几类不确定非线性系统的稳定性与控制研究
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摘要
不确定性与非线性广泛存在于实际工程系统中。因此,研究不确定非线性系统的控制问题具有重要的理论和实际意义。本文的工作和研究成果主要体现如下：
1、针对一类具有模型不确定性的非线性系统,提出基于扰动观测器的线性控制策略。该控制策略基本思想为：模型不确定性对系统的影响必定会反映到系统状态轨迹当中,通过构造新颖的线性扰动观测器在线从系统状态信息中分离出模型不确定性的相关信息,进而设计结构简单的线性补偿器对模型不确定性进行实时补偿。该控制策略的结构与算法简单,具有较好的工程意义。理论上也给出闭环系统稳定的充分条件
2、针对一类单输入单输出(Single-input-single-output, SISO)不确定非仿射非线性系统,在状态不完全可测的情况下,提出基于扰动观测器的输出反馈控制策略。该控制策略基本思想为：针对系统的非仿射特性,通过等价变换来简化被控对象模型；基于此,利用可测的状态信息构造新颖的动态线性扰动观测器在线获取模型不确定性的相关信息,进而设计结构简单的线性控制器。相比于已有文献,该控制策略的结构与算法简单,所需条件宽松,具有较好的工程意义。
3、针对一类多输入多输出(Multi-input-multi-output, MIMO)不确定非仿射非线性系统,提出一种基于扰动观测器的控制策略。该控制策略基本思想为：引入一个新的关于多变量的隐函数定理,并利用该定理来证明多变量系统存在理想的控制器；基于此,通过等价变换简化被控对象模型,构造新颖的扰动观测器在线获取模型不确定性的相关信息,进而设计全状态反馈控制器；当系统状态不完全可测时,构造状态观测器对系统不可测的状态进行估计,进而设计输出反馈控制器。该控制策略不仅可以导出简单的控制结构与算法,而且避免了解耦问题,具有较好的工程意义。理论上也给出闭环系统稳定的充分条件。
4、对不确定非线性系统提出一种新颖的自适应神经网络控制策略。该控制策略首先针对一类控制系数为未知函数的SISO仿射非线性系统进行展开,其基本思想为：针对自适应控制对模型不确定性进行估计时可能出现的控制奇异问题,提出通过等价变换将系统模型的仿射项分为二项：一项控制系数为常数,另一项控制系数为未知函数；基于此,构造自适应神经网络控制器对模型不确定性进行补偿,同时使得仿射项中控制系数为未知函数的一项在Lyapuno(?)函数的导数中保持半负定,从而避免了控制奇异问题。接着,将该控制策略推广到具有块三角的MIMO非仿射非线性系统当中,并且能够有效地避免了MIMO非仿射非线性系统的控制奇异问题与解耦问题。
In practice, physical systems under study possess inherent characteristics of uncertainties and nonlinearities. Therefore, it is important theoretical and practical significant to study on the stability and control of uncertain nonlinear systems. The main contributions of this dissertation are as follows:
1. For a class of nonlinear systems with model uncertainties, linear control strategies are proposed based on novel disturbance observers. The basic idea of the proposed strategies is that, since the effects of the model uncertainties must be reflected in the trajectories of the system states once the uncertainties affect the controlled systems, novel linear disturbance observers are constructed to separate the relative information of the model uncertainties from the the state trajectories, and then linear compensators are designed by using the obtained information to compensate the model uncertainties in real-time. The proposed strategies are of great significance in engineering due to their simple control structure and algorithm.
2. For a class of single-input-single-output (SISO) uncertain non-affine nonlinear systems, output feedback control strategies are presented based on novel disturbance observers. The basic idea of the proposed strategies is that, to deal with the non-affine appearance of the control input, equivalent transformation is firstly used to transform the controlled system into an affine form; and then novel linear disturbance observers are built to obtain the estimates of the model uncertainties, and linear compensators are presented by using the obtained estimates to compensate the model uncertainties in real-time. Compared with the literature, the proposed strategies are of great significance in engineering due to their simple control structure and algorithm and their relaxed conditions.
3. For a class of multi-input-multi-output (MIMO) uncertain non-affine nonlinear systems, feedback control strategies are presented based on novel disturbance observers. The basic idea of the proposed strategies is that, a new multivaluable implicit function theorem is firstly proposed to prove that there exists an ideal controller for the considered multivaluable systems; secondly equivalent transformation is used to transform the controlled system into an affine form, and novel disturbance observers are presented to estimate the model uncertainties, and subsequently full-state feedback controller is developed based on the estimations:when only system outputs are available for feedback, then the state observer is designed to estimate the unmeasurable state, and output feedback controller is presented to compensate the model uncertainties in real-time. The proposed strategies are of great significance in engineering since they possess simple control structure and algorithm and avoid the decoupling problem.
4. Novel adaptive neural control strategies are presented for uncertain nonlinear systems. The proposed control strategies are firstly used to sovled a class of SISO affine nonlinear systems with the control coefficients being unknown functions. Control singularity problem possibly exists in the adaptive control when the unknown control coefficients are approximated. To tackle such a problem, the basic idea of the proposed control strategies is that, the control coefficients is firstly divided by equivalent transformation into two iterms:the one iterm that the control coefficients are constants and the other iterm that the control coefficients are unknow functions:based on such a new form, adaptive neural controllers are designed to compensate the model uncertainties, and meanwhile guarantee the iterm that the control coefficients are unknow functions to be non-positive in the derivatives of Lyapunov function candidates, and subsequently avoid the control singularity problem. And then the proposed control strategies are applied to a more general class of MIMO uncertain nonlinear systems in block-triangular form, where all subsystems within these MIMO nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders. The control strategies can avoid the decoupling problem, the possible control singularity problem and the circular control construction problem.
