EQUIVARIANTS OF MECHANICAL CONTROL SYSTEMS

作者：Respondek Witold^*; Ricardo Sandra

来源：SIAM Journal on Control and Optimization, 2013, 51(4): 3027-3055.

DOI：10.1137/11086104X

• equivariants
• mechanical state equivalence
• state equivalence
• structure functions
• geodesic accessibility
• affine connection control systems
• mechanical control systems

In this paper we find a complete set of equivariants of mechanical control systems that satisfy the geodesic accessibility property. These equivariants are structure functions on the configuration manifold and are used to completely characterize the mechanical state equivalence of two mechanical control systems. Further, with the aid of our equivariants, we also characterize the state equivalence of the corresponding control systems, defined on the tangent bundle of the configuration manifolds, under extended point transformations as well as under arbitrary diffeomorphisms of the tangent bundle.

• 出版日期2013