A Performance-Adaptive Self-Organizing Control of a Class of Distributed Systems

The multidimensional Kiefer-Wolfowitz stochastic approximation algorithm is proposed for the performance-adaptive self-organizing control of a class of distributed systems. The class of systems considered is that which can be modeled mathematically by the general linear second-order elliptic equation with unknown coefficients and are defined on a fixed and bounded domain ¿. Noisy measurements of the response are assumed available at a finite number of fixed points in ¿. The minimum number of measurement points necessary for recovery of the significant part of the response is determined by application of an n-dimensional extension of the sampling theorem.