Identification of Continuous-Time Systems with Time Delays by Global Optimization Algorithms and Ant Colony Optimization

Abstract

There are systems which have inherent time delay. If the time delay used for controller design does not coincide with the real process time delay, than a close-loop system can be unstable, or may cause efficiency lost (Bjorklund & Ljung, 2003; Boukas, 2003; Li & Wan, 2002). The identification of linear systems with unknown time delay is important and should be treated as first task during system analysis and control design. This problem can become more complicated for the multi-input single-output (MISO) system, where the solution space is multi-modal. The most of conventional system identification techniques, such as those based on the nonlinear estimations method, for example separable nonlinear least squares (SEPNLS) method, are in essence gradient-guided local search methods. They require a smooth search space or a differentiable performance index. The conventional approaches in the multi-modal optimisation can easily fail in obtaining the global optimum and may be stopped at a local optimum (Chen & Hung, 2001; Harada et al., 2003). One of the possible solution of this problem is use of a SEPNLS methods with global optimisation elements (Chen & Wang, 2004), for example Global SEPNLS (GSEPNLS), known from the literature (Previdi & Lovera, 2004). New possibility in identification of systems with multi modal solution space is opened by application of the computational intelligence methods (Paplinski, 2004; Path & Savkin, 2002; Shaltaf, 2004; Yang et al., 1997). Ant Colony Optimization (ACO) is one among them. Ants are known as a social insects. They exhibit adaptive and flexible collective behavior to achieve various tasks. The macro-scale complex behavior emerges as a result of cooperation in micro-scale. This paper considers the problem of parameter estimation for continuous-time systems with unknown time delays from sampled input-output data. The iterative separable nonlinear least-squares (SEPNLS) method and global separable nonlinear least-squares (GSNLS) method (Westwick & Kearney, 2001) are presented. We have extended this method by using the ACO. The ACO proposed in the paper is looking for the time delays. Another parameters of linear system are obtained during evaluation of leaving pheromone, by using the SEPNLS method.