Adaptive Control For Nonlinear Systems With Unknown Control Directions

In last two decades, the nonlinear system control theory is one of the hot topics in automatic control realm. The backstepping technique is a method to investigate the nonlinear control system,in addition, the adaptive backstepping method ensures the tracking error of the unmatched nonlinear system with time-invariant uncertainties convergences to zero asymptotically. Furthermore, when the nonlinear system with unknown control directions, the control problem becomes rather complex, in the case, the Nussbaum-gain technique is an effective way to deal with it. Thus, how to deal with the unknown control direction problem by incorporating the adaptive Backstepping control method and the Nussbaum-gain technique is worth studying.Motivated by the above discussions, this paper mainly includes the following aspects:Firstly, based on the state observer and the Backstepping method, a kind of adaptive output feedback controller is designed for a class of nonlinear systems with unknown control directions and unknown disturbances. The control schemes can guarantee the system is stable and all the closed-loop signals are bounded, especially, all the states converge to zero asymptotically. Finally, a simulation example is given to verify the effectiveness of the proposed controller.Secondly, for a class of nonlinear cascade time-delay systems with unknown control directions, the partial-state feedback asymptotic regulating control scheme is introduced to deal with the uncertainties of system, and the unknown time delays terms are compensated by bouding technique. Then, Nussbaum-type functions are used to deal with the unknown control directions. Lastly, the partial-state feedback controllers are constructed by using the backstepping method. It is proven that the system is stable and its states converge to zero asymptotically by constructing appropriate Lyapunov-Krasovskii functionals, meanwhile, all the closed-loop signals are bounded. Finally, a simulation example is given to illustrate the effectiveness of the proposed controller.Thirdly, for a class of nonlinear cascade systems with unknown control directions, through a linear state transformation, the unknown control coefficients are lumped together. Based on the Backstepping algorithm and the Nussbaum gain functions,the adaptive output-feedback controller is constructed. The controller not only guarantees the stability of the systems but also ensures the systems states converge to the origin and the boundeness of all the closed-loop signals. Lastly, a simulation example is given to show the effectiveness of the proposed controller.