不确定非线性系统的输出调节及其应用
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摘要
非线性系统的输出调节问题是控制理论及应用中的重要问题之一，涵盖了系统的镇定、跟踪给定的参考信号和抑制干扰等特殊的控制问题。输出调节的目标是寻找反馈控制器使所得到的闭环系统信号最终一致有界，并且能够渐近跟踪参考输入或抑制干扰。当参考输入和非期望扰动由一类被称为外系统的自治微分方程生成时，该问题也称为伺服问题。
本文在以往工作的基础上，着重讨论了具有不确定性的非线性系统的控制问题。先针对系统状态已知，部分状态未知及状态具有时滞的情况对不确定非线性系统的镇定问题进行研究。然后又进一步研究了不确定系统的输出调节问题，并将输出调节理论应用到微型飞行器的姿态跟踪和干扰抑制问题。文中作了如下工作：
第一，针对输出调节问题的特殊情况，研究了三类不确定非线性系统的镇定问题。先针对一类具有奇次幂的不确定非线性高阶系统，在假设状态已知的情况下，基于有限时间稳定引入加幂积分器并设计能够应对系统具有不确定性的非-Lipschitz连续的状态反馈控制律。然后针对一类状态不可直接测量的纯反馈非线性系统，用模糊逻辑系统去逼近未知非线性函数，利用滤波解决了一般控制器中遇到的代数循环问题，结合广义的高增益观测器和Lyapunov稳定性理论提出了自适应的输出反馈控制器。最后考虑系统状态中具有时滞的情况，在不确定的非线性是高阶的假设条件下，提出了具有时滞的齐次系统的概念和延拓的齐次占优定理，在齐次增长条件下，基于延拓的齐次占优定理和低增益的观测器证明了跟时滞无关的输出反馈控制器的存在性。
第二，针对一类不确定性不能被已知光滑函数界定且具有线性外系统的不确定非线性系统，研究了其输出调节问题。引入动态面控制法避免了“膨胀项”的产生，减少计算量。同时引入具有误差的内模方程，利用外系统信息镇定控制项，提出一种具有动态面控制的光滑的状态反馈控制律。将非光滑分析理论应用到Backstepping设计方法中，避免了所求的虚拟控制一定为光滑函数，结合内模原理给出非光滑的状态反馈的控制律。
第三，针对系统状态不可直接测量的一类具有动态不确定性的不确定非线性系统，研究了由非线性外系统驱动的的输出调节问题。利用动态信号去处理不匹配的动态，利用高增益的状态观测器去估计状态，设计非线性内模，结合模糊逻辑控制和自适应Backstepping设计方法，设计出模糊自适应的输出反馈控制律和自适应律。
第四，针对一类含有时滞非线性不确定系统，研究了具有线性外系统的输出调节问题。在Backstepping设计的框架下，引入Lyapunov-Krasovskii泛函，结合模糊观测器和内模原理去设计自适应的输出反馈控制器。
第五，利用输出调节问题的结论去解决飞行器的姿态跟踪和干扰抑制问题。该问题的复杂性在于受控对象本身包含的不确定性，以及来自外部系统产生的干扰。利用浸入系统设计线性内模，结合自适应控制理论设计了状态反馈自适应控制器以达到处理系统的不确定性和外系统的不确定性的目的。
The problem of nonlinear output regulation is one of the most important issues inthe control theory and its application, which involves nonlinear stabilizaion, tracking ref-erence control and disturbance rejection as special cases. The objective of the output reg-ulation is to design a feedback control law to achieve tracking a class of reference inputand rejecting in the presence of a class of disturbances while maintaining the closed-loopsystem overall signals uniform ultimate boundedness. When the reference input and theexpected disturbances are generated by autonomous diferential equation which is calledthe exosystem, the problem is also called servomechanism problem.
