Exponential Stabilization of Relative Equilibria for Mechanical Systems with Symmetries
نویسنده
چکیده
This paper proposes a systematic procedure for the exponential stabilization of relative equilibria of mechanical systems. The emphasis is on 1 dimensional symmetries. A key design idea is to distinguish between horizontal forces, which preserve the momentum, and vertical forces that affect it. A proportional, derivative control in the horizontal directions and a first order regulator in the vertical direction lead to exponential stability of the closed loop provided some assumptions hold. In particular, two necessary conditions are that the relative equilibrium be Lyapunov stable and that the system satisfy a certain linear controllability test. Relevant applications to autonomous vehicle control are described.
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