Note: A zipped up postscript version of this paper is also available.

State Space Projection onto Linear DAE Manifolds Using Conservation Principles

Pieter J. Mosterman
Institute of Robotics and System Dynamics
DLR Oberpfaffenhofen
P.O. Box 1116
D-82230 Wessling
Pieter.J.Mosterman@dlr.de

Abstract:

Continuous physical system behavior can be effectively modeled by differential equations, possibly supplemented by a number of algebraic constraints. The time-derivative variables form the system state, and behavior evolves in state space. Algebraic equations define a manifold in state space to which behavior evolution is confined. Efficient algorithms exist to solve the additional constraints on the state variables to give the gradient of behavior along the manifold. However, initial state values may be such that they are not on the manifold, and, therefore, a projection is required before behavior evolution can proceed. The projection may cause discontinuities in state variables values, and, therefore, require impulses on their derivatives. This paper applies physical conservation laws to derive a consistent projection of state variable values onto the manifold of semi-explicit DAE systems with linear constraints. These correspond to a large class of dynamic system models based on physical principles.