幾類時滯動力系統(tǒng)的穩(wěn)定性分析與控制設計
發(fā)布時間：2019-01-10 09:58
【摘要】：時滯(Time delay,TD)現(xiàn)象普遍的存在于許多實際工程應用中,例如航天航空、冶金、石化、通信、電力、生物、人口和經濟等系統(tǒng)。由于時滯動力系統(tǒng)有著廣泛的應用價值而受到國內外很多學者的關注。同時,時滯經常是導致動力系統(tǒng)不穩(wěn)定、震蕩、甚至系統(tǒng)性能降低的一個重要根源。于是時滯動力系統(tǒng)的穩(wěn)定性分析和控制設計是目前研究的熱點問題。如何掌握和運用時滯動力系統(tǒng)的性能是一個重要的研究課題。基于Lyapunov-Krasovskii泛函(Lyapunov-Krasovskii functional,LKF)理論、Shur補引理、時滯分割方法、不等式處理技巧、線性矩陣不等式(LMIs)等工具,研究了中立型時滯神經網絡(Neural Networks,NNs)、分布時滯NNs、混合時滯NNs以及時滯Lurie系統(tǒng)(Lurie Systems,LSs)的穩(wěn)定性分析和控制設計。本文研究的主要成果如下:1.中立型時滯NNs的穩(wěn)定性分析。通過構建新的包含三重積分和四重積分的LKF,導出了改進的時滯依賴穩(wěn)定準則。我們充分的考慮了二次凸組合方法,二次凸函數的性質和激活函數的信息,進一步降低結果的保守性。最后提供四個數值例子和仿真實驗來表明了所得理論結果的可行性和優(yōu)越性。2.分布時滯NNs的穩(wěn)定性分析。本章的主要思想是借助一個新的積分不等式,它已被證實它的保守性比詹森不等式的保守性還小,由于它充分考慮了Leibniz-Newton公式中各項之間的關系。通過采用更普遍的時滯分割方法,構造一個合適的LKF�；谶@個新的積分不等式和時滯分割方法,得到拓展的時滯依賴穩(wěn)定準則。最后給出四個數值算例和仿真實驗來說明了所提出方法的有效性和優(yōu)越性。3.混合時滯NNs的穩(wěn)定性分析。借助一個多重積分不等式,它可以提供比Jensen’s不等式更好的上界,建立了新的穩(wěn)定準則。通過構建一個包含多重積的LKF,獲得改進穩(wěn)定條件,這些條件以LMIs形式表現(xiàn)出來。再者,把分布時滯區(qū)間分割成多個不等式子區(qū)間,推導出保守性較小的穩(wěn)定結果。最后給出三個數值例子和仿真實驗來展現(xiàn)了所得理論結果的可行性和優(yōu)越性。4.時滯NNs的H∞控制設計。本章的主要目標是設計一個有效的H∞控制器,使得閉環(huán)系統(tǒng)在擾動衰減性能指標γ0下漸近穩(wěn)定。通過引入恰當的LKF和提出更一般的時滯分割方法,新穎的時滯依賴穩(wěn)定準則被建立。再者,通過充分利用改進的Wirtinger’s的積分不等式,獲得了一個改善的充分條件,而確保了H∞控制問題的存在性。最后給出兩個數值例子和仿真實驗來說明了所提出方法的有效性和可行性。5.不確定中立型混合時滯LSs的穩(wěn)定性分析。這個系統(tǒng)不僅包含實變不確定項和扇形有界非線性項,而且還有離散和分布時滯。通過構建合適的LKF和有效的數學技術,導出保守性較小的魯棒穩(wěn)定條件。最后提供三個數值例子和仿真實驗來表明了所得理論結果的可行性和優(yōu)越性。6.混沌Lurie系統(tǒng)(Chaotic Lurie Systems,CLSs)同步的時滯反饋控制設計。通過引入兩個可調節(jié)的是實參數,一個新的積分不等式被提出,它可以把改進的Wirtinger’s積分不等式和詹森積分不等式作為兩種特殊情況。通過引入一個擴張的LKF,它充分的考慮了時變時滯的范圍,保守性較小的時滯依賴同步準則被建立。再者,基于新的非線性函數條件,理想的控制增益矩陣被成功設計。最后給出兩個關于Chua’s電路系統(tǒng)的數值例子和仿真實驗來展現(xiàn)了所設計方法的可行性和優(yōu)越性。7.時滯CLSs同步的采樣控制設計。本章提出了一種新的積分不等式來研究時滯CLSs的主從同步問題。首先,假定采樣區(qū)間是任意有界變量。通過充分考慮采樣區(qū)間的信息和非線性函數條件,以及時滯分割方法,一個新地擴張的LKF被構建。其次,為了獲得保守性較小的同步準則,引入一個可變的是參數,建立了一個新的積分不等式。再者,基于雙重積分的Wirtinger-based積分不等式,一個較長的采樣周期被獲得。最后通過三個數值例子和數值仿真來驗證了所提出方法的優(yōu)越性和可行性。8.CLSs同步的隨機采樣控制設計。本章通過一種新的方法來研究CLSs主從同步的隨機采樣控制設計問題。首先我們假定采樣區(qū)間發(fā)生的概率是個固定的常數,且滿足Bernoulli分布。為了充分考慮采樣區(qū)間的信息,基于改善的Wirtinger積分不等式,我們引入了一個改進的LKF。其次,通過利用新的自由矩陣積分不等式,導出一個保守性較小的指數均方同步穩(wěn)定準則,用來分析相應的誤差同步系統(tǒng)。再者,基于上述方法,一個理想的反饋增益矩陣被成功設計。最后通過三個數值例子和數值仿真來說明了所提出方法的優(yōu)越性和可行性。
[Abstract]:Time delay (TD) phenomena are common in many practical engineering applications, such as aerospace, metallurgy, petrifaction, communication, power, biology, population and economy. Due to the wide application value of time-delay power system, many scholars at home and abroad are concerned. At the same time, time-delay is an important source of the instability, oscillation and even system performance of the power system. Therefore, the stability analysis and control design of the time-delay power system is a hot issue in the current research. How to master and apply the performance of time-delay power system is an important research subject. The neutral-type time-delay neural network (NNs), the distributed time-delay