非线性时滞系统最优输出跟踪控制律的近似设计
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摘要
最优输出跟踪问题是最优控制学科的一个重要研究方面,该理论随着最优控制理论在二十世纪五十年代末六十年代初逐渐形成与发展而不断地发展起来。近年来,随着现代工业、国防等各个行业的发展,最优输出跟踪理论在海洋信息探测技术、空间技术、经济运行系统、智能机器人、化工等工业领域得到了越来越多的应用。另外,实际中普遍存在的非线性时滞系统由于其双重复杂性,相关的最优输出跟踪理论研究成果还不多见,因而对于该问题的研究具有重要的理论和现实意义。
本文首先综述了国内外非线性、时滞系统最优输出跟踪问题的研究现状。然后针对一类参考输入信号由外系统给定的非线性、时滞系统,深入地研究了其最优输出跟踪问题,给出了系统控制律的存在唯一性条件及其近似设计方法,并讨论了其物理可实现问题。全文主要研究内容如下:
1.首先介绍了输出跟踪的相关问题和当前的主要研究现状。详细介绍了当前国内外对于双线性系统、非线性系统、带状态时滞的非线性系统和受扰非线性时滞系统的最优输出跟踪问题研究现状。最后给出了课题的意义和本文的研究内容。
2.讨论了一类特殊的非线性系统-双线性系统基于二次型性能指标的最优输出跟踪问题。对于由系统的状态向量和控制向量的乘积描述的双线性项,将其看成系统的摄动加以处理。通过引入一个伴随向量对此双线性项加以补偿,可以将由极大值原理的必要条件导致的非线性两点边值问题变换为由伴随向量方程和状态方程组成的新的两点边值问题。通过逐次逼近法将此问题转化为一族解耦的线性非齐次两点边值问题序列,从而通过求解该问题序列得到系统的前馈-反馈次优控制律。证明了该线性两点边值问题的解序列一致收敛于原最优输出跟踪问题的解。
3.对于系统的参考输入信号的动态特性由外系统给定的最优输出跟踪问题,本文避开构造增广系统的思路,利用参考输入外系统的状态来构造前馈控制作用。前馈增益可以通过求解矩阵方程而精确得到,这样加入系统的前馈控制作用
The optimal output tracking (OOT) problem is one of the important application areas of the optimal control (OC) theory. The theory of OOT has made a development with the formulation and development of the OC theory at the end of 1950s and the start of 1960s. In recent years, Modern industries and national defenses have achieved great advancement, which results in more and more applications of the theory of OOT in the ocean information detection technique, space technique, economic systems, intelligent robot, and chemical industry and so on. Moreover, there are few results on the OOT problem of nonlinear time-delay systems. The reason generally arises from its double complexity. Therefore, the analysis of OOT problem for nonlinear time-delay systems is a significant research both in theory and in practice.
Firstly, the relative studies on the OOT problem for nonlinear time-delay systems up to now are given in detail. Then, based on the maximum principle, this dissertation considers the OOT problem for a class of nonlinear, time-delay systems whose reference input to be tracked is produced by a general exosystem. The existence and uniqueness of the OOT control law are studied and an approximate design processdure of the law is given. The physical realization problem of the feedforward control is discussed. The main contents are given as follows.
1. Some problems relative to OOT are presented with their main research methods at first. Then, a detail expression of studies is introduced on the OOT problem for bilinear systems, nonlinear systems, nonlinear systems with the time-delay in the state, and nonlinear time-delay systems under external disturbances. The objective and contents of this dissertation are given finally.
2. The OOT problem for a class of bilinear systems with a quadratic index performance is studied. The bilinear term described by a product of the state vector and the control vector in the systems’equation is considered as the perturbation of systems. By introducing an adjoint vector, the nonlinear two-point boundary value (TPBV) problem derived form the necessary condition of the maximum principle is replaced by a new TPBV problem which is described by a state equation and an
本文首先综述了国内外非线性、时滞系统最优输出跟踪问题的研究现状。然后针对一类参考输入信号由外系统给定的非线性、时滞系统,深入地研究了其最优输出跟踪问题,给出了系统控制律的存在唯一性条件及其近似设计方法,并讨论了其物理可实现问题。全文主要研究内容如下:
1.首先介绍了输出跟踪的相关问题和当前的主要研究现状。详细介绍了当前国内外对于双线性系统、非线性系统、带状态时滞的非线性系统和受扰非线性时滞系统的最优输出跟踪问题研究现状。最后给出了课题的意义和本文的研究内容。
2.讨论了一类特殊的非线性系统-双线性系统基于二次型性能指标的最优输出跟踪问题。对于由系统的状态向量和控制向量的乘积描述的双线性项,将其看成系统的摄动加以处理。通过引入一个伴随向量对此双线性项加以补偿,可以将由极大值原理的必要条件导致的非线性两点边值问题变换为由伴随向量方程和状态方程组成的新的两点边值问题。通过逐次逼近法将此问题转化为一族解耦的线性非齐次两点边值问题序列,从而通过求解该问题序列得到系统的前馈-反馈次优控制律。证明了该线性两点边值问题的解序列一致收敛于原最优输出跟踪问题的解。
3.对于系统的参考输入信号的动态特性由外系统给定的最优输出跟踪问题,本文避开构造增广系统的思路,利用参考输入外系统的状态来构造前馈控制作用。前馈增益可以通过求解矩阵方程而精确得到,这样加入系统的前馈控制作用
The optimal output tracking (OOT) problem is one of the important application areas of the optimal control (OC) theory. The theory of OOT has made a development with the formulation and development of the OC theory at the end of 1950s and the start of 1960s. In recent years, Modern industries and national defenses have achieved great advancement, which results in more and more applications of the theory of OOT in the ocean information detection technique, space technique, economic systems, intelligent robot, and chemical industry and so on. Moreover, there are few results on the OOT problem of nonlinear time-delay systems. The reason generally arises from its double complexity. Therefore, the analysis of OOT problem for nonlinear time-delay systems is a significant research both in theory and in practice.
Firstly, the relative studies on the OOT problem for nonlinear time-delay systems up to now are given in detail. Then, based on the maximum principle, this dissertation considers the OOT problem for a class of nonlinear, time-delay systems whose reference input to be tracked is produced by a general exosystem. The existence and uniqueness of the OOT control law are studied and an approximate design processdure of the law is given. The physical realization problem of the feedforward control is discussed. The main contents are given as follows.
1. Some problems relative to OOT are presented with their main research methods at first. Then, a detail expression of studies is introduced on the OOT problem for bilinear systems, nonlinear systems, nonlinear systems with the time-delay in the state, and nonlinear time-delay systems under external disturbances. The objective and contents of this dissertation are given finally.
2. The OOT problem for a class of bilinear systems with a quadratic index performance is studied. The bilinear term described by a product of the state vector and the control vector in the systems’equation is considered as the perturbation of systems. By introducing an adjoint vector, the nonlinear two-point boundary value (TPBV) problem derived form the necessary condition of the maximum principle is replaced by a new TPBV problem which is described by a state equation and an
引文
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