In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...
In this paper, we consider general nonlinear systems with observations,
containing a (single) unknown function . We study the possibility to
learn about this unknown function the observations: if it is possible to
determine the [values of the] unknown function from any experiment [on the set
of states visited during the experiment], and for any arbitrary input
function, on any time interval, we say that the system is “identifiable”.
For systems without controls, we give a more or less complete...
In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic case, we study some non-generic generalizations in the analytic case.
This paper is devoted to the general problem of reconstructing the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular classes...
In this paper, we study the for
generic sub-Riemannian metrics of co-rank one. We give explicit
expressions for the metric complexity (in the sense of Jean
[CITE]), in terms of the elementary invariants of
the problem. We construct asymptotic optimal syntheses. It turns out
that among the results we show, the most complicated case is the
3-dimensional. Besides the generic
case, we study some
non-generic generalizations in the analytic case.
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