本文選題：隨機(jī)系統(tǒng) + LaSalle定理��； 參考：《南京理工大學(xué)》2016年博士論文

【摘要】：作為非線性系統(tǒng)的重要組成部分,非線性隨機(jī)系統(tǒng)因考慮了多種多樣的環(huán)境噪聲,已被廣泛應(yīng)用到電力系統(tǒng)、通信系統(tǒng)等實(shí)際工程領(lǐng)域,并且在這些領(lǐng)域中發(fā)揮出了十分重要的作用.此外,由于隨機(jī)干擾的復(fù)雜性,使得對(duì)隨機(jī)系統(tǒng)的分析與控制比確定性情形更加困難、更加復(fù)雜.因此,研究非線性隨機(jī)系統(tǒng)的穩(wěn)定性分析與控制器設(shè)計(jì)是一項(xiàng)具有非常重要的理論意義和實(shí)際應(yīng)用價(jià)值的研究課題.本文針對(duì)幾類重要的非線性隨機(jī)系統(tǒng),基于時(shí)變控制方法、自適應(yīng)控制方法、隨機(jī)LaSalle定理、隨機(jī)Lyapunov-Krasovskii泛函穩(wěn)定理論和多Lyapunov函數(shù)技術(shù)等理論方法,深入研究了反饋控制器設(shè)計(jì)以及穩(wěn)定性分析問題,提出了有效的控制策略,獲得了新的穩(wěn)定性判定條件.本文的主要研究工作包括:1.針對(duì)一類具有未知增長(zhǎng)速率的隨機(jī)上三角系統(tǒng),研究了基于時(shí)變控制方法的狀態(tài)反饋控制問題.首先,通過引入廣義弱正定函數(shù),給出LaSalle定理的推廣形式.其次,采取時(shí)變方法而非自適應(yīng)技術(shù)抑制了不確定增長(zhǎng)速率的影響,并結(jié)合Backstepping技術(shù)給出了狀態(tài)反饋控制器設(shè)計(jì)方法.最后,利用LaSalle定理,證明了閉環(huán)系統(tǒng)具有全局唯一解并且解過程幾乎必然收斂到零.2.針對(duì)一類大規(guī)模隨機(jī)高階上三角時(shí)滯系統(tǒng),研究了分散狀態(tài)反饋控制問題.結(jié)合Backstepping方法和增加冪次積分技術(shù),設(shè)計(jì)了分散無記憶狀態(tài)反饋控制器.利用Lyapunov-Krasovskii穩(wěn)定性理論,證明了閉環(huán)系統(tǒng)的隨機(jī)全局漸近穩(wěn)定性.提供的仿真算例驗(yàn)證了設(shè)計(jì)方法的有效性.3.針對(duì)一類大規(guī)模非線性隨機(jī)時(shí)滯系統(tǒng),研究了分散自適應(yīng)輸出反饋控制問題.首先設(shè)計(jì)濾波器以估計(jì)不可測(cè)狀態(tài),在此基礎(chǔ)上通過使用Backstepping技術(shù),逐步設(shè)計(jì)出無記憶的虛擬控制信號(hào)和實(shí)際控制器.通過引入四次Lyapunov函數(shù),利用LaSalle定理證明了閉環(huán)系統(tǒng)的所有信號(hào)幾乎必然有界并且系統(tǒng)狀態(tài)幾乎必然收斂到零.提供的仿真算例驗(yàn)證了設(shè)計(jì)方法的有效性.4.研究了帶有隨機(jī)脈沖的非線性隨機(jī)系統(tǒng)的噪聲輸入狀態(tài)穩(wěn)定和全局漸近穩(wěn)定性.所考慮的隨機(jī)噪聲具有有限的二階矩,并且隨機(jī)脈沖是由一列隨機(jī)變量決定的脈沖浮動(dòng).首先,給出了保證系統(tǒng)具有全局唯一解的一般判定條件.基于此,當(dāng)連續(xù)動(dòng)態(tài)是穩(wěn)定的而脈沖序列消穩(wěn)時(shí),利用平均脈沖區(qū)間方法,提出了此類系統(tǒng)的噪聲輸入狀態(tài)穩(wěn)定和全局漸近穩(wěn)定的判據(jù).然后,當(dāng)連續(xù)動(dòng)態(tài)是不穩(wěn)定的而脈沖序列起鎮(zhèn)定作用時(shí),利用逆平均脈沖區(qū)間方法,給出了使得系統(tǒng)噪聲輸入狀態(tài)穩(wěn)定和全局漸近穩(wěn)定的充分條件.最后,通過仿真算例驗(yàn)證了以上理論.5.研究了具有二階矩隨機(jī)過程的切換隨機(jī)系統(tǒng)的穩(wěn)定性問題.首先,建立了系統(tǒng)具有全局唯一解的充分條件.其次,針對(duì)一類隨機(jī)切換信號(hào),考慮了系統(tǒng)的噪聲輸入狀態(tài)穩(wěn)定性.然后,采用平均駐留時(shí)間方法研究了系統(tǒng)的噪聲輸入狀態(tài)穩(wěn)定和全局漸近穩(wěn)定.關(guān)于解的存在性以及系統(tǒng)的穩(wěn)定性判定法則均以多Lyapunov函數(shù)的形式給出.最后,提供的仿真算例驗(yàn)證了理論結(jié)果的正確性.6.研究了具有二階矩隨機(jī)過程的隨機(jī)馬爾科夫跳變系統(tǒng)的穩(wěn)定性及跟蹤控制問題.與已有的文獻(xiàn)不同,隨機(jī)馬爾科夫跳變系統(tǒng)的解的存在與唯一性并未作為先驗(yàn)信息給出,而是通過一般條件保證其成立.然后,利用Lyapunov函數(shù)方法研究了系統(tǒng)的噪聲輸入狀態(tài)穩(wěn)定性以及解的有界性.最后,借助得到的結(jié)論研究了輸出跟蹤問題,給出了狀態(tài)反饋跟蹤控制器的設(shè)計(jì)過程,證明了輸出信號(hào)能夠漸近跟蹤給定的參考信號(hào),并通過仿真結(jié)果驗(yàn)證了所提設(shè)計(jì)方法的有效性.
[Abstract]:As an important part of nonlinear systems, nonlinear stochastic systems have been widely used in practical engineering fields, such as power systems, communication systems, and other practical engineering fields, because of their consideration of various environmental noises. In addition, the analysis of random systems is made due to the complexity of random interference. It is more difficult and more complex than control. Therefore, the study of stability analysis and controller design for nonlinear stochastic systems is a research subject with very important theoretical significance and practical application value. This paper is based on several kinds of important nonlinear stochastic systems, based on time-varying control method and adaptive control method. The stochastic LaSalle theorem, the stochastic Lyapunov-Krasovskii functional stability theory and the multi Lyapunov function technique are used to study the design of the feedback controller and the stability analysis. The effective control strategy is proposed and the new stability criteria are obtained. The main research work of this paper includes 1. for a class of unknown variables. The problem of state feedback control based on time-varying control method is studied. First, by introducing generalized weak positive definite function, the generalized form of LaSalle theorem is given. Secondly, the effect of time-varying method and non adaptive technology is taken to restrain the influence