Energy-based methods for stabilization of controlled lagrangian systems

Abstract

In this final chapter we briefly discuss two recent energy-based methods for stabilizing second-order nonlinear systems and their application to nonholonomic systems. The first is the method of controlled Lagrangians (or Hamiltonians) and “matching.” This is developing into a rather large subject, which we just touch on here in order to explain something of the role of connections in the subject and its potential applications to nonholonomic systems. The second is a geometric approach to averaging second-order systems that arise as models of controlled superarticulated (or underactuated) mechanical (Lagrangian) systems. While not yet constituting a complete theory, the results of this chapter may be thought of as intrinsically second-order versions of the results on kinematically nonholonomic systems presented in Chapters 4 and 6 Needless to say, this chapter just touches on the vast subject of energy-based stabilization.