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ASYMPTOTIC STABILITY AND FEEDBACK STABILIZATION

ASYMPTOTIC STABILITY AND FEEDBACK STABILIZATION,R. W. Brockett

ASYMPTOTIC STABILITY AND FEEDBACK STABILIZATION   (Citations: 960)
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We consider the loca1 behavior of control problems described by (* = dx/dr)
Published in 1982.
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    • ...Apart from the fundamental obstruction indicated in Brockett (1983) and Zabczyk (1989) where the nonexistence of continuous state-dependent asymptotic stabilisers was proved, realisation of the control tasks for GNT and nSNT vehicles turns out to be even more problematic...

    Maciej Michałek. Application of the VFO method to set-point control for the N-trailer v...

    • ...According to Brocket’s theorem, a nonholonomic system cannot be stabilized to a goal configuration via continuous and time-invariant state-feedback [1] (i.e., either time-varying and/or discontinuous feedback may provide a solution)...
    • ...Definition 1 [32]: Let F be a collision-free area for an autonomous vehicle and let (xd ,y d) be the goal position in the interior of F .Am apVh : F → [0, 1] is a navigation function if it is smooth on F (at least aC 2 function), has a unique...

    Augie Widyotriatmoet al. Navigation Function-Based Control of Multiple Wheeled Vehicles

    • ...A well-known result by Brockett [28] states that a necessary condition for the existence of a time-invariant (i.e., not explicitly dependent on time) continuous state feedback law, , that makes asymptotically stable, is that the image of the mapping contains some neighbourhood of . A result by Coron and Rosier [29] states that a control system that can be asymptotically stabilized (in the Filippov sense [29]) by a time-invariant ...
    • ...Proof: The result by Brockett [28] states that the mapping must map an arbitrary neighborhood of onto a neighbourhood of . For this to be true, points of the form must be contained in this mapping for some arbitrary because points of this form are contained in every neighbourhood of . However, these points do not exist for the system in (47) because , , and means that ...

    Pål Liljebacket al. Controllability and Stability Analysis of Planar Snake Robot Locomotio...

    • ...The design of the lower level feedback controllers is more difficult for non-holonomic systems such as wheeled robots, because it is well known that they cannot be stabilized from point to point using a static feedback law and hence, a time varying feedback law has to be used to achieve the stabilization [26], [27]...

    Suman Chakravortyet al. Generalized Sampling-Based Motion Planners

    • ...Remark 4. It is a classic result [13] that, if a system such as (II.2) is nonholonomic, there exists no smooth controller that stabilizes y? asymptotically...

    Andrea Censiet al. Bootstrapping bilinear models of robotic sensorimotor cascades

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