Stochastic Adaptive Control Using the Robust Least Squares Algorithm
Vojislav Filipoviæ
This paper considers properties of the Astrom-Wittenmark self tuning tracker for MIMO systems described with the ARX model. It is supposed that the stochastic noise has the non-Gaussian distribution (condition always present in practice). The consequence of that fact is a nonlinear transformation of the tracking error in the direct adaptive minimum variance controller. The system under consideration is the minimum phase with different dimensions for input and output vectors. Using the concept of the Kronecker product it is possible to represent unknown parameters in the form of a vector. The tensor calculus is thus avoided. Global stability is proved without any modification of the matrix gain in the recursive algorithm. The paper also discusses the relation of the assumption about the absolutely continuous finite-dimensional distributions and different modifications of a high-frequency gain. The paper presents theoretical results but the adaptive control methodology has already been present for many years in military systems (CH-47 helicopter and X-15 aircraft).
Key words: adaptive control, ARX model, non-Gaussian disturbance, self-tuning tracker, system stability, least squares method.