Bond-Graph-Based Computational Approach to Hybrid System Dynamics

Abstract

For a class of hybrid systems frequently encountered in the engineering practice, the dynamics corresponding to each causal bond graph topology can be expressed in terms of a continuous semigroup of linear operators. Consequently any sequence of modes yields a composite map that allows deriving a closed form expression for arbitrary state space trajectories. This expression is particularized for the dynamics in the vicinity of the steady state. Some key points that are unanimously accepted by engineers, but do not have yet a mathematically rigorous support, are addressed on the basis of a conjecture. All the theoretical results are envisaging the development of computational tools for exploring both general and steady state dynamics. An example gives a brief overview of the applicability to the quantitative analysis of a physical system behavior, using standard software environments for scientific computation.