1、针对一类具有模型不确定性的非线性系统,提出基于扰动观测器的线性控制策略。该控制策略基本思想为：模型不确定性对系统的影响必定会反映到系统状态轨迹当中,通过构造新颖的线性扰动观测器在线从系统状态信息中分离出模型不确定性的相关信息,进而设计结构简单的线性补偿器对模型不确定性进行实时补偿。该控制策略的结构与算法简单,具有较好的工程意义。理论上也给出闭环系统稳定的充分条件
2、针对一类单输入单输出(Single-input-single-output, SISO)不确定非仿射非线性系统,在状态不完全可测的情况下,提出基于扰动观测器的输出反馈控制策略。该控制策略基本思想为：针对系统的非仿射特性,通过等价变换来简化被控对象模型；基于此,利用可测的状态信息构造新颖的动态线性扰动观测器在线获取模型不确定性的相关信息,进而设计结构简单的线性控制器。相比于已有文献,该控制策略的结构与算法简单,所需条件宽松,具有较好的工程意义。
3、针对一类多输入多输出(Multi-input-multi-output, MIMO)不确定非仿射非线性系统,提出一种基于扰动观测器的控制策略。该控制策略基本思想为：引入一个新的关于多变量的隐函数定理,并利用该定理来证明多变量系统存在理想的控制器；基于此,通过等价变换简化被控对象模型,构造新颖的扰动观测器在线获取模型不确定性的相关信息,进而设计全状态反馈控制器；当系统状态不完全可测时,构造状态观测器对系统不可测的状态进行估计,进而设计输出反馈控制器。该控制策略不仅可以导出简单的控制结构与算法,而且避免了解耦问题,具有较好的工程意义。理论上也给出闭环系统稳定的充分条件。
4、对不确定非线性系统提出一种新颖的自适应神经网络控制策略。该控制策略首先针对一类控制系数为未知函数的SISO仿射非线性系统进行展开,其基本思想为：针对自适应控制对模型不确定性进行估计时可能出现的控制奇异问题,提出通过等价变换将系统模型的仿射项分为二项：一项控制系数为常数,另一项控制系数为未知函数；基于此,构造自适应神经网络控制器对模型不确定性进行补偿,同时使得仿射项中控制系数为未知函数的一项在Lyapuno(?)函数的导数中保持半负定,从而避免了控制奇异问题。接着,将该控制策略推广到具有块三角的MIMO非仿射非线性系统当中,并且能够有效地避免了MIMO非仿射非线性系统的控制奇异问题与解耦问题。
In practice, physical systems under study possess inherent characteristics of uncertainties and nonlinearities. Therefore, it is important theoretical and practical significant to study on the stability and control of uncertain nonlinear systems. The main contributions of this dissertation are as follows:
1. For a class of nonlinear systems with model uncertainties, linear control strategies are proposed based on novel disturbance observers. The basic idea of the proposed strategies is that, since the effects of the model uncertainties must be reflected in the trajectories of the system states once the uncertainties affect the controlled systems, novel linear disturbance observers are constructed to separate the relative information of the model uncertainties from the the state trajectories, and then linear compensators are designed by using the obtained information to compensate the model uncertainties in real-time. The proposed strategies are of great significance in engineering due to their simple control structure and algorithm.
2. For a class of single-input-single-output (SISO) uncertain non-affine nonlinear systems, output feedback control strategies are presented based on novel disturbance observers. The basic idea of the proposed strategies is that, to deal with the non-affine appearance of the control input, equivalent transformation is firstly used to transform the controlled system into an affine form; and then novel linear disturbance observers are built to obtain the estimates of the model uncertainties, and linear compensators are presented by using the obtained estimates to compensate the model uncertainties in real-time. Compared with the literature, the proposed strategies are of great significance in engineering due to their simple control structure and algorithm and their relaxed conditions.
3. For a class of multi-input-multi-output (MIMO) uncertain non-affine nonlinear systems, feedback control strategies are presented based on novel disturbance observers. The basic idea of the proposed strategies is that, a new multivaluable implicit function theorem is firstly proposed to prove that there exists an ideal controller for the considered multivaluable systems; secondly equivalent transformation is used to transform the controlled system into an affine form, and novel disturbance observers are presented to estimate the model uncertainties, and subsequently full-state feedback controller is developed based on the estimations:when only system outputs are available for feedback, then the state observer is designed to estimate the unmeasurable state, and output feedback controller is presented to compensate the model uncertainties in real-time. The proposed strategies are of great significance in engineering since they possess simple control structure and algorithm and avoid the decoupling problem.
4. Novel adaptive neural control strategies are presented for uncertain nonlinear systems. The proposed control strategies are firstly used to sovled a class of SISO affine nonlinear systems with the control coefficients being unknown functions. Control singularity problem possibly exists in the adaptive control when the unknown control coefficients are approximated. To tackle such a problem, the basic idea of the proposed control strategies is that, the control coefficients is firstly divided by equivalent transformation into two iterms:the one iterm that the control coefficients are constants and the other iterm that the control coefficients are unknow functions:based on such a new form, adaptive neural controllers are designed to compensate the model uncertainties, and meanwhile guarantee the iterm that the control coefficients are unknow functions to be non-positive in the derivatives of Lyapunov function candidates, and subsequently avoid the control singularity problem. And then the proposed control strategies are applied to a more general class of MIMO uncertain nonlinear systems in block-triangular form, where all subsystems within these MIMO nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders. The control strategies can avoid the decoupling problem, the possible control singularity problem and the circular control construction problem.
引文
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