严格反馈不确定非线性时滞系统的自适应模糊控制
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摘要
随着现代科学技术的发展,对严格反馈不确定非线性时滞系统控制问题的研究受到越来越多的关注。Backstepping方法和动态面控制方法是研究严格反馈不确定非线性时滞系统控制问题的有效途径。本论文以backstepping方法和动态面控制方法为基本工具,结合自适应模糊逼近理论、时滞泛函微分方程理论、Lyapunov稳定性理论以及关联大系统分散控制理论,重点研究了如何消除未知时滞和不确定因素对系统稳定性的影响,以及如何简化控制器的结构。主要工作概况如下:
1.针对系统输出中含有完全未知时滞的情况,提出一种时滞代换方法。考虑到系统最终将跟踪给定的参考信号,而参考信号是事先指定的,即已知的,因此可以采用参考信号代换上述无法利用的时滞信号,然后采用自适应鲁棒技术处理代换误差,消除了时滞对闭环系统的影响。
2.将自适应backstepping控制理论和自适应动态面控制理论延伸到了含完全未知时滞的不确定非线性系统。分别提出了一种自适应模糊backstepping控制方法和自适应模糊动态面控制方法,取消了对时滞的常用假设,克服了因完全未知时滞的存在而导致的控制器设计困难,去除了时滞对闭环系统稳定性的影响。跟踪误差可以收敛到原点附近任意小的邻域内。
3.将自适应backstepping控制和自适应动态面控制理论延伸到了含完全未知时滞和未知关联项的非线性大系统。分别提出了一种自适应模糊分散backstepping控制方法和自适应模糊分散动态面控制方法,取消了对系统未知关联项和未知时滞常作的假设,去除了未知时滞对闭环系统和分散控制器构造的影响。这两种控制方法均可保证闭环大系统的稳定性。
4.针对一类输出反馈的不确定非线性时滞系统,提出了一种基于单逼近器的自适应模糊动态面控制方法。控制器中仅需一个模糊逼近器,便使得系统的所有未知项得到补偿,进而仅带来一个未知参数和逼近误差,减少了需要在线调整的自适应参数的个数,简化了控制器的结构,避免了“计算膨胀”的问题。通过构造合适的Lyapunov-Krasovskii泛函,去除了未知时滞的影响。
5.提出了一种基于单逼近器的自适应模糊分散动态面控制方法。对于含有未知时滞和未知关联项的输出反馈非线性时滞关联大系统,每个子系统中仅需一个模糊逼近器,来消除系统未知关联项的影响,减少了在线调整的自适应参数个数,简化了分散控制器的结构,避免了“计算膨胀”问题。所构造的Lyapunov-Krasovskii泛函同样可以消除未知时滞的影响。
6.针对一类含未知时滞和未知增益函数的非线性时滞系统,提出了一种自适应模糊动态面控制方法。基于时滞代换的思想处理系统中完全未知的时滞,取消了对时滞的常用假设。通过综合系统中的未知非线性函数和未知虚拟控制系数,使得系统的每一阶仅需引入一个逼近器,简化了控制器的结构,同时避免了控制奇异性问题。基于构造类加权形式的Lyapunov-Krasovskii泛函,确保了闭环系统的稳定性。
As the development of science and technology, the control problem of uncertainnonlinear time-delay systems is paid more and more attention to. Backstepping tech-nique and dynamic surface control (DSC) technique are efficient tools to study thecontrol problem of strict-feedback uncertain nonlinear time-delay systems. This dis-sertation uses backstepping and dynamic surface control as basic tools, combines adap-tive fuzzy approximation theory, stability theory of time-delay functional differentialequations, Lyaponov stability theory and decentralized control theory of interconnectedlarge-scale systems. We preliminarily focus on the problems of how to eliminate thein?uence of unknown time-delays and uncertainties which may harm to the stability ofthe system, and how to simplify the structure of the controller. The main contributionsare outlined as follows:
1. For the control problem of systems with completely unknown time-delays inthe outputs, a novel technique called delay replacement is proposed. Considering thesystems outputs will eventually track the reference signals, and the reference signals areused to be known as prior knowledge, so the delayed signals can be replaced with thereference signals. Adaptive robust technique is employed to deal with the replacementerror, and the in?uence of time-delays to the closed-loop systems is eliminated.
