Robust Identification of Dynamic Systems

Abstract

<p>The problem of identification (estimation of system parameters and characteristics) is considered. The aspect emphasized is the robustness in identification. By saying robustness, two points are meant. One is the robustness with respect to bad pieces of data and the other is the numerical robustness with respect to truncation and round-off errors in computation.</p> <p>A thorough study has been made on the robust statistical principles and their applicability in system identification is critically evaluated. Off-line and on-line identification algorithms are proposed, which are resilient to undetectable spurious errors in the data and at the same time computationally simple and efficient. The convergence of these algorithms is theoretically established. Besides, a robust recursive algorithms is also proposed which jointly estimates the states and parameters of a linear system in a bootstrap manner. This algorithm is also proven to be converging with probability one. In addition to this, a very general method is developed for evaluating the asymptotic efficiency of robust identification methods. The superiority of the proposed approaches in contrast with the conventional identification methods (least squares and its genaralizations) is illustrated with the help of several simulated as well as real-life examples.</p> <p>The numerical instability caused by improper choice of sampling rates is also subjected to considerable study in the context of identification of continuous-time systems from samples of input-output data. Methods are suggested to overcome this problem. Also, numerically robust schemes are introduced for transforming discrete-time models to their continuous-time equivalents and their performance is compared with other existing methods.</p>