NNs, the hybrid time-delay NNs and the time-delay Lurie systems (Lurie Systems) are studied based on the Lyapunov-Krasovskii functional (LKF) theory, the Shur complement approach, the time-delay segmentation method, the inequality processing technique, the linear matrix inequality (LMIs), and the like. The stability analysis and control design of LSs. The main results of this study are as follows: 1. Stability analysis of neutral time-delay NNs. The improved time-delay-dependent stability criterion is derived by the construction of new LKF with triple integral and four-point integration. We fully consider the secondary convex combination method, the property of the secondary convex function and the information of the activation function, and further reduce the conservativeness of the result. Finally, four numerical examples and simulation experiments are provided to show the feasibility and superiority of the obtained theoretical results. Stability analysis of distributed time-delay NNs. The main idea in this chapter is to use a new integral inequality, which has been proved to be more conservative than that of the Johnson's inequality, because it fully considers the relationship between the various Leibniz-Newton formulas. A suitable LKF is constructed by adopting a more general time-delay segmentation method. Based on this new integral inequality and time-delay segmentation, the extended time-delay-dependent stability criterion is obtained. Finally, four numerical examples and simulation experiments are given to illustrate the effectiveness and superiority of the proposed method. Stability analysis of mixed time-delay NNs. By means of a multi-integral inequality, it can provide a better upper boundary than the Jensen's inequality, and set up a new stability criterion. Improved stability conditions are obtained by constructing an LKF that contains multiple products, which are presented in the form of LMIs. In addition, the distribution time-delay interval is divided into a plurality of inequalities subintervals, and a stable result with less conservative property is derived. Finally, three numerical examples and simulation experiments are given to show the feasibility and advantages of the obtained theoretical results. The H-type control design of the time-delay NNs. The main objective of this chapter is to design a valid H-controller, so that the closed-loop system is asymptotically stable under the condition of disturbance attenuation performance. A novel time-delay-dependent stability criterion is established by the introduction of the appropriate LKF and a more general time-delay segmentation method. Furthermore, by making full use of the improved Wirtinger's integral inequality, an improved sufficient condition is obtained to ensure the existence of the H-level control problem. Finally, two numerical examples and simulation experiments are given to illustrate the effectiveness and feasibility of the proposed method. The