Trajectory sensitivity analysis of hybrid systems

TLDR

The hybrid system model provides the foundation for subsequent trajectory sensitivity analysis. The paper develops trajectory sensitivity analysis for hybrid systems, proposing a differential‑algebraic‑discrete model. The authors derive jump conditions for sensitivities at discrete events, discuss efficient computation, and illustrate the theory with examples. Trajectory sensitivities reveal system behavior insights unattainable by conventional simulation.

Abstract

The development of trajectory sensitivity analysis for hybrid systems, such as power systems, is presented in the paper. A hybrid system model which has a differential-algebraic-discrete (DAD) structure is proposed. This model forms the basis for the subsequent sensitivity analysis. Crucial to the analysis is the development of jump conditions describing the behavior of sensitivities at discrete events, such as switching and state resetting. The efficient computation of sensitivities is discussed. A number of examples are presented to illustrate various aspects of the theory. It is shown that trajectory sensitivities provide insights into system behavior which cannot be obtained from traditional simulation.