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Adaptive control of highly uncertain nonlinear dynamic systems has been an important research area in the past decades, and in the meantime neural networks control has found extensive application for a wide variety of areas and has attracted the attention of many control researches due to its strong approximation capability. Many significant results on these topics have been published in the literatures (Lewis et al., 1996 ; Yu & Li 2002; Yesidirek & Lewis 1995). It is proved to be successful that neural networks are used in adaptive control. However, most of these works are applicable for a kind of affine systems which can be linearly parameterized. Little has been found for the design of specific controllers for the nonlinear systems, which are implicit functions with respect to control input. We can find in literatures available there are mainly the results of Calise et al. (Calise & Hovakimyan 2001) and Ge et al. (Ge et al. 1997). Calise et al. removed the affine in control restriction by developing a dynamic inversion based control architecture with linearly parameterized neural networks in the feedback path to compensate for the inversion error introduced by an approximate inverse. However, the proposed scheme does not relate to the properties of the functions, therefore, the special properties are not used in design. Ge, S.S. et al., proposed the control schemes for a class of non-affine dynamic systems, using mean value theorem, separate control signals from controlled plant functions, and apply neural networks to approximate the control signal, therefore, obtain an adaptive control scheme. Furthermore, when controlling large-scale and highly nonlinear systems, the presupposition of centrality is violated due to either due to problems in data gathering when is spread out or due to the lack of accurate mathematical models. To avoid the difficulties, the decentralized control architecture has been tried in controller design. Decentralized control systems often also arise from various complex situations where there exist physical limitations on information exchange among several subsystems for which there is insufficient capability to have a single central controller. Moreover, difficulty and uncertainty in, measuring parameter values within a large-scale system may call for adaptive techniques. Since these restrictions encompass a large group of applications, a variety of decentralized adaptive techniques have been developed (Ioannou 1986).

Adaptive Control for a Class of Non-affine Nonlinear Systems via Neural Networks