摘要
近年来，非线性H_∞控制问题备受关注，取得了一系列重要成果，但是仍然有许多工作需要深入去做，相关的理论需要改进，已有的结果也亟待创造性地运用。
本论文从耗散系统原理的角度对非线性H_∞控制理论进行了总结和补充，籍此研究了不确定非线性系统，特别是多时滞非线性系统的H_∞控制问题以及与H_∞控制相关的其他问题，取得了如下成果：
1．探讨了仅存在状态摄动的不确定非线性系统的鲁棒H_∞控制问题，给出了此类系统的状态反馈、输出反馈以及基于观测器的输出反馈的H_∞控制问题有解的充分条件和控制器的设计方法；在此基础上，进一步探讨了同时含有状态摄动和状态导数摄动的不确定非线性系统的鲁棒性能准则设计问题。
2．运用H_∞控制原理研究了多时滞非线性系统的干扰抑制问题，得出了状态反馈和输出反馈控制器的设计方法。特别地，利用线性矩阵不等式方法设计了该类系统的输出反馈控制器，并给出了此类控制器各参数矩阵的计算方法；将H_∞控制原理和自适应设计原理相结合，给出了一类多时滞非线性系统的自适应鲁棒控制和自适应H_∞控制设计。
3．将H_∞控制理论应用到非线性系统的模型简化问题、输出跟踪问题和滤波问题中。探讨了多时滞非线性系统的H_∞模型简化问题，将高阶的不确定多时滞非线性系统分别简化为低阶的线性时滞系统、低阶的线性系统甚至简单的零阶输入输出映射；应用H_∞控制理论解决了受扰非线性系统的输出跟踪问题，给出了分析此类问题的一般方法；总结并说明了H_∞滤波问题可解的充分条件。
4．探讨了非线性系统混合H_2／H_∞控制问题可解的充分条件，并揭示了非线性系统H_2控制、H_∞控制以及混合H_2／H_∞控制问题之间的关系，给出了三者的统一表达式。
5．应用非线性H_∞和H_2／H_∞控制理论解决了刚体姿态系统和机器人系统的H_∞控制问题、干扰近似解耦问题等，验证了论文有关结论的合理性和有效性。
Although much attention has been paid to the nonlinear H∞ control and many important achievements have been obtained in recent years, lots of work are still to be done. The relevant nonlinear H∞ control theories need to be improved, while the existing results should be applied urgently.
In this dissertation, the basic theoretic results on nonlinear H∞ control theory are summarized and developed firstly from the perspective of dissipation theory, then the robust H∞ control problems of uncertain nonlinear systems, especially those of the nonlinear systems with multiple time delays, and several other problems related to the H∞ control are investigated based on the theoretic results above. The contributions of this dissertation are as follows.
1. The robust H∞ control problems of nonlinear systems with state perturbations are studied. The corresponding sufficient conditions for the solvability of H∞ control problems via the state feedback control, the output control and the output control based on observers are put forward, while the design methods of these kind controller are proposed. Then the performance criteria design is discussed for a class of nonlinear uncertain systems with state perturbations and state's derivative perturbations as well.
2. Robust disturbance attenuation problems for uncertain upper-bounded nonlinear systems with multiple time delays are solved. The design methods via the state feedback control and the output control are put forward. Particularly, an output feedback controller is constructed by using the LMI method and the matrices related to the controller are parameterized. Combining H∞ control theory and adaptive control theory, I designed adaptive controllers for robust stabilization and robust disturbance attenuation of uncertain nonlinear systems with multiple time delays whose upper bounds are partially known are designed.
3. The H∞ control theories are applied to solve model reduction problems, output tracking problems and filtering problems. The H∞ model reduction problem of a
kind of uncertain nonlinear systems with multiple time delays is studied. Model reduction methods are presented that can simplify the uncertain nonlinear systems with multiple time delays to be low order linear delayed systems or low order linear systems, or even the zero order input-output mappings. The output tracking problem of disturbed nonlinear systems is solved by the H∞ control theory, the analysis method is proposed. The sufficient conditions for the solvability of the H∞ filtering problem of nonlinear systems are obtained.
4. The mixed H2/H∞ control problem of nonlinear systems is investigated. The relationships among the H∞ control, the H∞ control and the mixed H∞/H∞ control are explained. A unified formula for the H∞ control, the H∞ control and the mixed H∞/H∞ control is deduced.
5. The nonlinear H∞ and H2/H∞ control theories are applied to solve the problem of robust H∞ control and the problem of disturbance almost decoupling of the rigid body attitude systems and the robot systems to verify the rationality and the validity of the results proposed in this dissertation.
引文
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