Jump Conditions for Second-Order Trajectory Sensitivities at Events

Abstract

Trajectory sensitivity analysis has been widely used to analyze the dynamic behaviour of complex systems such as power system. It is common to use first-order sensitivities, which have been fully described for hybrid dynamical system. However, second-order trajectory sensitivities have only been analyzed for continuous systems. This paper derives the jump conditions describing the behaviour of second-order trajectory sensitivities at switching and reset events. This enables second-order sensitivity analysis of general hybrid dynamical systems. The jump conditions are illustrated using a simple power system example and the results are compared with first-order sensitivities. It is shown that incorporating second-order sensitivity increases the accuracy of trajectory approximation.