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Authors
Anton S. Shiriaev; Leonid B. Freidovich; Ian R. Manchester

Digital Object Identifier (DOI)
10.3182/20070829-3-RU-4912.00005

Page Numbers:
32-43

Index Terms
transverse linearization,orbital stabilization,periodic motions,underactuated mechanical systems,virtual holonomic constraints

Abstract
This paper provides an introduction to several problems and techniques related to controlling periodic motions of dynamical systems. In particular, we define and discuss problems of motion planning and orbit planning, analysis methods such as the classical Poincaré first-return map and the transverse linearization, and exponentially orbitally stabilizing control designs. We begin with general nonlinear systems, and then specialize to a class of underactuated mechanical systems for which a particularly rich structure allows many of the problems to be solved analytically. The paper concludes with a discussion of numerical issues related to control design via periodic Riccati equations.

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