Controller Design For A Class Of Unmatched High-Order Nonlinear Systems With Lower Triangular Structure

With the rapid development of industrial automation and science,the structure of control objects is becoming more and more complicated.The control methods of linear systems can not satisfy the design requirements of these complex systems.Therefore,the control problem of nonlinear systems has attracted more and more researchers' attention.Among them,the unmatched nonlinear systems with lower triangular structure are representative systems in the field of nonlinear systems control,which widely exist in various practical projects.The emergence of many problems,such as unmodelled dynamics,uncertain parameters,unmeasurable system state variables and so on,has a serious influence on the stability of the system.At the same time,it will increase the difficulty of the controller design.By recursive design method and based on Lyapunov stability theory,effective control strategies are proposed for unmatched high-order nonlinear systems with lower triangular structure in this paper.Firstly,the research background of unmatched high-order nonlinear systems with lower triangular structure is introduced in this paper.And then some technical methods used in the controller design progress,such as Backstepping recursive design,MT-filters,quantizers and prescribed performance control,are introduced and analyzed.Secondly,the non-smooth state feedback prescribed performance control for a class of p-normal form lower triangular unmatched high-order interconnected nonlinear systems with unmodeled dynamics is studied.We deal with the effects of unmodelled dynamics by using the idea of changing supply function.Considering the asymmetric prescribed performance function,the singularity problem in the process of controller design is avoided by introducing a novel state transformation.By using recursive design method,a non-smooth state feedback prescribed performance controller is designed.It ensures that all signals of the closed-loop system are uniformly ultimately asymptotically stable,and the performance of the system outputs is within the predefined range.The effectiveness of the proposed control strategy is proved by simulation experiments.Finally,for a class of unmatched high-order nonlinear multi-agent systems withunknown parameters,a hysteresis quantizer is designed to reduce jitter caused by the presence of input quantization.For the case that the system states are unmeasured,MT-filter is designed to estimate the unmeasurable state variables in the system.The problem of overestimation is avoided by estimating the norms of unknown parameters.The distributed adaptive output feedback control strategies are proposed by combining the recursive design method with the dynamic surface control technology.It is ensured that all the signals in the system are semi-globally uniformly ultimately bounded.And the effectiveness of the designed controller is verified by a simulation example in MATLAB.