of uncertain growth rate, and the form of Backstepping is given. In the end, using the LaSalle theorem, it is proved that the closed loop system has a global unique solution and the solution process is almost bound to converge to zero.2. for a class of large-scale random high order upper triangular time-delay systems. The decentralized state feedback control problem is studied. Combined with the Backstepping method and the power integration technique, the design is designed. The decentralized feedback controller is distributed. Using the Lyapunov-Krasovskii stability theory, the stochastic global asymptotic stability of the closed loop system is proved. The simulation example shows that the effectiveness of the design method.3. is used to study the decentralized adaptive output feedback control problem for a class of large-scale nonlinear stochastic time-delay systems. First, the design of the decentralized adaptive output feedback control problem is designed. The filter is used to estimate the unmeasurable state, and on this basis, by using the Backstepping technology, the memory free virtual control signal and the actual controller are gradually designed. By introducing the four Lyapunov functions, the LaSalle theorem is used to prove that all the signals of the closed loop system are almost bound and the state of the system almost inevitably converges to zero. The simulation example verifies the effectiveness of the design method.4. to study the stability and global asymptotic stability of the noise input state of a nonlinear stochastic system with random pulses. The random noise considered has a finite two order moment, and the random pulse is a pulse floating by a random variable. First, the guarantee system is given. Based on this, a criterion for the stability and global asymptotic stability of the noise input state of this kind of system is proposed by means of the mean pulse interval method when the continuous dynamic is stable and the pulse sequence is stable. Then, when the continuous dynamic is unstable and the pulse sequence plays a stabilizing effect, the inverse mean is used. The sufficient conditions for the stability of the system noise input state and the global asymptotic stability are given by the pulse interval method. Finally, the stability problem of the switched random system with two order moment random processes is studied by the simulation example. First, the sufficient conditions for the system with a global unique solution are established. Secondly, the problem is given. The stability of the system noise input state is considered for a class of random switching signals. Then, the state stability and global asymptotic stability of the noise input state are studied by means of the mean standing time method. The existence of the solution and the stability determination rule of the system are given in the form of multiple Lyapunov functions. Finally, the simulation example is provided. The correctness of the theoretical results.6. is given to study the stability and tracking control of a stochastic Markoff jump system with two order moment random processes. Unlike the existing literature, the existence and uniqueness of the solution of the stochastic Markoff jump system are not given as a priori information, but are guaranteed by the general conditions. The Lyapunov function method is used to study the stability of the noise input state and the boundedness of the solution. Finally, the output tracking problem is studied with the help of the obtained conclusion. The design process of the state feedback tracking controller is given. It is proved that the output signal can asymptotically track the given reference signal, and the simulation results verify the proposed design. The effectiveness of the method is calculated.

【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O211.6;O231

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