Adaptive Neural Network Control For A Class Of Uncertain Nonlinear Systems

In recent years, controller design, stability analysis and observer design of the uncertain nonlinear system have been studied by many researchers. Especially, the study of adaptive control strategies of the uncertain nonlinear system has been attracted more attention. Function approximation ability of neural network (NN) provides a new way to solve the control problem of nonlinear system. Since the non-smooth nonlinear input often exist in the actual systems, adaptive control for uncertain nonlinear system with non-smooth nonlinear input become more and more important. According to the above, we mainly research the following contents:(1) Compared with the results of most results have been studied with the unknown backlash-type hysteresis, this paper will present a new algorithm to reduce the computational burden for nonlinear system. Adaptive laws are designed based on the estimation of norm on unknown parameter vector, and thus, it can reduce the computational burden. Based on Lyapunov theory, all the signals in the closed-loop system are bounded. An example for hard disk drives with hysteresis friction is given to illustrate the feasibility of the proposed approach.(2) Based on a class of nonlinear signal-input-signal-output (SISO) system with unknown non-symmetric dead-zone input, unknown control gain coefficient and unknown function, an adaptive control method will be proposed by using radial basis function neural network (RBFNN). Finally, by using the Lyapunov approach, all the signals in the close-loop system are proven to be bounded.(3) An adaptive state feedback control for tracking of a class of direct-current (DC) motor system with an unkown dead-zone will be developed. The unknown functions in the DC system are approximated by using RBFNN. An Asymmetric Barrier Lyapunov Function approach is integrated to relax the requirements on the initial conditions. Finally, the system is proved stabled. It is verified the effectiveness of the proposed control by applying it on an actual DC motor system.(4) The adaptive control for a class of uncertain nonlinear discrete-time system with dead-zone will be studied. Firstly, an adaptive NN algorithm is designed for a strict feedback system with unknown functions, external disturbance and unknown discrete-time non-symmetric dead-zone input by using backsteeping method. Secondly, the computational burden of a pure feedback discrete-time system is reduced by using the mean value theorem and assuming that the norm of the optimal parameter vectors is bounded. Finally, simulation results are provided to confirm the effectiveness of the proposed approach.