50,832 research outputs found
Quasi-optimal robust stabilization of control systems
In this paper, we investigate the problem of semi-global minimal time robust
stabilization of analytic control systems with controls entering linearly, by
means of a hybrid state feedback law. It is shown that, in the absence of
minimal time singular trajectories, the solutions of the closed-loop system
converge to the origin in quasi minimal time (for a given bound on the
controller) with a robustness property with respect to small measurement noise,
external disturbances and actuator noise
Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering
In this paper, we study the minimum time planar tilting maneuver of a
spacecraft, from the theoretical as well as from the numerical point of view,
with a particular focus on the chattering phenomenon. We prove that there exist
optimal chattering arcs when a singular junction occurs. Our study is based on
the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F.
Borisov. We give sufficient conditions on the initial values under which the
optimal solutions do not contain any singular arc, and are bang-bang with a
finite number of switchings. Moreover, we implement sub-optimal strategies by
replacing the chattering control with a fixed number of piecewise constant
controls. Numerical simulations illustrate our results.Comment: 43 pages, 18 figure
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