Diagnosing chaos in non-linear dynamical systems by trajectory predictionsand innovation tests of the Kalman filter

We report the use of the Kalman filter to detect the onset of chaos in a no n-linear system for which the model is exactly known. The procedure is base d on predicting the trajectories of a non-linear dynamical system and testi ng the innovation sequence for the predicted trajectory using the local ove rall method tests (LOMT). This is applied to the Rossler-Wegmann model of t he Zhabotinskii reaction system. The Rossler-Wegmann model is a three dimen sional set of non-linear ordinary differential equations, the solution to w hich gives the time-evolution of the concentrations of the major species in the Zhabotinskii reaction. With suitable parameters and starting values of concentrations, stable, oscillatory and chaotic solutions may be found. Fi ve thousand points were generated from the model, for each of the three spe cies in the model, by fourth order Runge-Kutta integration. For a complex o scillatory case the LOMT showed no chaos, and when parameters that lead to chaos were used the LOMT quickly revealed the mismatch between predicted an d actual trajectories. It is concluded that the Kalman filter with LOMT is a quick and accurate method of diagnosing chaos, which could be used in a m onitoring and on-line controlling system for a chemical process. (C) 1999 E lsevier Science B.V. All rights reserved.