On Adaptive Output Feedback Control Of Nonlinear Systems With Input Unmodeled Dynamics

In practical nonlinear control systems, many uncertainty and unmodeled dynamics exist in the controlled objects, such as measurement noise, external disturbances, modeling errors, controller dead-zone and saturation,and input unmodeled dynamics which exist between controller and control system and can not be measured directly, they all can severely degrade the closed-loop system performance. In this paper, based on traditional nonlinear output feedback and state feedback system, we consider two kinds of unmodeled dynamics subsystems, calling them state unmodeled dynamics and input unmodeled dynamics. Also we consider that the nonlinear functions in system state function are unknown, so the systems we study are more general. For the unmeasurement states, we design corresponding observers. Neural networks are used to approximate the unknown nonlinear functions. Based on dynamic surface control technique and by introducing the first order filter in traditional backstepping design, the repeated differentiations of virtual control is avoided and the complexity of controller design is reduced. Also combined with adaptive control, the disturbances induced by input unmodeled dynamics are effectively dealt with. In this paper,as the unmodeled dynamics satisfy certain assumption conditions,several adaptive output feedback tricking control schemes are proposed for some classes of nonlinear systems with input unmodeled dynamics and states dynamic uncertainties. Also the control schemes are used in inverted pendulum control system which is on the small cart. Through theoretical analysis and simulation results, it is shown that all the signals in the closed-loop system are semi-global uniformly ultimately bounded. The main works in this paper are summarized as follows:Firstly, through the construction of the system state observer and based on the approximation capability of neural networks, an adaptive dynamic surface controller design scheme is proposed for a class of output feedback systems with input unmodeled dynamics. By introducing the first order filter in traditional backstepping design, the repeated differentiations of virtual control is avoided, and combined with adaptive control, the disturbances induced by input unmodeled dynamics are effectively dealt with. Through theoretical analysis and simulation results, it is shown that all the signals in the closed-loop system are semi-global uniformly ultimately bounded.Secondly, through the construction of K-filters to estimate the unmeasured states and based on the approximation capability of neural networks, an adaptive output feedback tricking control scheme is proposed for a class of output feedback systems with input unmodeled dynamics and states dynamic uncertainties. By combining dynamic surface control technique and introducing the first order filter in traditional backstepping design, the repeated differentiations of virtual control is avoided, and combined with adaptive control, the disturbances induced by input unmodeled dynamics are effectively dealt with. Through theoretical analysis and simulation results, it is shown that all the signals in the closed-loop system are semi-global uniformly ultimately boundedThirdly, on the basis of the last section work, by designing a high-gain observer to estimate the unmeasured states, an adaptive neural networks tracking control scheme is proposed for a class of state feedback nonlinear systems with input unmodeled dynamics and state unmodeled dynamics. The number of input variables of neural networks used to approximate unknown continuous function generated in stability analysis is obviously reduced by using Young’s inequality, and only one learning parameter needs to be tuned online, and the burdensome computation of the algorithm can be alleviated. This controller design scheme just needs a little of system information. The control system is general, so it can contain a large class of control systems.Through the research in this paper, the design and analysis problems on several classes of nonlinear systems with input unmodeled dynamics and state unmodeled dynamics have been properly solved. Theoretical analysis and numerical simulation experiments of the control schemes demonstrate their effectiveness and practicability.