Expanding subinterval random search for system identification and control

Abstract
A random search technique defined sequentially over an expanding subinterval has the property of locating the global minimum of a sequence of instantaneous performance measures as well as their sum. Therefore, such a technique is mostly suitable as a search technique to identify a set of unknown system parameters by minimizing a mean-square error type criterion on or equivalently to locate sequentially the optimal control coefficients of a feedback stochastic process with unknown dynamics by minimizing a performance criterion defined over the whole process. Several identification schemes based on this search technique have been developed for unknown nondynamic, nonlinear dynamic, open-loop linear dynamic, and closed-loop linear dynamic stochastic systems, respectively, and are discussed in this paper. The results of the investigation are compared with the results obtained by the author using stochastic approximation schemes. The comparison results are overwhelmingly in favor of the random search algorithm in terms of speed of convergence, globality of the search, etc. The major contribution of the method is that it yields unbiased estimates for dynamic feedback systems which utilize the identification information for state estimation and control, without the use of perturbation inputs required by the stochastic approximation method. The results used for the comparison of the two methods in this paper, have been obtained through simulations of four case studies like the chemical process of the pyrolysis of benzene, the linearized model of the booster stage of a space-vehicle, etc. Therefore, in addition the paper presents a new parameter identification method for feasibility studies which is important for the practicing engineer.

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