【作者】 李爽；

【导师】 王芳；

【作者基本信息】 燕山大学 ， 数学， 2024， 硕士

【摘要】 目前非线性系统控制问题的研究已受到广泛关注,非线性系统需要考虑物理条件、系统性能及安全等因素,系统的输出/状态/输出误差需要满足约束要求。否则,可能会导致系统性能下降,甚至引发系统的不稳定。输入时延和外界干扰问题给非线性系统控制器的设计带来了一定的挑战。本文针对输出约束/延迟全状态约束/输出误差约束影响下的非线性系统,提出滤波反步控制策略,主要内容如下:首先,针对输入时延和输出约束影响下的非线性系统,提出基于误差补偿机制的反步控制策略。设计正切型非线性状态变换函数解决输出约束问题。采用一阶滤波器解决反步控制的“计算爆炸”问题,设计辅助系统解决输入时延问题。根据Lyapunov理论证明闭环系统的有界稳定性,通过机械臂系统的对比仿真,验证控制策略的有效性。其次,针对延迟全状态约束影响下的非线性系统,提出基于动态事件触发机制的有限时间反步控制策略。考虑系统初值违反约束的情形,设计平移函数,对超出约束的系统初值进行修正,使其在预定时间内返回到约束范围内。为解决全状态约束问题,设计非线性状态变换函数。设计有限时间滤波器解决反步控制的“计算爆炸”问题,并设计误差补偿机制减小滤波误差对控制系统的影响。在此基础上,设计动态事件触发机制,减少控制器的更新次数。通过Lyapunov稳定性理论证明闭环系统的实际有限时间稳定性,通过机械臂系统仿真验证所提控制策略的有效性。最后,针对外界干扰和输出误差约束影响下的非线性系统,提出固定时间滤波反步控制策略。设计预定性能函数解决输出误差约束问题。为解决反步控制的“计算爆炸”问题,设计固定时间滤波器。设计固定时间干扰观测器估计外界干扰,且估计误差在固定时间内收敛到零。通过Lyapunov稳定性理论证明闭环系统在固定时间内有界稳定,通过对比仿真验证控制策略的有效性。更多还原

【Abstract】 At present,the research on the control problem of nonlinear systems has received extensive attention.Nonlinear systems need to consider physical conditions,system performance and safety.The output/state/output error of the system needs to meet certain constraints.Otherwise,it may lead to system performance degradation and even cause system instability.The problems of input delay and external disturbance bring some challenges to the controller design of nonlinear system.In this paper,a filtered backstepping control strategy is proposed for nonlinear systems under the influence of output constraint/deferred full state constraints/output error constraints.The main contents are as follows:Firstly,a backstepping control strategy based on error compensation mechanism is proposed for nonlinear systems with input delay and output constraints.A tangent nonlinear state transformation function is designed to solve the output constraint problem.The firstorder filter is used to solve the“explosion of complexity”problem of backstepping control.An auxiliary system is designed to solve the problem of input delay.According to the Lyapunov theory,the bounded stability of the closed-loop system is proved,and the effectiveness of the control strategy is verified by the comparative simulation of the manipulator system.Secondly,a finite-time backstepping control strategy based on dynamic event-triggered mechanism is proposed for nonlinear systems under the influence of deferred full-state constraints.Considering that the initial value of the system violates the constraint,a shifting function is designed to revise the initial value of the system beyond the constraint so that it returns to the constraint range within a predetermined time.In order to solve the problem of full state constraints,a nonlinear state transformation function is designed.A finite-time filter is designed to solve the“explosion of complexity”problem of backstepping control,and an error compensation mechanism is designed to reduce the influence of filter error on the control system.Based on it,a dynamic event-triggered mechanism is designed to reduce the number of controller updates.The practical finite-time stability of the closed-loop system is proved by Lyapunov stability theory,and the effectiveness of the proposed control strategy is verified by the manipulator system simulation.Finally,a fixed-time filtered backstepping control strategy is proposed for nonlinear systems under the influence of external disturbances and output error constraints.A prescribed performance function is designed to solve the output error constraints problem.In order to solve the "explosion of complexity" problem of backstepping control,a fixed-time filter is designed.A fixed-time disturbance observer is designed to estimate the external disturbance,and the estimation error converges to zero in a fixed time.The Lyapunov stability theory is used to prove that the closed-loop system is bounded stable in a fixed time,and the effectiveness of the control strategy is verified by the compared simulation.更多还原