Robust Adaptive Control For Uncertain Nonlinear Systems With Unknown Unknown Signals

Because of the nonlinear system is widely used in real life, for the study of nonlinear system always is a focus of research in the control theory. In the real application of nonlinear system is often affected by many uncertain factors, such as the model error, dead zone, input saturation,hysteresis and external disturbances and so on. For such nonlinear systems, it is difficult to use accurate mathematical model describing the dynamic behavior of the system. With the development of control theory research, for uncertainty problem of the nonlinear system, many scholars put forward the effective control algorithm. However, most of this control is in the control coefficient of known and uncertain part bounded under the assumption of the design.This paper mainly study the stability problem of unknown nonlinear systems with unknown high-frequency gain and unknown control directions, based on the backstepping method, for the systems with unknown high-frequency gain in the form of output feedback, because of the unavailable states, therefore we introduce the k-filter in the design, by choosing appropriate Nussbaum function as well as the introduction of auxiliary function in the first step to solve the influence of high frequency gain unknown symbol; And for the nonlinear system with unknown control directions, by applying the tunning function to solve the problem of the overparametrization.Considering in the actual engineering application, the part of the system parameters are known or unknown. According to these conditions, In this paper, for the above two robust adaptive control of nonlinear systems, the proposed control algorithm without control coefficient and a priori knowledge of parameter variables, through the online estimation of unknown parameters and auxiliary function to eliminate environmental change and the influence of interference on the controlled object, and clever use the tunning function and Nussbaum function in the control law. The two conclusions are as follows:(1) For a class of nonlinear systems containing unknown high frequency gain, a robust adaptive controller is designed, on the basis of the Backstepping method, base on the Lyapunov theory and the introduction of auxiliary function to eliminate the influence of high frequency gain unknown symbols, so as to prove that all closed-loop signals are bounded.(2) For the unknown nonlinear systems without a prior knowledge of control directions, studied the tracking problem of the system and solve the overparametrization problems of systems.Then using the Lyapunov theory, by designing appropriate adaptive control law, based on the backstepping method, select the appropriate Nussbaum function to make system track the desired trajectory, and the tracking error asymptotically converge to zero; Select the appropriate adjustment function to solve the overparametrization problem, so as to make the system stable.