stability analysis of the neutral-type mixed-time-delay LSs is not determined. The system not only includes real variable uncertainty and sector-bound non-linear terms, but also has a discrete and distributed time-delay. By constructing the appropriate LKF and efficient mathematical techniques, the stable condition of the low-conservative Rurod is derived. Finally, three numerical examples and simulation experiments are provided to show the feasibility and advantages of the obtained theoretical results. Time-delay feedback control design for synchronous Lurie Systems (CLSs). By introducing two adjustable real parameters, a new integral inequality is proposed, which can use the modified Wirtinger's integral inequality and the Jensen integral inequality as two special cases. By introducing an extended LKF, it fully considers the range of time-varying time-delay, and the time-delay-dependent synchronization criterion with less conservative property is established. Furthermore, based on the new nonlinear function, the ideal control gain matrix is successfully designed. Finally, two numerical examples and simulation experiments on the Chua's circuit system are given to show the feasibility and advantages of the designed method. The sampling control design for the time-delay CLSs synchronization. In this chapter, a new integral inequality is proposed to study the master-slave synchronization of the time-delay CLSs. First, it is assumed that the sampling interval is any bounded variable. A newly expanded LKF is constructed by taking full consideration of the information of the sampling interval and the non-linear function condition and the time-delay splitting method. Secondly, in order to obtain a small conservative synchronization criterion, a variable parameter is introduced, and a new integral inequality is established. Furthermore, a longer sampling period is obtained based on the double-integral Wirtinger-based integral inequality. Finally, the superiority and feasibility of the proposed method are verified by three numerical examples and numerical simulation. This chapter studies the design of the random sampling control of the master-slave synchronization of the CLS by a new method. First we assume that the probability of occurrence of the sampling interval is a fixed constant and the Bernoulli distribution is satisfied. In order to take full consideration of the information of the sampling interval, we introduce an improved LKF based on the improved Wirtinger integral inequality. Secondly, by using the new free-matrix integral inequality, a conservative and low-index homogeneous stability criterion is derived, which is used to analyze the corresponding error synchronization system. Furthermore, based on the above-described method, an ideal feedback gain matrix is successfully designed. Finally, three numerical examples and numerical simulation are used to illustrate the advantages and feasibility of the proposed method.
