Neural-Networks-Based Adaptive Control For High-Order Systems

A nonlinear system,which input powers are positive odd integers and are larger than one,is usually called a high-order nonlinear system.Compared to the traditional nonlinear systems,especially strict-feedback nonlinear systems,due to the existence of the higher input power,which is larger than 1,additional items will be generated in the process of the stability analy sis of the closed-loop system.Classic control technologies and methods are too difficult to deal with the additional items,so the stability control of high-order nonlinear systems is more challenging.Furthermore,if the powers of the system input are unknown,the stability control of such systems becomes more difficult.In recent years,although many experts and scholars have studied high-order nonlinear systems with uncertainty,relevant research is not sufficient yet,especially for the systems with unknown input powers.Hence,further research is needed.In this paper,stability control problems are studied for uncertain high-order nonlinear systems,and the corresponding control schemes are proposed.The details are as follows:Firstly,the stability of a class of high order nonlinear systems with unknown control direction is studied and two new control strategies are designed to achieve global stability of the system respectively.Compared with the existing results,the proposed control strategies not only cancel the assumption that the control direction is known,but also remove the assumption that the system input power is known.Combined with Nussbaum gain method and adaptive control technology,corresponding controllers were designed respectively for the two cases and the stability and effectiveness of the closed-loop system were proven based on Lyapunov stability theory.Finally,the validity of the proposed methods are verified by two examples.Secondly,the tracking problem of a class of uncertain nonlinear high-order systems is studied and a new adaptive tracking feedback controller is designed to achieve the tracking control goal.Compared with the control strategies in the existing literatures,the proposed control strategy does not require the assumption that the upper and lower bounds of the system input powers are known.Based on Lyapunov stability theory,the stability and effectiveness of the closed-loop system are analyzed,and the boundedness and the convergence are proved.Further,it is proven that the tracking error converges a neighborhood of the origin.Simulation results verify the effectiveness of the proposed controller.Finally,the distributed control design is studied for a class of high order nonlinear leaderfollower systems.Each follower in the system not only has unknown higher input powers,but is subject to unmodeled dynamics.An adaptive distributed control strategy is proposed to make each follower asymptotically synchronize to the leader,and the synchronization errors meet the preset performance.Finally,simulation results verify the effectiveness of the proposed control strategy.