基于时滞分解方法的不确定时滞系统的分析和综合
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摘要
在航空、航天以及工业生产过程等领域,大量存在的不确定和时滞现象使得被控对象难以用精确的数学模型来描述,通常也是系统不稳定和系统镇定及控制设计问题难以解决的根源。因此,不确定时滞系统的研究因其具有广泛工程背景和深刻的理论价值而受到系统与控制领域的广大学者的普遍关注。基于时滞分解方法的Lyapunov稳定性及在此基础上的分析和综合问题是近年来鲁棒控制邻域的前沿课题。本论文在总结前人的工作的基础上,系统、深入地研究了基于时滞分解方法的不确定Takagi-Sugeno模糊时滞系统和时滞Markov跳变系统的稳定性及性能分析、状态反馈控制器综合以及滤波器设计等问题,以一个统一的框架提出了不确定时滞系统基于时滞分解方法的分析和综合方法,并将部分理论成果应用于水下机器人的鲁棒潜深控制研究。
首先针对范数有界型的参数不确定Takagi-Sugeno模糊时滞系统,以严格的线性矩阵不等式形式给出了基于时滞分解方法的新的鲁棒稳定条件及H∞性能准则。在此基础上,进一步研究了参数不确定Takagi-Sugeno模糊时滞系统的模糊状态反馈控制器、鲁棒模糊H∞控制器、鲁棒模糊H2滤波器和鲁棒模糊H∞滤波器的设计方法,将控制器、滤波器的存在条件转化为一组线性矩阵不等式可行解问题。其次将本论文的结论推广到范数有界型的参数不确定时滞Markov跳变系统的鲁棒随机稳定及H∞和广义H2性能分析,状态反馈控制器、鲁棒H∞控制器、广义鲁棒H2滤波器和鲁棒H∞滤波器的设计问题。鉴于目前广泛采用的附加松弛矩阵变量为代价,从而获得较低保守性和处理复杂问题具有较大的局限性,本论文所得到的结论与目前这一领域的主要研究成果相比,因其引进了更具有一般意义的Lyapunov泛函且不再引进附加松弛矩阵变量,因而大大降低了鲁棒分析的保守性和复杂性。
最后将论文中提出的状态反馈控制器的设计方法应用于水下机器人的鲁棒潜深控制。首先在分析机器人的基本功能基础上,将水下机器人的潜深控制问题在数学上表述为一个不确定Takagi-Sugeno模糊时滞系统控制问题。鉴于水下机器人的下潜速度是有界的,提出了鲁棒状态反馈控制策略。将水下机器人的潜深控制器的设计转化为受线性矩阵不等式约束的凸优化问题,设计实例验证了所提出了控制策略的可行性。这一部分是时滞分解方法向工程实际问题的尝试性应用,即进一步发展了时滞分解思想,又为工程实际研究人员提供了可以借鉴的设计思想。
Time delays and uncertainties are frequently encountered in aerospace, astronautics and industrial process, which are the source of instability and make the problem (e.g. stabilization and controller design) difficult to solve. Generally, it is difficult to characterize the dynamics of the controlled object exactly by a mathematic model. So investigations on the robust stability analysis and synthesis for uncertain system with time delays are of great theoretical and practical significance, which have long drawn much attention from researchers working in systems and control areas. Delay-decomposition Lyapunov stability and its related analysis and synthesis problem are research frontiers in robust control theory. Based on previous works of others, this thesis systematically and deeply investigates the problems of stability and performance analysis, state-feedback controller synthesis and filter design for uncertain Takagi-Sugeno (T-S) fuzzy time-delay systems and uncertain Markov time-delay systems based on delay-decomposition Lyapunov functions, and presents analysis and synthesis methodologies for uncertain nonlinear time-delay systems in the unified delay-decomposition framework. Part of the developed theories is applied to the robust dive control for autonomous undersea vehicle (AUV).
First the robust stability analysis and H∞performance analysis results are presented in terms of linear matrix inequality for uncertain T-S fuzzy time-delay systems with norm bounded uncertainties based on delay-decomposition approach. Based on the stability and analysis results, the design method is proposed for the robust state feedback fuzzy controller, robust H∞fuzzy controller, robust H2 fuzzy filters and robust H∞fuzzy filters of uncertain T-S fuzzy time-delay systems with norm bounded uncertainties, which converts the existence condition of admissible controllers and filters into the feasibility of convex problems subject to linear matrix inequality (LMI). Next the proposed approach is also applied to investigate the problem of robust stochastic stability analysis and H∞and generalize H2 performance analysis, robust state feedback fuzzy controller, robust H∞fuzzy controller, robust generalize H2 fuzzy filters and robust H∞fuzzy filters of uncertain Markov jump time-delay systems with norm bounded uncertainties. Some free-weighting matrices variables or slack matrices variables are introduced to obtain less conservative results in previous works. In this thesis, based on delay-decomposition Lyapunov functional and metrical integral inequality, new robust stability and performance analysis results for uncertain time-delay systems are developed. Because none additional matrices variables apart from Lyapunov matrices variables are used in our results, our results are less conservative and complex than previous results in this area.