【學位授予單位】：電子科技大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TP13
本文編號：2406201
[Abstract]:Time delay (TD) phenomena are common in many practical engineering applications, such as aerospace, metallurgy, petrifaction, communication, power, biology, population and economy. Due to the wide application value of time-delay power system, many scholars at home and abroad are concerned. At the same time, time-delay is an important source of the instability, oscillation and even system performance of the power system. Therefore, the stability analysis and control design of the time-delay power system is a hot issue in the current research. How to master and apply the performance of time-delay power system is an important research subject. The neutral-type time-delay neural network (NNs), the distributed time-delay NNs, the hybrid time-delay NNs and the time-delay Lurie systems (Lurie Systems) are studied based on the Lyapunov-Krasovskii functional (LKF) theory, the Shur complement approach, the time-delay segmentation method, the inequality processing technique, the linear matrix inequality (LMIs), and the like. The stability analysis and control design of LSs. The main results of this study are as follows: 1. Stability analysis of neutral time-delay NNs. The improved time-delay-dependent stability criterion is derived by the construction of new LKF with triple integral and four-point integration. We fully consider the secondary convex combination method, the property of the secondary convex function and the information of the activation function, and further reduce the conservativeness of the result. Finally, four numerical examples and simulation experiments are provided to show the feasibility and superiority of the obtained theoretical results. Stability analysis of distributed time-delay NNs. The main idea in this chapter is to use a new integral inequality, which has been proved to be more conservative than that of the Johnson's inequality, because it fully considers the relationship between the various Leibniz-Newton formulas. A suitable LKF is constructed by adopting a more general time-delay segmentation method. Based on this new integral inequality and time-delay segmentation, the extended time-delay-dependent stability criterion is obtained. Finally, four numerical examples and simulation experiments are given to illustrate the effectiveness and superiority of the proposed method. Stability analysis of mixed time-delay NNs. By means of a multi-integral inequality, it can provide a better upper boundary than the Jensen's inequality, and set up a new stability criterion. Improved stability conditions are obtained by constructing an LKF that contains multiple products, which are presented in the form of LMIs. In addition, the distribution time-delay interval is divided into a plurality of inequalities subintervals, and a stable result with less conservative property is derived. Finally, three numerical examples and simulation experiments are given to show the feasibility and advantages of the obtained theoretical results. The H-type control design of the time-delay NNs. The main objective of this chapter is to design a valid H-controller, so that the closed-loop system is asymptotically stable under the condition of disturbance attenuation performance. A novel time-delay-dependent stability criterion is established by the introduction of the appropriate LKF and a more general time-delay segmentation method. Furthermore, by making full use of the improved Wirtinger's integral inequality, an improved sufficient condition is obtained to ensure the existence of the H-level control problem. Finally, two numerical examples and simulation experiments are given to illustrate the effectiveness and feasibility of the proposed method. The stability analysis of the neutral-type mixed-time-delay LSs is not determined. The system not only includes real variable uncertainty and sector-bound non-linear terms, but also has a discrete and distributed time-delay. By constructing the appropriate LKF and efficient mathematical techniques, the stable condition of the low-conservative Rurod is derived. Finally, three numerical examples and simulation experiments are provided to show the feasibility and advantages of the obtained theoretical results. Time-delay feedback control design for synchronous Lurie Systems (CLSs). By introducing two adjustable real parameters, a new integral inequality is proposed, which can use the modified Wirtinger's integral inequality and the Jensen integral inequality as two special cases. By introducing an extended LKF, it fully considers the range of time-varying time-delay, and the time-delay-dependent synchronization criterion with less conservative property is established. Furthermore, based on the new nonlinear function, the ideal control gain matrix is successfully designed. Finally, two numerical examples and simulation experiments on the Chua's circuit system are given to show the feasibility and advantages of the designed method. The sampling control design for the time-delay CLSs synchronization. In this chapter, a new integral inequality is proposed to study the master-slave synchronization of the time-delay CLSs. First, it is assumed that the sampling interval is any bounded variable. A newly expanded LKF is constructed by taking full consideration of the information of the sampling interval and the non-linear function condition and the time-delay splitting method. Secondly, in order to obtain a small conservative synchronization criterion, a variable parameter is introduced, and a new integral inequality is established. Furthermore, a longer sampling period is obtained based on the double-integral Wirtinger-based integral inequality. Finally, the superiority and feasibility of the proposed method are verified by three numerical examples and numerical simulation. This chapter studies the design of the random sampling control of the master-slave synchronization of the CLS by a new method. First we assume that the probability of occurrence of the sampling interval is a fixed constant and the Bernoulli distribution is satisfied. In order to take full consideration of the information of the sampling interval, we introduce an improved LKF based on the improved Wirtinger integral inequality. Secondly, by using the new free-matrix integral inequality, a conservative and low-index homogeneous stability criterion is derived, which is used to analyze the corresponding error synchronization system. Furthermore, based on the above-described method, an ideal feedback gain matrix is successfully designed. Finally, three numerical examples and numerical simulation are used to illustrate the advantages and feasibility of the proposed method.
【學位授予單位】：電子科技大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TP13
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