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.


93B52 Feedback control
93D15 Stabilization of systems by feedback
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