Page 803 - Mechanical Engineers' Handbook (Volume 2)

794 Neural Networks in Feedback Control Systems

Figure 2 Two-layer NN.

loop feedback control applications. If the first-layer weights V are fixed, then the NN is
linear in the adjustable parameters W (LIP). It has been shown that, if the first-layer weights
V are suitably fixed, then the approximation property can be satisfied by selecting only the
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output weights W for good approximation. For this to occur, (V x) must provide a basis.
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It is not always straightforward to pick a basis (V x). It has been shown that the cerebellar
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model articulation controller (CMAC), radial basis function (RBF), fuzzy logic, and other
structured NN approaches allow one to choose a basis by suitably partitioning the compact
set S. However, this can be tedious. If one selects the activation functions suitably (e.g., as
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sigmoids), then it was shown in Ref. 7 that (V x) is almost always a basis if is selected
randomly.
2.2 NN Control Topologies
Feedback control involves the measurement of output signals from a dynamical system or
plant and the use of the difference between the measured values and certain prescribed
desired values to compute system inputs that cause the measured values to follow, or track,
the desired values. In feedback control design it is crucial to guarantee by rigorous means
both the tracking performance and the internal stability or boundedness of all variables.
Failure to do so can cause serious problems in the closed-loop system, including instability
and unboundedness of signals that can result in system failure or destruction.
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The use of NNs in control systems was first proposed by Werbos and Narendra and
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Parthasarathy. NN control has had two major thrusts: approximate dynamic programming,