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Stability of manoeuvre regulation using arbitrary transverse foliations

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2 Author(s)
R. Hindman ; Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA ; J. Hauser

In previous work (Hauser and Hindman, 1995, and Hindman and Hauser, 1996), we have shown that a trajectory tracking control law could be converted to a manoeuvre regulation control law by using a manoeuvre projection derived from a valid Lyapunov function. The given sufficient condition provided a safe way to construct a manoeuvre regulation control law (providing essentially orbital stability). In this paper, we explore the converse of this problem. The specific question of study is: given a trajectory tracking control law and a manoeuvre projection, can we find a compatible Lyapunov function? We show that this question is equivalent to an (infinite dimensional) convex feasibility problem. Using this result, we develop and implement an algorithm for constructing such a Lyapunov function (if feasible). An example is given that illustrates the nature of the problem, providing key new insights

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American Control Conference, 1999. Proceedings of the 1999  (Volume:6 )

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