發(fā)布時(shí)間：2018-07-03 02:36

  本文選題：非線性系統(tǒng) + 隨機(jī)系統(tǒng)��； 參考：《曲阜師范大學(xué)》2016年博士論文

【摘要】：在實(shí)際系統(tǒng)中,非線性、時(shí)滯、外部隨機(jī)干擾等是普遍存在的.近幾年,一類高階非線性系統(tǒng)的控制設(shè)計(jì)問題得到了廣泛的研究,尤其對(duì)其有限時(shí)間的鎮(zhèn)定問題更成為目前的研究熱點(diǎn).本文針對(duì)幾類不同結(jié)構(gòu)的高階非線性(隨機(jī))系統(tǒng),研究了它們的控制器設(shè)計(jì)和穩(wěn)定性分析問題.主要研究成果包括:1.針對(duì)一類具有高、低階次非線性項(xiàng)的高階非線性系統(tǒng),研究了全局漸近輸出反饋鎮(zhèn)定問題.主要解決了以下問題:(i)非線性項(xiàng)不僅同時(shí)具有高階次和低階次,并且高、低階次同時(shí)被放寬到區(qū)間任意實(shí)數(shù).(ii)由于非線性項(xiàng)中高、低階次的一般性,符號(hào)函數(shù)被引入到控制器設(shè)計(jì)當(dāng)中.(iii)基于增加冪次積分,齊次占優(yōu)法和Lypunov穩(wěn)定性定理,系統(tǒng)的輸出反饋鎮(zhèn)定控制器被設(shè)計(jì)并且保證了閉環(huán)系統(tǒng)平衡點(diǎn)全局漸近穩(wěn)定性.2.對(duì)一類高階多時(shí)變時(shí)滯非線性系統(tǒng),研究了它的狀態(tài)反饋漸近鎮(zhèn)定問題.系統(tǒng)非線性項(xiàng)高、低階次的同時(shí)出現(xiàn)及其形式的一般,再加上多時(shí)變時(shí)滯的出現(xiàn)使得系統(tǒng)更具一般性.通過引入新的Lyapunov-Krasovskii(L-K)泛函,結(jié)合運(yùn)用增加冪次積分法和符號(hào)函數(shù),設(shè)計(jì)了一個(gè)全局狀態(tài)反饋漸近鎮(zhèn)定控制器.3.針對(duì)一類具有高、低階次非線性項(xiàng)的高階非線性下三角系統(tǒng),基于有限時(shí)間Lyapunov穩(wěn)定性定理,結(jié)合動(dòng)態(tài)增益法和增加冪次積分法,設(shè)計(jì)了一個(gè)具有動(dòng)態(tài)增益的全局有限時(shí)間鎮(zhèn)定控制器.4.針對(duì)一類高階非線性上三角系統(tǒng),研究了它的有限時(shí)間輸出反饋鎮(zhèn)定問題.根據(jù)齊次占優(yōu)法,在一組坐標(biāo)變換下,首先為標(biāo)稱系統(tǒng)設(shè)計(jì)一個(gè)輸出反饋控制器.然后通過構(gòu)造一個(gè)降階觀測(cè)器并確定觀測(cè)增益來得到完整系統(tǒng)的一個(gè)有限時(shí)間輸出反饋控制器.最后,通過分析和仿真舉例驗(yàn)證了有限時(shí)間輸出反饋鎮(zhèn)定控制器設(shè)計(jì)方案的有效性.5.研究了具有更弱非線性假設(shè)條件的高階隨機(jī)非線性系統(tǒng)的依概率有限時(shí)間鎮(zhèn)定問題.主要有兩方面的難點(diǎn):(i)去掉了系統(tǒng)非線性項(xiàng)的上界必須具有線性項(xiàng)的限制.(ii)理論分析了解的存在唯一性這一研究前提.6.研究了高階隨機(jī)非線性前饋系統(tǒng)的依概率有限時(shí)間鎮(zhèn)定問題.基于隨機(jī)Lyapunov有限時(shí)間穩(wěn)定性定理和齊次占優(yōu)法,通過構(gòu)造了一個(gè)2 Lyapunov函數(shù)以及驗(yàn)證解的存在唯一性,設(shè)計(jì)了一個(gè)連續(xù)依概率有限時(shí)間鎮(zhèn)定控制器.最后的仿真實(shí)例驗(yàn)證了設(shè)計(jì)方案的有效性.7.研究了高階隨機(jī)非線性前饋系統(tǒng)的依概率有限時(shí)間輸出反饋鎮(zhèn)定問題.基于隨機(jī)Lyapunov有限時(shí)間穩(wěn)定性定理和齊次占優(yōu)法,通過構(gòu)造了一個(gè)降階隨機(jī)觀測(cè)器以及驗(yàn)證解的存在唯一性,設(shè)計(jì)并分析了一個(gè)依概率有限時(shí)間輸出反饋鎮(zhèn)定控制器.
