Stochastic adaptive control of multivariable systems with a class of amplitude‐dependent non‐linearities

Abstract

AbstractThis paper presents a novel direct stochastic adaptive control scheme for a non‐linear multivariable system which is given by a cascade connection of a two‐segment piecewise‐linear asymmetric non‐linear matrix followed by a linear multivariable system with a general interactor matrix. An optimal control law for the non‐linear multivariable system is derived from a cost function in which the non‐linear parameter matrix of the discussed model is included. This control law results in the closed‐loop dynamic property of the non‐linear system being the same as that of its linear portion. A switching gain sequence matrix is introduced to overcome parameter estimation problems. The scheme can deal with systems whose linear portions are open‐loop unstable and/or non‐minimum phase processes. The algorithm will ensure that the closed‐loop system is globally stable and convergent.