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Nonlinear inversion-based output tracking. (English) Zbl 0859.93006
The paper deals with nonlinear control systems of the form $$\dot x= f(x)+g(x)u$$, $$y=h(x)$$. The problem considered in the paper is the stable inversion problem: given a smooth reference output trajectory $$y_d(\cdot)$$, find a control input $$u_d(\cdot)$$ and a state trajectory $$x_d(\cdot)$$ that satisfy the system equation, and such that exact output tracking is achieved and in addition $$u_d(\cdot)$$ and $$x_d(\cdot)$$ should be bounded. For a minimum phase nonlinear system the proposed solution corresponds to standard inversion techniques. In the non-minimum phase case a noncausal $$u_d(\cdot)$$ is computed. With the addition of a stabilizing feedback, asymptotically exact output tracking is achieved. A numerical example illustrates how to obtain a truncation of the noncausal inverse trajectory.

##### MSC:
 93A99 General systems theory 93C10 Nonlinear systems in control theory 93B28 Operator-theoretic methods
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