Global Adaptive Control Of Nonlinear Time-delay Systems With Triangular Structure

The control problem of nonlinear systems has been a very challenging topic.There is not a unified control theory and method due to the inherently nonlinear property,therefore,the control problem can only be investigated for different types of nonlinear systems.On the other hand,time delay is frequently encountered in practical systems,which brings much more difficulties to system control and design.As a matter of fact,in order to generalize the control schemes for delay-independent systems to time-delay systems,some extra restrictive assumptions are usually required,which results in a lot of conservatism.To reduce the conservatism,it is necessary to introduce some new ideas or improve the existing techniques and methods.Based on the existing theory and methods,this paper will make a further study to reduce conservatism and give some significant generalization,details can be seen as follows:1.For several classes of inherently nonlinear time-delay systems,global adaptive state reg-ulation is achieved by developing several memory less state feedback controllers.First,by improving the existing adaptive recursive design method,a class of lower-triangular systems are handled in the absence of nonlinear growth restrictive conditions and in the presence of more parametric uncertainty.Then,the control problem of a class of upper-triangular systems with higher and lower order growth nonlinearities is solved by integrating dynamic scaling technique and adding a power integrator approach.Finally,the control problem of another class of upper-triangular systems with homogeneous-like growth nonlinearities is addressed by using homogeneous domination control idea.2.For a class of upper-triangular nonlinear time-delay systems with an uncertain output function,one designs a low-gain and input-driven observer and a novel dynamic gain.With the help of Backstepping method and dynamic scaling technique,a memoryless output feedback control law is proposed to achieve global asymptotic regulation of the original system state and the observer state,which guarantees all the closed-loop signals to be bounded.3.For a class of upper-triangular nonlinear systems with uncertain state and input dis-tributed delays,it is transformed into a form consisting of non-delay main part and per-turbed nonlinear term by using the Newton-Leibniz formula.Then,according to Back-stepping method and dynamic scaling technique,a low-gain and input-driven observer and a memoryless output feedback control law are obtained to achieve global asymp-totic regulation of the original system state and the observer state,which simultaneously ensures that all the closed-loop signals are bounded.4.For two classes of uncertain nonlinear time-delay systems in triangular form,without using the Backstepping method,two memoryless global output feedback controllers are designed to achieve global asymptotic regulation of the original system state and the observer state,and guarantee that all the closed-loop signals are bounded.First,by using the method of dynamic low-gain observer and dynamic scaling technique,the control problem of more general upper-triangular systems is considered.Next,in the spirit of universal adaptive idea and dynamic scaling technique,one constructs the reduced-order observer and controller with complex dynamic gains,which solves the output feedback adaptive regulation for more general class of lower-triangular systems.