In proceedings IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Princeton, March 2000.
An energy-based Lyapunov function for physical systems
Marwan U. Bikdash and Richard A. Layton

A new expression of the first law of thermodynamics is obtained for nonholonomic lumped-parameter systems. The input power due to the constraints is expressed in the framework of Lagrangian differential-algebraic equations using Lagrange multipliers. General procedures to prove the stability of autonomous systems and to design control laws for them using the method of Lyapunov are then outlined and discussed. The approach is based on (a) postulating a Lyapunov function candidate consisting of the total energy stored in the system (expressed in terms of momenta not flows) augmented by a simple positive definite function of the displacements, (b) computing its time-derivative using the first law of thermodynamics, and (c) designing control laws as to make the time-rate of the candidate function negative definite. The procedure is applicable to systems where the control actuation appears through effort sources (such as voltage sources and applied forces), or flow sources (such as current or velocity sources).

©2000 International Federation of Automatic Control

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Richard A. Layton
Last modified: 29 Jun 02