Identification of Continuous-Time Systems with Multiple Unknown Time Delays from Sampled Data

The purpose of this work is to identify a multiple-input single-output (MISO) continuous time (CT) system with various unknown time delays using sampled data. A novel technique for simultaneously estimating system parameters and various time delays may be developed using a gradient algorithm. Indeed, we propose a new formulation of the identification problem which permits defining the generalized vector containing the time delays and the dynamic parameters. The gradient optimization algorithm with exact derivatives of the objective function with respect to the adjustable parameters has been suggested as an alternative for solving this optimization problem. The identification method can be easily implemented by a filtering procedure to generate the input/output time derivatives. In this sense, the proposed method, which is based on a state variable filter, intrinsically allows data filtering and thus simplifies the use of the method in a practical case. An analysis is then presented which proves the convergence of the algorithm, and robustness issues are discussed as well. Finally, the suggested technique is evaluated on simulated instances to ensure its validity and performance.