A state event detecting algorithm for hybrid dynamic systems

摘要

Accurately detecting state events is critical for hybrid dynamic systems. However, it is difficult to locate the exact point of a state event in systems with singularities or systems in which event functions are of multiple roots. Overcoming these difficult situations depends on accurately predicting event functions and a reliable root-finding method. A carefully constructed extrapolation polynomial, which is derived from a variable-step multi-step integration method, is applied to predict values of event functions. Due to not using state values of the next time point, the polynomial can be employed to determine the integration step size by checking potential events in all situations. The extended interval Newton's method is employed to find all roots in a certain time interval, which is determined by the existing integration method. The procedure of the root non-existence test and root finding are combined into one. Simulation results show that the algorithm is effective under several different critical situations. By the algorithm, model singularities are found on time and simulation failures are avoided. The event detecting algorithm can be combined with the existing integration method.