Keywords: Output feedback, nonlinear systems, asymptotic stability, adaptive control, neural networks. Abstract This paper presents a direct adaptive output feedback control design method for uncertain non-affine nonlinear systems, which does not rely on state estimation. The approach is applicable to systems with unknown, but bounded dimensions and with known relative degree. A neural network is employed to approximate and adaptively make ineffective unknown plant nonlinearities. An adaptive control law for the weights in the hidden layer and the output layer of the neural network are also established so that the entire closed-loop system is stable in the sense of Lyapunov. Moreover, the tracking error is guaranteed to be uniformly and asymptotically stable, rather than uniformly ultimately bounded with the aid of an additional adaptive robustifying control part. The proposed control algorithm is relatively strightforward and no restrictive conditions on the design parameters for achieving the systems stability are required. The efficiency of the proposed scheme is shown through the simulation of a non-affine nonlinear system with unmodelled dynamics. 1 Introduction Control system design for complex nonlinear systems has been widely studied in the last decade. Many remarkable results in this area have been reported, including feedback linearization techniques [1, 2] and backstepping design [3] for systems with unmatched uncertainties [4]. Most of these researches are conducted for certain systems in affine form. Several adaptive schemes have been developed in dealing with the problem of parametric uncertainties [5, 6] for affine nonlinear systems. However, there are some practical systems such as chemical reactions [7] in which the input variables cannot be expressed in an affine form. So using classic approaches such as feedback linearisation, the control of such systems may be difficult or impossible. In recent years, several methods based on Neural Networks (NNs) have been presented to control nonlinear systems by removing the unknown nonlinear part of the system [7]-[13]. Most of these approaches have been proposed based upon the state feedback [9, 10] or output feedback [11]-[13]. In particular, because of approximation errors inherent in NNs, when the number of neurons is limited, most of these methods can guarantee only uniformly ultimately bounded (UUB) stability. To remove this obstacle and to compensate the approximation errors, a method has been widely used in which an extra robustifying input part is considered [8, 14]. In this method the gain is computed from the suitable information about an upper bound of the system uncertainties, which is normally unavailable and there is no direct method for obtaining it. Therefore, these methods yield an overestimate resulting from a conservative design. To overcome this problem, an adaptive robustifying control part based on states of system is introduced in [15]. In this approach, the system states should be available or be estimated, and the dimension of system must also be known a priori. In this paper an adaptive robustifying control part which guarantees asymptotic stability of tracking error, is proposed. The overall proposed control law is based on output feedback control methods and estimates of the states are not required. Therefore, the plant dimension is not necessary to be known a priori and for designing the controller only the relative degree of system is required. Since the control law comprises of the stabiliser, adaptive and robustifying parts, the closed-loop system is robust against unmodelled dynamics and asymptotically stabilises the system. In addition, the method is applicable to a class of nonlinear systems with any relative degree. The method is based on strictly positive realness (SPR) condition of the closed-loop error dynamics and the Kalman-Yakobovich’s lemma as well as NN techniques. This paper is organised as follows: Section 2 describes the class of nonlinear systems to be controlled and the problem of the tracking error. The structure and approximation properties of the neural networks are addressed in Section 3. In Section 4, the stability of the closed-loop system is proved. An example which illustrates the effectiveness of the proposed controller is presented in Section 5. Conclusions are given in Section 6. ROBUST ADAPTIVE CONTROL OF NONLINEAR SYSTEMS USING NEURAL NETWORKS S Mohammad-Hoseini * , M Farrokhi *,† and A J Koshkouei †† * Department of Electrical Engineering, Iran University of Science and Technology, Tehran 16846, IRAN † Centre of Excellence for Power System Operation and Automation, Iran University of Science and Technology, Tehran 16846, IRAN E-mails: {sm_hoseini, farrokhi}@iust.ac.ir †† Control Theory and Applications Centre, Coventry University, Coventry, UK