Adaptive Neural Control Of Two Kinds Of MIMO Nonlinear Systems

Most practical systems have the characteristics of nonlinearity, coupling, time-varying and time-delay, which is insufficient to explicitly explain the complex dynamics features of nonlinear systems and the controller design is becoming more difficult and challenging. In all, many researches are focus on the SISO nonlinear systems, few in MIMO systems. Meanwhile, the adaptive controller design based on intelligent algorithm has received rapid development. In this paper, we focus on dealing with two specific kinds of MIMO nonlinear systems, and using adaptive controller techniques, neural networks, backstepping method, and dynamic surface technology as the tools to design controllers, and employing the Lyapunov stability theory as a criterion to proof the stability of the closed-loop system. In summary, the main contents of this paper are listed as follows:First, overcoming the coupling among variables is greatly necessary to obtain accurate, rapid and independent control of the real nonlinear systems. In this paper, the main methodology, on which the method is based, are dynamic neural networks(DNN) and adaptive control with the Lyapunov methodology for the time-varying, coupling, uncertain and nonlinear system. Under the framework, the DNN is developed to accommodate the identification, and the weights of DNN are iteratively and adaptively updated through the identification errors. Based on the neural network identifier, the adaptive controller of complex system is designed in the latter. To guarantee the precision and generality of decoupling tracking performance, Lyapunov stability theory is applied to prove the error between the reference inputs and the outputs of unknown nonlinear system is uniformly ultimately bounded(UUB). The simulation results verify that the proposed identification and control strategy can achieve favorable control performance.Second, the adaptive neural network control is presented for a class of multi-input multi-output(MIMO) nonaffine pure-feedback nonlinear systems with unknown time delays and perturbed disturbances. The MIMO systems are composed of n subsystems and each of subsystem is in the lower triangular form. To overcome the design difficulty from the nonaffine structure of pure-feedback system, based on the implicit function theorem and mean value theorem, we are transforming the nonaffine form into the affine appearance of state variables. By combining the use of dynamic surface technique(DSC) and the novel quadratic Lyapunov function, the inherent problem of “explosion of complexity” in the traditional backstepping design and the circular construction of controller in the pure-feedback form is avoided. At the same time, the design difficulties from unknown time-delay functions are overcome using the function separation technique, the Lyapunov-Krasovskii functional, and the desirable property of hyperbolic tangent functions. In addition, the RBF neural networks are used to the virtual control and actual control design. The proposed control scheme can guarantee the semiglobal uniformly ultimate boundedness of solution of the closed-loop system. A simulation experiment is utilized to demonstrate the feasibility of the proposed design approach.