非线性迭代学习控制理论及其在机器人控制中的应用
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摘要
本文以建立非线性系统迭代学习控制的基本理论为目的，研究了非线性连续系统、离散系统、分布参数系统、广义系统的迭代学习控制方法，以及系统在不满足一般收敛条件下的学习控制方法。最后，我们还讨论了迭代学习控制方法在机器人系统中的应用问题。
本文共分六部分，第一部分为第一章的绪论，主要介绍了迭代学习控制理论产生的背景、迭代学习控制理论国内外研究的现状，指出目前迭代学习控制理论研究中主要存在的问题，阐明了研究目的和研究内容。
第二部分为第二章和第三章。第二章主要研究了一般非线性系统的迭代学习控制方法，并介绍了一个新的概念—(λ，ζ)范数，在充分利用控制系统先前控制经验的基础上，将控制量和输出量作为一个整体来进行讨论，使得算法不象已有结果那样，只是局部收敛，而是全局收敛。第三章主要研究了一类退化系统目标跟踪的迭代学习控制的吸引流形方法，在系统不满足一般收敛条件的情况下，我们通过构造一个相应于所给系统稳定而吸引的流形，导出所满足要求的迭代学习控制，该方法对系统有较好的鲁棒性。
第三部分包括第四章和第五章，主要研究了一般非线性离散系统及一类不确定离散系统的目标跟踪问题。对于一般非线性离散系统，引进了离散的(λ，ζ)范数，所给的算法不依赖于学习控制算法中的初始数据，对于一类不确定离散系统的状态跟踪问题，我们也采用迭代学习控制的方法，将相应的学习控制问题转化为一个下三角动力系统的平凡解全局稳定性问题，获得了对系统理想状态的跟踪结果，并对所给的算法的收敛性进行了分析。
第四部分包括第六章、第七章、第八章，主要研究了一般非线性分布参数系统、不确定分布参数系统的迭代学习控制方法，获得了系统轨线于L_2(Ω)空间和W~(1，2)(Ω)空间中跟踪期望目标的结果，所给的学习算法避免了其收敛性要依赖于理想控制输入这一不确定的条件，拓宽了系统的鲁棒裕度；对于不确定的系数矩阵只是一个定性的要求——有界，而没有定量的要求——是多少。另外，对不确定分布参数系统，我们还给出了一种二阶P-型学习算法，该算法有较好的收敛性。
第五部分为第九章，主要研究了一类滞后广义非线性系统状态跟踪的迭代学
This paper aims at the basic theory of nonlinear iterative learning control, and have studied the iterative learning control methods of nonlinear continuous systems、 discrete-time systems、 distributed parameter systems、 singular systems, and the application of the iterative learning control when a general convergence condition doesn't be satisfied. Finally, we have also discussed the application problems of the iterative learning control on robot systems.
This paper contains six parts. The first part is the chapter I, Introduction, Which mainly introduced the background of the iterative learning control theory and the research status of this theory in our country and abroad, and points out the main existing problems in current studies, and elucidats the research purpose and contents of this paper.
The second part includes chapter II, chapter III. We mainly presents the popular nonlinear system iterative learning control method in the chapter II, and introduces a new concept—(λ,ξ) norm, Based on using fully former control experiences, we studies the input and output as a whole, which makes the algorithm having the global convergence instead of local convergence in the existing results. We study the attractive manifold method of the iterative learning control for a class of degenerate systems in the chapter III. When the learning control systems don't satisfy the convergence condition, we present the learning control method satisfying the condition by constructing a stable and attractive manifold corresponding system. This method makes the system with better robustness.