2. The adaptive backstepping control theory and the adaptive DSC theory areextended to uncertain nonlinear systems with completely unknown time-delays. Anadaptive fuzzy backstepping control approach and an adaptive fuzzy DSC approach areproposed. The common assumptions on the delays are removed; the controller designdifficulty and the in?uence to stability of the closed loop system caused by the delaysare eliminated. It is proved that the tracking error can converge to an arbitrary smallneighborhood of the origin.
3. The adaptive backstepping control theory and the adaptive DSC theory areextended to nonlinear large-scale systems with comeletely unknown time-delays andunknown interconnections. An adaptive fuzzy decentralized backstepping control ap-proach and an adaptive fuzzy decentralized DSC approach are proposed. The commonassumptions on the delays and the interconnections are removed; the controller designdifficulty and the in?uence to stability of the closed loop system caused by the delaysare eliminated. All of these two control approaches can garantee the stability of the closed loop large-scale systems.
4. Based on a single approximator, an adaptive fuzzy DSC approach is proposedfor output-feedback uncertain nonlinear time-delay systems. Only one fuzzy logic sys-tem is employed in the controller design procedure, so that all the unknown items ofthe systems are compensated for. Thus, only one unknown parameter and one approxi-mation error are needed to be adjusted, so that the controller structure is simplified. Atthe same time, the“explosion of items”problem is avoided by using DSC technique.The proposed approached can ensure stability of the closed-loop systems and arbitrarysmall tracking errors are achieved.
5. Based on a single approximator, an adaptive fuzzy decentralized dynamic sur-face controller is proposed. In each subsystem of output-feedback nonlinear time-delaylarge-scale systems with unknown interconnections and unknown delay signals, onlyone fuzzy approximator is needed to eliminate the in?uence of the unknown intercon-nections and time delays, so that the number of unknown parameters which are neededto be adjusted is reduced, and the controller structure is simplified. Based on LaSalle in-variance theory and the stability theory of time-delay functional differential equations,the closed loop system is proved to be bounded, and through adjusting parameters, thetracking errors can be arbitrary small.
6. An adaptive fuzzy DSC approach is proposed for a class of systems with un-known time-delays and unknown virtual control coefficients. Based on delay replace-ment technique, the completely unknown delay signals are dealt with and the commonassumption about time-delays are not needed any more. Through integrating the non-linear functions and the unknown virtual control coefficients of the systems, one ap-proximator is used in each step of the controller design, so that the controller structureis simplified, and the control singularity problem is avoided. Based on constructingquasi-weighted Lyapunov-Krasoviskii functional, the stability of the closed-loop sys-tems can be ensured.
1.针对系统输出中含有完全未知时滞的情况,提出一种时滞代换方法。考虑到系统最终将跟踪给定的参考信号,而参考信号是事先指定的,即已知的,因此可以采用参考信号代换上述无法利用的时滞信号,然后采用自适应鲁棒技术处理代换误差,消除了时滞对闭环系统的影响。
2.将自适应backstepping控制理论和自适应动态面控制理论延伸到了含完全未知时滞的不确定非线性系统。分别提出了一种自适应模糊backstepping控制方法和自适应模糊动态面控制方法,取消了对时滞的常用假设,克服了因完全未知时滞的存在而导致的控制器设计困难,去除了时滞对闭环系统稳定性的影响。跟踪误差可以收敛到原点附近任意小的邻域内。
3.将自适应backstepping控制和自适应动态面控制理论延伸到了含完全未知时滞和未知关联项的非线性大系统。分别提出了一种自适应模糊分散backstepping控制方法和自适应模糊分散动态面控制方法,取消了对系统未知关联项和未知时滞常作的假设,去除了未知时滞对闭环系统和分散控制器构造的影响。这两种控制方法均可保证闭环大系统的稳定性。
4.针对一类输出反馈的不确定非线性时滞系统,提出了一种基于单逼近器的自适应模糊动态面控制方法。控制器中仅需一个模糊逼近器,便使得系统的所有未知项得到补偿,进而仅带来一个未知参数和逼近误差,减少了需要在线调整的自适应参数的个数,简化了控制器的结构,避免了“计算膨胀”的问题。通过构造合适的Lyapunov-Krasovskii泛函,去除了未知时滞的影响。
5.提出了一种基于单逼近器的自适应模糊分散动态面控制方法。对于含有未知时滞和未知关联项的输出反馈非线性时滞关联大系统,每个子系统中仅需一个模糊逼近器,来消除系统未知关联项的影响,减少了在线调整的自适应参数个数,简化了分散控制器的结构,避免了“计算膨胀”问题。所构造的Lyapunov-Krasovskii泛函同样可以消除未知时滞的影响。
6.针对一类含未知时滞和未知增益函数的非线性时滞系统,提出了一种自适应模糊动态面控制方法。基于时滞代换的思想处理系统中完全未知的时滞,取消了对时滞的常用假设。通过综合系统中的未知非线性函数和未知虚拟控制系数,使得系统的每一阶仅需引入一个逼近器,简化了控制器的结构,同时避免了控制奇异性问题。基于构造类加权形式的Lyapunov-Krasovskii泛函,确保了闭环系统的稳定性。