In this thesis, the problems with non-parametric uncertain nonlinear systems areconsidered. Firstly the stabilization problem is investigated for diferent uncertain nonlin-ear systems for example, with known state variables, with partly known state variables orwith time delay. Then output regulation problem is addressed, and the result is applied toa tracking control problem associated with micro spacecraft. The main contributions aresummarized as follows:
1. The stabilization problem of uncertain nonlinear systems is studied as a specialcase of the output regulation problem. First of all, the global stabilization problem foruncertain nonlinear systems with odd integer in lower triangular form is solved, underthe assumption that the state variables are known, with a non-lipschitz continuous statefeedback control designed by using finite-time stability theorem and non-smooth feed-back design. Then an adaptive fuzzy output feedback backstepping control method isdeveloped for a class of nonlinear pure-feedback systems whose state variables are notdirectly available. Fuzzy logic systems are introduced to approximate the unknown non-linear functions. The filtered signals are utilized to solve the algebraic loop problemsencountered in the implementation of the usual controllers. An adaptive fuzzy control isproposed using generized observer and Lyapunove stability theorem. At last the problemof global output feedback stabilization for a glass of upper-triangular nonlinear systemswith time-delay in the state is considered. The delay-independent output feedback con-troller is proved to be exist based on extended homogeneous domination approach andlow gain observer.
2. When the state variables are available for feedback, the output regulation prob-lem for uncertain nonlinear systems driven by linear exosystems is investigated. Theuncertainties are supposed to be bounded by known functions. Firstly a linear internal isdesigned and a dynamic smooth state feedback control is proposed by making use of theinternal model. Then we apply nonsmooth analysis theory to backstepping method foravoiding the restriction that the virtual controls must be smooth functions. We introducethe error internal model and utilize exosystem information to stabilize feedback inputitems. A nonsmooth state feedback control is prosposed to solve the output regulationproblem.
3. The output regulation problem for uncertain nonlinear systems where the statevariables are not always available is addressed. We focus on the nonlinear systems withdynamic uncertaity and nonlinear exosystem. K-filters are designed to estimate the un-measured states.A fuzzy output feedback control is proposed by using linear internal.Using the designed high-gain observer of state estimation, and combining the fuzzy adap-tive control with backstepping approach, an adaptive control fuzzy backstepping controlscheme is obtained for a class of SISO uncertain system with nonlinear exosystem.
4. The output regulation problem with time delay uncertain nonlinear systems driv-en linear exosystem is studied. At the backstepping frame, using appropriate Lyapunov-Krasovskii functional, an adaptive fuzzy output feedback control is developed by com-bining fuzzy observer and internal model.
5. Some results of output regulation problem are applied to solve the problem ofattitude tracking and disturbance rejection. The complexity of the question is in that thesystems contains the uncertain element and the disturbance contained by the exosystem.A linear internal model with parametric uncertainty is designed utilizing the immersiontechnique. By combining adaptive control theory and Lyapunov theory, state feedbackcontrollers to deal with the uncertainty of the systems and the parametric uncertainty ofthe exosystem are designed.
本文在以往工作的基础上，着重讨论了具有不确定性的非线性系统的控制问题。先针对系统状态已知，部分状态未知及状态具有时滞的情况对不确定非线性系统的镇定问题进行研究。然后又进一步研究了不确定系统的输出调节问题，并将输出调节理论应用到微型飞行器的姿态跟踪和干扰抑制问题。文中作了如下工作：
第一，针对输出调节问题的特殊情况，研究了三类不确定非线性系统的镇定问题。先针对一类具有奇次幂的不确定非线性高阶系统，在假设状态已知的情况下，基于有限时间稳定引入加幂积分器并设计能够应对系统具有不确定性的非-Lipschitz连续的状态反馈控制律。然后针对一类状态不可直接测量的纯反馈非线性系统，用模糊逻辑系统去逼近未知非线性函数，利用滤波解决了一般控制器中遇到的代数循环问题，结合广义的高增益观测器和Lyapunov稳定性理论提出了自适应的输出反馈控制器。最后考虑系统状态中具有时滞的情况，在不确定的非线性是高阶的假设条件下，提出了具有时滞的齐次系统的概念和延拓的齐次占优定理，在齐次增长条件下，基于延拓的齐次占优定理和低增益的观测器证明了跟时滞无关的输出反馈控制器的存在性。
第二，针对一类不确定性不能被已知光滑函数界定且具有线性外系统的不确定非线性系统，研究了其输出调节问题。引入动态面控制法避免了“膨胀项”的产生，减少计算量。同时引入具有误差的内模方程，利用外系统信息镇定控制项，提出一种具有动态面控制的光滑的状态反馈控制律。将非光滑分析理论应用到Backstepping设计方法中，避免了所求的虚拟控制一定为光滑函数，结合内模原理给出非光滑的状态反馈的控制律。
第三，针对系统状态不可直接测量的一类具有动态不确定性的不确定非线性系统，研究了由非线性外系统驱动的的输出调节问题。利用动态信号去处理不匹配的动态，利用高增益的状态观测器去估计状态，设计非线性内模，结合模糊逻辑控制和自适应Backstepping设计方法，设计出模糊自适应的输出反馈控制律和自适应律。
第四，针对一类含有时滞非线性不确定系统，研究了具有线性外系统的输出调节问题。在Backstepping设计的框架下，引入Lyapunov-Krasovskii泛函，结合模糊观测器和内模原理去设计自适应的输出反馈控制器。