At last, the idea of designing controller developed in this thesis is applied to dive control of autonomous undersea vehicle (AUV). By analyzing the basic functions of AUV and considering the delay in signal transportation, the dive control for AUV is mathematically translated into an uncertain T-S fuzzy system. Under assumption that the diving velocity of AUV is bounded, the robust state feedback control strategy is proposed, which convert the existence condition of dive control for AUV into the feasibility of convex problems subject to linear matrix inequality (LMI). The simulation examples are presented to illustrate the feasibility of our proposed control strategy. This part constitutes an attempt of applying the delay-decomposition idea to practical engineering problems, which extends the delay-decomposition Lyapunov stability theory and provides an example for practical engineers' reference as well.
首先针对范数有界型的参数不确定Takagi-Sugeno模糊时滞系统,以严格的线性矩阵不等式形式给出了基于时滞分解方法的新的鲁棒稳定条件及H∞性能准则。在此基础上,进一步研究了参数不确定Takagi-Sugeno模糊时滞系统的模糊状态反馈控制器、鲁棒模糊H∞控制器、鲁棒模糊H2滤波器和鲁棒模糊H∞滤波器的设计方法,将控制器、滤波器的存在条件转化为一组线性矩阵不等式可行解问题。其次将本论文的结论推广到范数有界型的参数不确定时滞Markov跳变系统的鲁棒随机稳定及H∞和广义H2性能分析,状态反馈控制器、鲁棒H∞控制器、广义鲁棒H2滤波器和鲁棒H∞滤波器的设计问题。鉴于目前广泛采用的附加松弛矩阵变量为代价,从而获得较低保守性和处理复杂问题具有较大的局限性,本论文所得到的结论与目前这一领域的主要研究成果相比,因其引进了更具有一般意义的Lyapunov泛函且不再引进附加松弛矩阵变量,因而大大降低了鲁棒分析的保守性和复杂性。
最后将论文中提出的状态反馈控制器的设计方法应用于水下机器人的鲁棒潜深控制。首先在分析机器人的基本功能基础上,将水下机器人的潜深控制问题在数学上表述为一个不确定Takagi-Sugeno模糊时滞系统控制问题。鉴于水下机器人的下潜速度是有界的,提出了鲁棒状态反馈控制策略。将水下机器人的潜深控制器的设计转化为受线性矩阵不等式约束的凸优化问题,设计实例验证了所提出了控制策略的可行性。这一部分是时滞分解方法向工程实际问题的尝试性应用,即进一步发展了时滞分解思想,又为工程实际研究人员提供了可以借鉴的设计思想。
Time delays and uncertainties are frequently encountered in aerospace, astronautics and industrial process, which are the source of instability and make the problem (e.g. stabilization and controller design) difficult to solve. Generally, it is difficult to characterize the dynamics of the controlled object exactly by a mathematic model. So investigations on the robust stability analysis and synthesis for uncertain system with time delays are of great theoretical and practical significance, which have long drawn much attention from researchers working in systems and control areas. Delay-decomposition Lyapunov stability and its related analysis and synthesis problem are research frontiers in robust control theory. Based on previous works of others, this thesis systematically and deeply investigates the problems of stability and performance analysis, state-feedback controller synthesis and filter design for uncertain Takagi-Sugeno (T-S) fuzzy time-delay systems and uncertain Markov time-delay systems based on delay-decomposition Lyapunov functions, and presents analysis and synthesis methodologies for uncertain nonlinear time-delay systems in the unified delay-decomposition framework. Part of the developed theories is applied to the robust dive control for autonomous undersea vehicle (AUV).
First the robust stability analysis and H∞performance analysis results are presented in terms of linear matrix inequality for uncertain T-S fuzzy time-delay systems with norm bounded uncertainties based on delay-decomposition approach. Based on the stability and analysis results, the design method is proposed for the robust state feedback fuzzy controller, robust H∞fuzzy controller, robust H2 fuzzy filters and robust H∞fuzzy filters of uncertain T-S fuzzy time-delay systems with norm bounded uncertainties, which converts the existence condition of admissible controllers and filters into the feasibility of convex problems subject to linear matrix inequality (LMI). Next the proposed approach is also applied to investigate the problem of robust stochastic stability analysis and H∞and generalize H2 performance analysis, robust state feedback fuzzy controller, robust H∞fuzzy controller, robust generalize H2 fuzzy filters and robust H∞fuzzy filters of uncertain Markov jump time-delay systems with norm bounded uncertainties. Some free-weighting matrices variables or slack matrices variables are introduced to obtain less conservative results in previous works. In this thesis, based on delay-decomposition Lyapunov functional and metrical integral inequality, new robust stability and performance analysis results for uncertain time-delay systems are developed. Because none additional matrices variables apart from Lyapunov matrices variables are used in our results, our results are less conservative and complex than previous results in this area.
At last, the idea of designing controller developed in this thesis is applied to dive control of autonomous undersea vehicle (AUV). By analyzing the basic functions of AUV and considering the delay in signal transportation, the dive control for AUV is mathematically translated into an uncertain T-S fuzzy system. Under assumption that the diving velocity of AUV is bounded, the robust state feedback control strategy is proposed, which convert the existence condition of dive control for AUV into the feasibility of convex problems subject to linear matrix inequality (LMI). The simulation examples are presented to illustrate the feasibility of our proposed control strategy. This part constitutes an attempt of applying the delay-decomposition idea to practical engineering problems, which extends the delay-decomposition Lyapunov stability theory and provides an example for practical engineers' reference as well.
引文
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