Saturation Control Of Lower-triangular Nonlinear Time-delay Systems

Lower-triangular nonlinear systems are widely studied.Many engineering prob-lems can be modelled as such systems,such as chemical reactor system,robot ma-nipulator system,and simple pendulum system and so on.In the modelling process,the phenomena of time delay and input saturation are inevitable,which affect the normal operation of control systems.Especially for nonlinear time-delay systems in lower triangular form,the negative effect of input saturation has not been well solved.Therefore,it is of great significance to study the lower-triangular nonlin-ear time-delay systems with input saturation.However,most of existing results are based on the backstepping method,and the design process is complex.Thus,it is particularly important to find a more concise and effective method to study such sys-tems.With the continuous expansion of industrial scale,it is difficult for a single system to describe some complex characteristics of the actual systems.In this case,multi-agent systems(MAS)have emerged,and its related research has gradually de-veloped.But there are relatively few researches on the lower-triangular nonlinear time-delay MAS with input saturation,which promotes the research of this thesis.In this thesis,the gain control method is used to study the saturation control problem of time-delay single system in lower triangular form,and time-delay MAS in lower triangular form.The main research contents are given as follows:·For the time-delay single system with input saturation and external distur-bances,the state feedback tracking control problem is investigated by using the dynamic gain control method.First,it is assumed that the growth condi-tion of nonlinear terms is related to the continuous function of system output,and an appropriate state transformation is introduced to facilitate the bound-edness analysis of the dynamic gain.Second,a state feedback controller is designed by using the dynamic gain control method and the characteristic of hyperbolic tangent function.Finally,based on the Lyapunov-Krasovskii(L-K)functional theorem,it is proved that all signals of closed-loop system are glob-ally bounded,and the tracking error can converge to a small neighbourhood of the origin by adjusting the design parameters properly.·For the time-delay MAS with input saturation,the state feedback tracking con-trol problem is considered by using the static gain control method.First,it is pointed out that the tracking control problem can be transformed into the boundedness problem of high-dimensional multivariable systems,and an ap-propriate state transformation is used to transform the boundedness problem into the static gain design problem.Second,the hyperbolic tangent function is introduced to eliminate the effect of input saturation.Finally,by the static gain control method,an adaptive state feedback control protocol is designed to realize the global boundedness of closed-loop system,and the tracking errors between leader and followers are analysed with the L-K functional.·For the time-delay MAS with input saturation,the output feedback tracking control problem is studied by using the static gain control method.First,a suitable state transformation is introduced to transform the tracking control problem into the static gain design problem,and a hyperbolic tangent function is utilized to deal with the input saturation.Second,in order to estimate those unmeasurable states in control systems,an observer is constructed.Based on this observer,an adaptive output feedback control protocol is designed.Finally,the L-K functional is constructed to prove the global boundedness of closed-loop system,and the adjustability of tracking errors between leader and followers are further analysed.