Sampled-Data Control Of Lower-Triangular Nonlinear Systems

The popularity of digital computers in industrial automation systems has made the research of nonlinear sampled-data control systems become a hot topic in the field of control theory.Although the sampled-data control theory has been greatly developed in recent decades,there are still many problems to be further explored in this area.In this dissertation,we focus on the design problem of the sampled-data control systems along the line of the direct design method.Based on the Lyapunov approach,adding a power integrator technique,KL stability estimates of sampled-data nonlinear systems,etc.,several novel sampled-data control schemes are proposed to reproduce performance of a continuous-time system as much as possible for several classes of nonlinear systems with lower-triangular structures.The main contributions of this dissertation are summarized as follows:Firstly,for a class of lower-triangular systems in the p-normal form,a multi-rate digital feed-back control scheme is proposed to achieve global strong stabilization of the sampled-data closed-loop system under some assumptions.In order to obtain better stabilizing perfor-mance,a multi-rate control method is developed to increase actual control inputs on each sampling interval.Unlike the design method based on the approximate discrete-time model,our controller is obtained from the exact discrete-time equivalent model which does not need to be computed completely.The approximate multi-rate digital controllers are proved to be effective in the practical implementation.It is showed that,compared with the emulated control scheme,our controller may provide faster decrease of Lyapunov function for each subsystem.This will lead to allow large sampling periods.Secondly,we investigate the problem of global sampled-data stabilization for a class of high-order nonlinear systems.Based on exact discrete-time equivalent model of the sampled-data system,a novel sampled-data controller with the form of a power series expansion is designed to achieve global asymptotic stability of the closed-loop system under some assumptions.Approximate solutions of the proposed controller are proved to be effective in practical implementation by a theoretical analysis.The results show that,compared with the emulated control scheme,the approximate controllers allow considering larger sampling periods and enlarge the domain of attraction for a given sampling period.The effectiveness of the proposed control algorithm is verified by a numerical simulation example.Thirdly,for a class of low-order lower-triangular nonlinear time-delay systems with the dif-ferent powers of the chained integrators,a novel sampled-data control scheme is presented to recover performance of the continuous-time system,and a discrete-time predictor is de-signed to compensate input delays with integer multiple length of a sampling period.In the design of the controller,an improved recursive design procedure is developed to over-come the drawback of different powers.Compared with the existing methods,the present strategy just need to know the approximate prediction of state variables,and performance of a continuous-time stabilizer can be maintained at the sampling instants.When the sam-pling period is sufficiently small,it is proved that the system is strongly stabilizable by an approximate solution of the proposed controller.Finally,we study the sampled-data control problem for a class of high-order nonlinear sys-tems with time delays in input.A predictor-based multi-rate sampled-data control scheme is proposed to achieve global asymptotic stability of the closed-loop system under some as-sumptions.Compared with the existing methods,the proposed controller can guarantee the stability of the closed-loop system in the case of larger sampling periods,and a computable predictor is provided to compensate arbitrarily long input delays.The approximate solutions of the proposed controller are proved to be effective in the practical implementation.It is shown that the approximate controllers achieve practical stability of the closed-loop system under some conditions.The obtained results are successfully applied to a trajectory tracking problem for a high-order planar system.