As the development of science and technology, the control problem of uncertainnonlinear time-delay systems is paid more and more attention to. Backstepping tech-nique and dynamic surface control (DSC) technique are efficient tools to study thecontrol problem of strict-feedback uncertain nonlinear time-delay systems. This dis-sertation uses backstepping and dynamic surface control as basic tools, combines adap-tive fuzzy approximation theory, stability theory of time-delay functional differentialequations, Lyaponov stability theory and decentralized control theory of interconnectedlarge-scale systems. We preliminarily focus on the problems of how to eliminate thein?uence of unknown time-delays and uncertainties which may harm to the stability ofthe system, and how to simplify the structure of the controller. The main contributionsare outlined as follows:
1. For the control problem of systems with completely unknown time-delays inthe outputs, a novel technique called delay replacement is proposed. Considering thesystems outputs will eventually track the reference signals, and the reference signals areused to be known as prior knowledge, so the delayed signals can be replaced with thereference signals. Adaptive robust technique is employed to deal with the replacementerror, and the in?uence of time-delays to the closed-loop systems is eliminated.
2. The adaptive backstepping control theory and the adaptive DSC theory areextended to uncertain nonlinear systems with completely unknown time-delays. Anadaptive fuzzy backstepping control approach and an adaptive fuzzy DSC approach areproposed. The common assumptions on the delays are removed; the controller designdifficulty and the in?uence to stability of the closed loop system caused by the delaysare eliminated. It is proved that the tracking error can converge to an arbitrary smallneighborhood of the origin.
3. The adaptive backstepping control theory and the adaptive DSC theory areextended to nonlinear large-scale systems with comeletely unknown time-delays andunknown interconnections. An adaptive fuzzy decentralized backstepping control ap-proach and an adaptive fuzzy decentralized DSC approach are proposed. The commonassumptions on the delays and the interconnections are removed; the controller designdifficulty and the in?uence to stability of the closed loop system caused by the delaysare eliminated. All of these two control approaches can garantee the stability of the closed loop large-scale systems.
4. Based on a single approximator, an adaptive fuzzy DSC approach is proposedfor output-feedback uncertain nonlinear time-delay systems. Only one fuzzy logic sys-tem is employed in the controller design procedure, so that all the unknown items ofthe systems are compensated for. Thus, only one unknown parameter and one approxi-mation error are needed to be adjusted, so that the controller structure is simplified. Atthe same time, the“explosion of items”problem is avoided by using DSC technique.The proposed approached can ensure stability of the closed-loop systems and arbitrarysmall tracking errors are achieved.
5. Based on a single approximator, an adaptive fuzzy decentralized dynamic sur-face controller is proposed. In each subsystem of output-feedback nonlinear time-delaylarge-scale systems with unknown interconnections and unknown delay signals, onlyone fuzzy approximator is needed to eliminate the in?uence of the unknown intercon-nections and time delays, so that the number of unknown parameters which are neededto be adjusted is reduced, and the controller structure is simplified. Based on LaSalle in-variance theory and the stability theory of time-delay functional differential equations,the closed loop system is proved to be bounded, and through adjusting parameters, thetracking errors can be arbitrary small.
6. An adaptive fuzzy DSC approach is proposed for a class of systems with un-known time-delays and unknown virtual control coefficients. Based on delay replace-ment technique, the completely unknown delay signals are dealt with and the commonassumption about time-delays are not needed any more. Through integrating the non-linear functions and the unknown virtual control coefficients of the systems, one ap-proximator is used in each step of the controller design, so that the controller structureis simplified, and the control singularity problem is avoided. Based on constructingquasi-weighted Lyapunov-Krasoviskii functional, the stability of the closed-loop sys-tems can be ensured.
引文
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