Adaptive Control For A Class Of Non-Affine Nonlinear Systems Via Neural Networks

Recently, the problems of controlling and designing complicated nonlinear systems have attracted the attention of many control researchers. Many had obtained significant achievements as feedback linearization, adaptive refutations, neural networks, fuzzy logical control. But most of the results are only for affine nonlinear systems, the results of non-affine nonlinear systems are relatively few. Many actual systems are not described by affine systems as chemical systems, aero craft control systems. The ripe designing methods of affine systems are not simply popularized to non-affine nonlinear systems. Obviously, the control of non-affine nonlinear systems is not form a systemized method.Therefore, based on the previous research results, utilized the specific character of this class of systems, this paper presents a neural network (NN based)adaptive control method for a general class of non-affine nonlinear systems, which are implicit function with respect to control input. The control algorithm is based on implicit function theorem, inverse function theorem and the design idea of pseudo-control. In this paper, the result we propose could be used by the affine nonlinear systems, so that we find a common method to solve this sort of problems.Firstly, remolding the literatures have been published, for a class of non-affine nonlinear systems, according to its implied differential equation designs a set of single hidden layer neural network-based adaptive control scheme, deducing the expression of controller. In order to let the system run smoothly and let the signals in the system tend to be smooth, the hyperbolic tangent function, instead of sign function, is adopted in design of the robust control terms. Later, based on the neural networks control algorithm, adding H~∞optimal control algorithm, design the adaptive law of the system, analyze the stability and the convergence of the system. The effectiveness of the proposed control scheme is illustrated through simulation.Finally, the controlled plants are extended to large-scale decentralized non-affine nonlinear systems which are based on pseudo-control technique. Design a neural networks-based adaptive control scheme with the assumption that the interconnections between subsystems in entire system are bounded linearly by the norms of the tracking filtered error. In every subsystem, a neural network is adopted which is used to approximate unknown function. The scheme proposed could be utilized by the control of large-scale non-affine nonlinear systems as the automatic highway of adjusting automobiles'vacant position and some chemical reactions process, etc.