第五，利用输出调节问题的结论去解决飞行器的姿态跟踪和干扰抑制问题。该问题的复杂性在于受控对象本身包含的不确定性，以及来自外部系统产生的干扰。利用浸入系统设计线性内模，结合自适应控制理论设计了状态反馈自适应控制器以达到处理系统的不确定性和外系统的不确定性的目的。
The problem of nonlinear output regulation is one of the most important issues inthe control theory and its application, which involves nonlinear stabilizaion, tracking ref-erence control and disturbance rejection as special cases. The objective of the output reg-ulation is to design a feedback control law to achieve tracking a class of reference inputand rejecting in the presence of a class of disturbances while maintaining the closed-loopsystem overall signals uniform ultimate boundedness. When the reference input and theexpected disturbances are generated by autonomous diferential equation which is calledthe exosystem, the problem is also called servomechanism problem.
In this thesis, the problems with non-parametric uncertain nonlinear systems areconsidered. Firstly the stabilization problem is investigated for diferent uncertain nonlin-ear systems for example, with known state variables, with partly known state variables orwith time delay. Then output regulation problem is addressed, and the result is applied toa tracking control problem associated with micro spacecraft. The main contributions aresummarized as follows:
1. The stabilization problem of uncertain nonlinear systems is studied as a specialcase of the output regulation problem. First of all, the global stabilization problem foruncertain nonlinear systems with odd integer in lower triangular form is solved, underthe assumption that the state variables are known, with a non-lipschitz continuous statefeedback control designed by using finite-time stability theorem and non-smooth feed-back design. Then an adaptive fuzzy output feedback backstepping control method isdeveloped for a class of nonlinear pure-feedback systems whose state variables are notdirectly available. Fuzzy logic systems are introduced to approximate the unknown non-linear functions. The filtered signals are utilized to solve the algebraic loop problemsencountered in the implementation of the usual controllers. An adaptive fuzzy control isproposed using generized observer and Lyapunove stability theorem. At last the problemof global output feedback stabilization for a glass of upper-triangular nonlinear systemswith time-delay in the state is considered. The delay-independent output feedback con-troller is proved to be exist based on extended homogeneous domination approach andlow gain observer.
2. When the state variables are available for feedback, the output regulation prob-lem for uncertain nonlinear systems driven by linear exosystems is investigated. Theuncertainties are supposed to be bounded by known functions. Firstly a linear internal isdesigned and a dynamic smooth state feedback control is proposed by making use of theinternal model. Then we apply nonsmooth analysis theory to backstepping method foravoiding the restriction that the virtual controls must be smooth functions. We introducethe error internal model and utilize exosystem information to stabilize feedback inputitems. A nonsmooth state feedback control is prosposed to solve the output regulationproblem.
3. The output regulation problem for uncertain nonlinear systems where the statevariables are not always available is addressed. We focus on the nonlinear systems withdynamic uncertaity and nonlinear exosystem. K-filters are designed to estimate the un-measured states.A fuzzy output feedback control is proposed by using linear internal.Using the designed high-gain observer of state estimation, and combining the fuzzy adap-tive control with backstepping approach, an adaptive control fuzzy backstepping controlscheme is obtained for a class of SISO uncertain system with nonlinear exosystem.
4. The output regulation problem with time delay uncertain nonlinear systems driv-en linear exosystem is studied. At the backstepping frame, using appropriate Lyapunov-Krasovskii functional, an adaptive fuzzy output feedback control is developed by com-bining fuzzy observer and internal model.
5. Some results of output regulation problem are applied to solve the problem ofattitude tracking and disturbance rejection. The complexity of the question is in that thesystems contains the uncertain element and the disturbance contained by the exosystem.A linear internal model with parametric uncertainty is designed utilizing the immersiontechnique. By combining adaptive control theory and Lyapunov theory, state feedbackcontrollers to deal with the uncertainty of the systems and the parametric uncertainty ofthe exosystem are designed.
引文
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