By Wilson J. Rugh
Linear method thought, moment Edition, outlines the fundamental thought of linear platforms in a unified, obtainable, and cautious demeanour, with parallel, self sustaining remedy of continuous-time and discrete-time linear platforms.
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Extra info for Linear system theory
In the adaptive linear approach the parameter estimation routine attempted to track parameter changes as a function of the changing operation point. This is only feasible if the operating point changes slowly. Even then, tracking the changing model parameters is inefficient. If computer memory is not expensive, it would be more efficient to store the model information as a function of the operating point and recall the model information as needed when the operating point changes. This is a motivation for adaptive approximation-based methods.
Parameter estimation can be designed for either a fixed batch of training data or for data that arrives incrementally at each control system sampling instant. The latter situation is typical for control applications; however, the batch situation is the focus for much of the traditional function approximation literature. In addition, much of the literature on function approximation is devoted to applications where the distribution of the training data in V can be specified by the designer. Since a control system is completing a task during the function approximation process, the distribution of training data usually cannot be specified by the control system designer.
Thediscussionofthefollowingtwosections will focus on the over and under constrained cases where 11. I/ denotes the p = 2 (Euclidean) norm. Solutions for other p norms are discussed, for example, in the references [54,309]. 1 Over-constrained Solution Consider the approximator structure of eqn. 6), which can be represented in matrix form as in eqn. 8). When N < m the problem is over-specified (more constraints than degrees of freedom). In this case, the matrix @ defined relative to eqn. 8) is not square and its inverse does not exist.