Adaptive control and stability analysis of nonlinear systems using neural networks

Wiener-Typed Nonlinear Systems' Output Feedback Control Algorithm Based on Dual-Mode Method

“…Then, if the following three assumptions A1) and A2) are fulfilled, it can be conclude that S and e S are invariant sets of ( ) k x and ( ) k e in the sense of (9) and (10), respectively. A1) (14) is satisfied, in addition, there exists …”

“…In 1997 [9] , Kalafatis and Wang proposed a method identifying the two parts of Wiener model at the same time, but an assumption must be satisfied that the inverse of the nonlinear element can be approximated by P order polynomials with satisfactory precision, which greatly limited its applications. In the same year [14] , Yamanaka et al developed a new kind of dynamic neural network which is composed by a Laguerre function filter and a memoryless nonlinear block. Based on this model they presented a model reference adaptive control scheme for Wiener-typed nonlinear systems.…”

“…Key words -Dual-Mode control algorithm, Wiener-typed nonlinear systems, Zeroin algorithm, invariant set, LMI I. INTRODUCTION uring a lot of real industrial processes such as distillation [9] , pH neutralization control [2,5] , heat-exchanger [16] , chemical reaction [14] , and biological visual process [16,17] , there widely exists a type of nonlinear systems which can be described by Wiener mode. The background of this model can be even extended to the areas of communication [11] , signal processing [11] , psychology [17] and sociology [17] .…”