Two Types Of Adaptive Dynamic Surface Control Of Uncertain Nonlinear Systems

Tracking control problem of uncertain nonlinear system is an important issue, more andmore scholars pay attention to it. In the process of controller design, we usually use adaptivebackstepping technique. However backstepping algorithm needs to differentiate repeatlly virtualcontrollers, it has the disadvantage of “differential explosion". The emergence of dynamic sufacecontrol overcomes this disadvantage and reduces the complexity of design. Based on dynamicsurface control method, the paper studies two classes of uncertain nonlinear systems.The main conclusions are as follows:(Ⅰ) Global practical tracking by state feedback for a class of uncertain nonlinearsystems with unknown control gain and uncertain disturbances.Consider a class of uncertain nonlinear systems with unknown disturbances，for the purposeto improve the system tracking control performance, we use a combination of adaptive dynamicsurface method and the neural network in this paper. Using neural network approximation theuncertainties, eliminate the external disturbance of the system. Then, we design state feedbackcontroller by combining with the adaptive dynamic surface control. On the handling ofparameter estimation, we adopt the estimation of the Euclidean normal square of weight vectors,greatly reducing the estimated the number of parameters. Then, we proved the stability of thewhole closed-loop system and give a simulation example. The simulation results show that thisdesign method can guarantee the stability of the closed-loop system, and makes the trackingerror arbitrarily small.(Ⅱ) Global asymptotic tracking by output feedback for a class of nonlinear systemswith unknown control gains and unmeasured states.Consider a class of nonlinear systems with unknown control gains and unmeasured states,we adopt output feedback control method. First, based on the system, we introduce a high-gainobserver with by a series of high-gain K-filters with one dynamic gain updated online. In theprocess of controller design, we use the dynamic surface control technique, it can overcome thecontrol of explosion in backstepping.we design the virtual controllers step-by-step, and thedesigned tracking controller by output feedback is successfully designed. If the designparameters are suitably chosen, the output feedback controller guarantees all the closed-loopstates to be bounded, and the tracking error to be arbitrarily small after enough long time. Finally, a simulation example is given to illustrate the efficiency of the proposed control method.