| In practical engineering applications,due to factors such as working condition change,device aging,sensor measurement delay,etc.,there are often many uncertainties in the system,resulting in unknown control direction,unknown disturbance,actuator failure and other problems.These problems have a wide range of application backgrounds.For example,in ship course control,aircraft attitude control,chemical reactor process control,robot formation control and other problems,due to environmental changes,actuator lag and other factors,there are problems of parameter perturbation and parameter uncertainty in the system model,and thus the control direction of the system can not be determined.This paper takes the problem of unknown control direction as the main entry point,comprehensively considers the uncertainty and time delay problems existing in the above systems,and uses the improved Nussbaum gain technology,adaptive technology,and dynamic gain technology to design control schemes to solve specific nonlinear system control problems.The main research content of the paper is as follows:(1)Firstly,the development process of Nussbaum technology was reviewed and summarized;Secondly,the similarities and differences in the limitations and applicability of Nussbaum lemmas were analyzed,and the conclusions obtained from the analysis were verified through numerical simulation;Finally,through longitudinal and transverse comparison and analysis,the existing problems and future research directions in this field were identified.(2)The problem of fault-tolerant control for a class of strict-feedback nonlinear systems with multiple actuators and unknown control directions is studied.Firstly,we propose a key theorem that indicates that Type-B Nussbaum functions can handle multiple time-varying unknown control coefficients under certain conditions.Then,based on this theorem and adaptive control technology,a new control scheme was proposed to handle unknown control directions and actuator faults.Theoretical analysis shows that the designed control scheme can achieve the predetermined control objectives.Finally,in order to verify the effectiveness of the control scheme,a class of numerical systems and a class of robotic systems are considered respectively for simulation verification.The results shows that the signals of the closed-loop system are bounded and the tracking error converges to zero asymptotically.(3)For a class of nonlinear time-delay systems with multiple actuators and unknown control directions,the asymptotic stability control problem is studied.Firstly,the dynamic gain technique is introduced to relax the assumptions of nonlinear functions;Secondly,the suitable Lyapunov-Krasovskii functional is introduced to handle the delay term;Then,the key theorem proposed in this article is used to handle multiple unknown control coefficients.Theoretical analysis shows that compared to existing results,this paper does not require the condition that the symbols of unknown control directions remain consistent.The designed control scheme can ensure that all signals in the system are bounded and the system state converges to zero asymptotically.Finally,the effectiveness of the proposed control scheme was verified through simulation examples. |