The third part includes chapter IV and chapter V, Which is mainly studies the trajectory tracking problems of a general nonlinear discrete-time system and a class of uncertain discrete-time systems. To the discrete-time systems, we introduce a new discrete-time (λ,ξ) norm, the algorithm given is not depend upon the initial data. For a class of uncertain discrete-time
本文共分六部分，第一部分为第一章的绪论，主要介绍了迭代学习控制理论产生的背景、迭代学习控制理论国内外研究的现状，指出目前迭代学习控制理论研究中主要存在的问题，阐明了研究目的和研究内容。
第二部分为第二章和第三章。第二章主要研究了一般非线性系统的迭代学习控制方法，并介绍了一个新的概念—(λ，ζ)范数，在充分利用控制系统先前控制经验的基础上，将控制量和输出量作为一个整体来进行讨论，使得算法不象已有结果那样，只是局部收敛，而是全局收敛。第三章主要研究了一类退化系统目标跟踪的迭代学习控制的吸引流形方法，在系统不满足一般收敛条件的情况下，我们通过构造一个相应于所给系统稳定而吸引的流形，导出所满足要求的迭代学习控制，该方法对系统有较好的鲁棒性。
第三部分包括第四章和第五章，主要研究了一般非线性离散系统及一类不确定离散系统的目标跟踪问题。对于一般非线性离散系统，引进了离散的(λ，ζ)范数，所给的算法不依赖于学习控制算法中的初始数据，对于一类不确定离散系统的状态跟踪问题，我们也采用迭代学习控制的方法，将相应的学习控制问题转化为一个下三角动力系统的平凡解全局稳定性问题，获得了对系统理想状态的跟踪结果，并对所给的算法的收敛性进行了分析。
第四部分包括第六章、第七章、第八章，主要研究了一般非线性分布参数系统、不确定分布参数系统的迭代学习控制方法，获得了系统轨线于L_2(Ω)空间和W~(1，2)(Ω)空间中跟踪期望目标的结果，所给的学习算法避免了其收敛性要依赖于理想控制输入这一不确定的条件，拓宽了系统的鲁棒裕度；对于不确定的系数矩阵只是一个定性的要求——有界，而没有定量的要求——是多少。另外，对不确定分布参数系统，我们还给出了一种二阶P-型学习算法，该算法有较好的收敛性。
第五部分为第九章，主要研究了一类滞后广义非线性系统状态跟踪的迭代学
This paper aims at the basic theory of nonlinear iterative learning control, and have studied the iterative learning control methods of nonlinear continuous systems、 discrete-time systems、 distributed parameter systems、 singular systems, and the application of the iterative learning control when a general convergence condition doesn't be satisfied. Finally, we have also discussed the application problems of the iterative learning control on robot systems.
This paper contains six parts. The first part is the chapter I, Introduction, Which mainly introduced the background of the iterative learning control theory and the research status of this theory in our country and abroad, and points out the main existing problems in current studies, and elucidats the research purpose and contents of this paper.
The second part includes chapter II, chapter III. We mainly presents the popular nonlinear system iterative learning control method in the chapter II, and introduces a new concept—(λ,ξ) norm, Based on using fully former control experiences, we studies the input and output as a whole, which makes the algorithm having the global convergence instead of local convergence in the existing results. We study the attractive manifold method of the iterative learning control for a class of degenerate systems in the chapter III. When the learning control systems don't satisfy the convergence condition, we present the learning control method satisfying the condition by constructing a stable and attractive manifold corresponding system. This method makes the system with better robustness.
The third part includes chapter IV and chapter V, Which is mainly studies the trajectory tracking problems of a general nonlinear discrete-time system and a class of uncertain discrete-time systems. To the discrete-time systems, we introduce a new discrete-time (λ,ξ) norm, the algorithm given is not depend upon the initial data. For a class of uncertain discrete-time
引文
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104 刘永清，唐功友，大型动力系统的理论与应用(卷3)—滞后·稳定与控制华南理工大学出版社
105 刘永清，温香彩，大型动力系统的理论与应用(卷6)—广义系统的变结构控制，华南理工大学出版社
106 刘永清，王伟，李远清，大型动力系统的理论与应用(卷7)—滞后广义系统解的基本理论与应用，华南理工大学出版社
107 刘永清，谢湘生，大型动力系统的理论与应用(卷8)—滞后广义系统的稳定镇定与控制，华南理工大学出版社
108 刘永清，高存臣，袁付顺，大型动力系统的理论与应用(卷9)—滞后系统的变结构控制，华南理工大学出版社
109 刘永清，谢胜利，大型动力系统的理论与应用(卷11)—滞后分布参数系统的稳定与变结构控制，华南理工大学出版社
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105 刘永清，温香彩，大型动力系统的理论与应用(卷6)—广义系统的变结构控制，华南理工大学出版社
106 刘永清，王伟，李远清，大型动力系统的理论与应用(卷7)—滞后广义系统解的基本理论与应用，华南理工大学出版社
107 刘永清，谢湘生，大型动力系统的理论与应用(卷8)—滞后广义系统的稳定镇定与控制，华南理工大学出版社
108 刘永清，高存臣，袁付顺，大型动力系统的理论与应用(卷9)—滞后系统的变结构控制，华南理工大学出版社
109 刘永清，谢胜利，大型动力系统的理论与应用(卷11)—滞后分布参数系统的稳定与变结构控制，华南理工大学出版社