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Numerically generated path stabilizing controllers: Use of preliminary feedback. (English) Zbl 0859.93021
The aim of this paper is to introduce a hybrid open-loop closed-loop control strategy for path following control problems, using a strategy due to Jankowski et al., but modified by a preliminary feedback.
The authors begin by considering the linear systems of the form: $x'=Ax+Bu, \qquad y=Cx+Du,$ for which they construct a stabilizing control $$u=F(x,\xi(t), \xi'(t),\dots, \xi^{(\nu)}(t))$$, $$\nu$$ being the index of the system, such that $$y(t)$$ converges exponentially to the path $$\xi(t)$$. Such control is called a descriptor predictive control and it gives, in a certain limiting case, the state-feedback control constructed in the context of paper, of the form: $$u(t)= K_\xi x(t)+R_\xi (d/dt)\xi(t)$$. The authors state a necessary and sufficient condition for the closed-loop system $$x'=(A+BK_\xi)x$$ to be stable. The extension to nonlinear systems and some tracking properties are discussed. Finally, two conclusive examples are given.
##### MSC:
 93B52 Feedback control 93D15 Stabilization of systems by feedback
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##### References:
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