Control of a Class of Distributed Systems with Noisy Measurements

摘要

The report presents an approach to the on-line control of a class of distributed systems, which can be modeled mathematically by the general second order elliptic equation with unknown coefficients. The domain of definition of the system is finite. The distributed and/or boundary control functions are approximated by a finite set of linearly independent and bounded functions and an unknown set of constant parameters. The control parameters are estimated using stochastic approximation and random optimization algorithms, and minimizing a mean-square error criterion, with noisy measurements of the response being available at a finite number of points in the domain of definition of the system. Sampling theory is used to determine the minimum number of measurement points. The feasibility of the approach is demonstrated by simple examples. Sensitivity analysis is used, by assuming partial knowledge of the form of the response for these examples, in order to increase the sensitivity of the search algorithms, and consequently, accelerate their convergence. An off-line control procedure is also presented for the same class of problems. It consists of identifying the response of the system, in the finite domain, to a number of different distributed and/or boundary control functions. (Author)