The problem of dynamic output stabilization is a very general and important problem in control theory. This problem is completely solved in the case where the system under consideration is strongly observable, i.e. observable whatever the control function applied to the system. On the contrary, there is almost no theoretical result in the case where certain “unobservable inputs” do exist. Moreover, this is the “generic” situation. It turns out that the basic kinematic model of a HALE drone (when the only observable quantity is the distance to the target) falls in this bad class of systems. In this paper, we assume that we are given a smooth stabilizing feedback control law (this concept is properly defined in the paper), and we exhaust a class of observer systems that reconstruct asymptotically the full information, in such a way that the fully coupled system “observer-feedback” is (almost) globally asymptotically stable. We provide some simulation results in the case of a slowly moving target.
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