Discrete modeling of uncertain continuous systems having an interval structure using genetic algorithms

In this paper, an evolutionary approach is proposed to obtain the discrete-time transfer function for uncertain continuous-time systems having interval uncertainties. Based on a worst-case analysis, the problem to derive the discrete-time model is first formulated as multiple mono-objective optimization problems for coefficients in the discrete model, and subsequently minimized and maximized via a proposed genetic algorithm to obtain the lower and upper bounds of the coefficient functions. The problem of non-linearly coupled coefficients with exponential nature occurred in the exact discrete-time transfer function is therefore circumvented while preserving the interval structure in the resulting discrete model by using this approach. Because of the time-consuming process that genetic algorithms generally exhibit, particularly the problem nature which requires undertaking a large number of evolution processes, parallel computation for the proposed evolutionary approach in a MATLAB-based working environment is therefore proposed to accelerate the derivation process.