On-line identification of continuous time-delay systems combining least-squares techniques with a genetic algorithm

This paper proposes a new approach to on-line identification of continuous timedelay systems from sampled input-output data. In order to track the time-varying time-delay and system parameters, the linear recursive least-squares (RLS) method is combined in a bootstrap manner with the genetic algorithm (GA) which has a high potential for global optimization. The time-delay is coded into binary bit strings and searched by the GA, while the system parameters are updated by the RLS method. Since only the time delay is searched by the GA, a small population size for the GA is sufficient and hence it is possible to implement the algorithm on line on the digital computers. Furthermore, this method (GALS method) is hybridized with the sequential nonlinear least-squares method which is effective in local search, to improve the speed of convergence. Simulation results show that both the GALS and the hybrid methods are quite efficient. It is also verified that, since the hybrid method is effective in both global and local optimizations, it has superior tracking performance over the GALS method especially in the case where the system parameters and time delay vary continuously with time.