, different models could be judged on the basis of how well the controller developed from each model meets the design specifications. The main difficulty associated with this approach is that it may be necessary to implement fully each and every design (developed from its own model) before a decision can be made on what is the best model. Consequently, it is generally more practicable to decide between models on the basis of simpler indirect criteria, such as minimization of mean square one-step-ahead prediction error, minimization of maximum prediction error, and so on.