Adaptive Control for Time-Variant Processes

This paper establishes conditions of global stability for adaptive predictive control systems (APCS), when applied to a general class of multivariable, stochastic, time-variant, stable-inverse processes with time delays. These conditions rely on assumed convergence properties of the APCS estimation scheme. Therefore, the design of stable APCS, or the research of APCS stability proofs, for time-variant processes proceeds, under this perspective, with the design and analysis of estimation schemes which may satisfy the required convergence properties. Using this approach, an asymptotically stable APCS is derived for a class of time-variant processes with a finite number of bounded changes in their parameter values and a perturbation vector with a finite l² norm. The methodology used to derive the convergent estimation scheme has a general scope and is conceptually simple.