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A sufficient condition for local controllability

A sufficient condition for local controllability,Siam Journal on Control and Optimization,H. J. Sussmann

A sufficient condition for local controllability   (Citations: 33)
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    • ...978-1-4244-7746-3/10/$26.00 ©2010 IEEE 2710 if intfR(x0;y0)g6= ?. The accessibility property is weaker than controllability [7] as controllability requires the state to lie in the interior of the reachable set...
    • ...We now study the small time local controllability (STLC) property for the DEP system S. Let us first review some results on STLC from [7]...
    • ...We now study the small time local controllability (STLC) property for the DEP system S. Let us first review some results on STLC from [7]. Theorem 9 ([7]): Consider a control system...

    Harsha Simhaet al. Reachability and controllability of a particle in a dielectrophoretic ...

    • ...As the important basic characters in the theory of modern control system, the controllability and stabilization of nonlinear systems have been investigated extensively over the past three decades, and considerable progress has been made in either analysis or synthesis by introducing some useful methods, including the well-known differential geometric method, see, for example, [4-6]...

    Sun Yiminet al. Globally Asymptotical Controllability of Nonlinear Systems

    • ...However, most of the existing results in the literature on controllability of general nonlinear systems are concerned with local ones only, see, for example, [3]∼[6]...

    Yimin Sunet al. Further Results On Global Controllability of Affine Nonlinear Systems

    • ...1. Introduction. The determination of useful necessary and sufficient conditions for local controllability of nonlinear systems remains an open problem, although significant progress has been made [2, 4, 19, 20, 34, 36]...
    • ...1. Introduction. The determination of useful necessary and sufficient conditions for local controllability of nonlinear systems remains an open problem, although significant progress has been made [2, 4, 19, 20, 34, 36]...
    • ...An initial systematic investigation of the local controllability properties of this class of systems was undertaken by Lewis and Murray [27]...
    • ...We begin in Section 2 with a general discussion of affine connection control systems, giving clear statements of the results of Lewis and Murray [27]...
    • ...We will assume the reader to be familiar with affine differential geometry to the extent that it is used in [27]...
    • ...We shall not devote any space to the physics involved in this representation, but refer to [27] for a few words along these lines...
    • ...2.2. Review of existing results. Let us briefly review the results of [27]...
    • ...The following result of Lewis and Murray [27] is derived from a result of Sussmann [36]...
    • ...Again, we provide a somewhat more thorough statement of the result than is given in [27]...
    • ...We adopt the convention that u0 = 1. We also regard an affine connection control system as a control-affine system in the usual manner by takingf0 to be the geodesic spray for r and f1,...,fm to be the vertical lifts of Y1,...,Ym [27]...
    • ...As shown by Lewis and Murray [27], Newton’s law with the forceF as shown in Figure 5.1 is equivalent to equation (2.1), if the affine connectionr is the Levi-Civita connection associated with g and if the vector fields {Y1,Y2} are chosen as follows:...
    • ...for a curve � on TQ, where Z is the geodesic spray for r and verlift(Ya) 2 ( TTQ) denotes the vertical lift of Ya. This is discussed in Lewis and Murray [27]...
    • ...r. Lewis and Murray [27] show that if we define Y1 and Y2 by...

    Francesco Bulloet al. Low-Order Controllability and Kinematic Reductions for Affine Connecti...

    • ...A sampling of the extensive literature includes the papers [3, 4, 5, 6, 12, 14, 17, 19, 20, 21, 24, 26, 27, 28, 29]...
    • ...The application of these techniques has been quite successful in the development of myriad sucient conditions for local controllability, and, particularly for single-input systems, necessary conditions [24, 27]...
    • ...This series has been presented in the papers [9, 11, 27]...
    • ...In the general development expounded on by Sussmann [27], one studies formal series of dierential operators...
    • ...The computations here are reminiscent of those in the proof of Proposition 6.3 in [27], although the multi-input setting we consider here does necessitate careful consideration when adapting the proof in [27]...
    • ...The computations here are reminiscent of those in the proof of Proposition 6.3 in [27], although the multi-input setting we consider here does necessitate careful consideration when adapting the proof in [27]...
    • ...To analyse the contribution of these terms, we also need the following estimate which is Lemma 4.2 of [27]...

    RON M. HIRSCHORNet al. Geometric local controllability: second-order conditions

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