一类不确定非线性系统反馈控制研究

发布时间：2018-03-20 19:51

本文选题：非线性系统　切入点：状态测量漂移　出处：《东南大学》2016年博士论文　论文类型：学位论文

【摘要】：实际系统中存在测量漂移、参数不确定性、时滞及随机干扰等因素,不可避免地对系统的控制性能产生影响。因此,对不确定非线性系统反馈控制问题的研究具有重要的理论和实际意义。本文基于齐次系统理论、Lyapunov稳定性理论和随机系统理论,利用增加幂积分方法、齐次压制方法和动态增益技术,针对一类不确定广义齐次非线性系统,研究其状态反馈、输出反馈以及自适应反馈控制问题。主要工作包括以下几个方面：第一,在确定型系统中,针对系统状态测量函数的指数中含有未知漂移量的情况,研究其鲁棒控制器设计问题。利用单调递减齐次度的概念和改进的增加幂积分方法,通过构造含有未知参数的Lyapunov函数,得到了一个具有单调递减齐次度的反馈控制器。通过求解一个优化问题,给出了未知指数漂移量的约束条件,同时保证了所设计的鲁棒控制器能够镇定该系统。第二,在随机型系统中,研究系统受到时滞、未知参数等不确定因素影响时反馈控制器的设计方法。(1)针对系统非线性函数中存在时滞且增长率未知的情况,研究其通用型输出反馈控制器的设计问题。基于通用控制的思想设计了一个动态输出反馈控制器,其增益随着系统输出和它的估计值之间的误差在线实时更新。最后,利用Lyapunov-Krasovskii泛函和随机Barbalat引理,证明了闭环系统的所有信号依概率强有界,且系统状态几乎必然收敛至原点。(2)针对系统输出增益和非线性函数增长率均未知的情况,构造一个全维齐次观测器来估计未知的系统状态。将增加幂积分方法与自适应控制相结合,设计了一个自适应输出反馈控制器。根据推广的随机Lyapunov稳定性定理,证明了系统状态几乎必然被调节至原点,进一步放宽了随机非线性系统需满足局部Lipschitz条件的限制。(3)针对系统的漂移项和扩散项满足下三角齐次增长条件的情况,研究其依概率有限时间反馈控制问题。基于齐次压制方法,设计了非光滑观测器和输出反馈控制器。进一步研究具有非线性参数化的系统。利用参数分离原则将未知非线性参数从非线性函数中分离出来,同时将增加幂积分方法与自适应技术相结合,构造了一种自适应状态反馈控制器。根据随机有限时间Lyapunov稳定性定理,证明了所提出的反馈控制器使得系统状态在有限时间内几乎必然收敛至原点。(4)针对系统中存在高阶次幂和时变时滞的情况,考虑其全局输出反馈镇定问题,进一步放宽了对系统高阶次幂和系统非线性函数的限制条件。通过选取恰当的Lyapunov-Krasovskii泛函,构造了齐次观测器和控制器。结合齐次压制方法证明了整个闭环系统依概率全局渐近稳定。最后,数值仿真验证了所提控制算法的有效性。
[Abstract]:There are some factors such as measurement drift, parameter uncertainty, time delay and random disturbance in the real system, which inevitably affect the control performance of the system. It is of great theoretical and practical significance to study the feedback control problem of uncertain nonlinear systems. Based on the Lyapunov stability theory and stochastic system theory of homogeneous systems, the method of adding power integral is used in this paper. For a class of uncertain generalized homogeneous nonlinear systems, the state feedback, output feedback and adaptive feedback control problems are studied by homogeneous suppression method and dynamic gain technique. The main work includes the following aspects: first, In the deterministic system, the robust controller design problem is studied for the condition that the exponent of the system state measurement function contains unknown drift quantity. The concept of monotone decreasing homogeneity degree and the improved method of increasing power integral are used. By constructing the Lyapunov function with unknown parameters, a feedback controller with monotone decreasing homogeneous degree is obtained. By solving an optimization problem, the constraint conditions of the unknown exponential drift are given. At the same time, the designed robust controller is guaranteed to stabilize the system. Secondly, in the stochastic system, the system is time-delay. The design method of feedback controller under the influence of uncertain factors such as unknown parameters. (1) aiming at the case where there is time delay and the growth rate is unknown in the nonlinear function of the system, A dynamic output feedback controller is designed based on the idea of universal control. The gain of the controller is updated in real time with the error between the system output and its estimated value. By using the Lyapunov-Krasovskii functional and stochastic Barbalat Lemma, it is proved that all the signals of the closed-loop system are strongly bounded by probability, and the state of the system almost necessarily converges to the origin. A full dimensional homogeneous observer is constructed to estimate the unknown state of the system. An adaptive output feedback controller is designed by combining the method of increasing power integral with adaptive control. According to the generalized stochastic Lyapunov stability theorem, a new adaptive output feedback controller is proposed. It is proved that the state of the system is almost necessarily adjusted to the origin, and the restriction of local Lipschitz condition for stochastic nonlinear systems is further relaxed. For the condition that the drift term and diffusion term of the system satisfy the lower triangular homogeneous growth condition, Based on the homogeneous suppression method, the feedback control problem based on probability finite time is studied. A non-smooth observer and an output feedback controller are designed to further study the nonlinear parameterized system. The unknown nonlinear parameters are separated from the nonlinear function by the principle of parameter separation. At the same time, an adaptive state feedback controller is constructed by combining the method of adding power integral with adaptive technique. According to the stochastic finite time Lyapunov stability theorem, It is proved that the proposed feedback controller makes the state of the system almost bound to converge to the origin in a finite time) in view of the existence of higher order power and time-varying delays in the system, the global output feedback stabilization problem is considered. The restrictions on the nonlinear function of the higher order power sum of the system are further relaxed. By selecting the appropriate Lyapunov-Krasovskii functional, The homogeneous observer and controller are constructed, and the global asymptotic stability of the closed-loop system is proved by the homogeneous suppression method. Finally, the effectiveness of the proposed control algorithm is verified by numerical simulation.
【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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