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**Adaptive control of Wiener type nonlinear systems.**
*(English)*
Zbl 0765.93042

Summary: This study is concerned with the problem of adaptive control of a Wiener type nonlinear process. It is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order, with stable inverse followed by a known time delay. The memoryless nonlinarity is one-to-one on a compact set and belongs to one of two classes: (1) piecewise linear with known breakpoints, or (2) smooth function (in which case an approximation is made). It is represented by linear splines. The output signal from the linear part is not available for measurement.

The global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints. Otherwise, there will be a residual tracking error which depends on the nonlinearity approximation error, but the boundedness of all signals can be assured. The proposed scheme is used for adaptive control of the pH-process in a continuous flow reactor.

The global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints. Otherwise, there will be a residual tracking error which depends on the nonlinearity approximation error, but the boundedness of all signals can be assured. The proposed scheme is used for adaptive control of the pH-process in a continuous flow reactor.

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### References:

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