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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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