[Abstract]:In practical systems, nonlinearity, time delay and external random disturbances are common. In recent years, the control design problem of a class of high order nonlinear systems has been widely studied, especially the stabilization of its finite time has become a hot research topic. In this paper, the controller design and stability analysis of several kinds of high order nonlinear (stochastic) systems with different structures are studied. The main research results include: 1. The global asymptotically output feedback stabilization problem is studied for a class of high order nonlinear systems with high and low order subnonlinear terms. The following problems are solved: the (i) nonlinear term not only has high order and low order, but also high and low order, and is extended to the generality of high and low order. (ii) because of the nonlinear term. The sign function is introduced into the controller design based on the addition of power integral, homogeneous dominant method and Lyapunov stability theorem. The output feedback stabilization controller of the system is designed and guaranteed the global asymptotic stability of the closed-loop system equilibrium point. The problem of state feedback asymptotic stabilization for a class of high order nonlinear systems with multiple time-varying delays is studied. The system is more general because of its high nonlinear term, low order simultaneous occurrence and its form, plus the appearance of multiple time-varying delays. By introducing a new Lyapunov-Krasovskii (L-K) functional, a global state feedback asymptotic stabilization controller. For a class of high order nonlinear lower triangular systems with high and low order nonlinear terms, based on the Lyapunov stability theorem of finite time, the dynamic gain method and the power adding integral method are combined. A global finite time stabilization controller .4. with dynamic gain is designed. For a class of high order nonlinear upper triangular systems, the finite time output feedback stabilization problem is studied. According to the homogeneous dominant method, an output feedback controller is designed for the nominal system under a set of coordinate transformations. Then a finite time output feedback controller for the complete system is obtained by constructing a reduced order observer and determining the observation gain. Finally, the effectiveness of the design scheme of finite time output feedback stabilization controller is verified by an analysis and simulation example. In this paper, the problem of time-dependent stabilization for higher order stochastic nonlinear systems with weaker nonlinear assumptions is studied. There are two main difficulties: (i) removed the upper bound of the nonlinear term of the system must have the limit of the linear term of the existence and uniqueness of the. (ii) theoretical analysis solution. 6. The probabilistic finite time stabilization problem for high order stochastic nonlinear feedforward systems is studied. Based on the stochastic Lyapunov finite time stability theorem and homogeneous dominant method, a continuous time-dependent finite time stabilization controller is designed by constructing a 2Lyapunov function and verifying the existence and uniqueness of the solution. Finally, a simulation example is given to verify the effectiveness of the design. 7. The problem of output feedback stabilization based on probability finite time for high order stochastic nonlinear feedforward systems is studied. Based on the stochastic Lyapunov finite time stability theorem and homogeneous dominant method, a reduced order stochastic observer is constructed and the existence and uniqueness of the solution is verified. A feedback stabilization controller based on probability finite time output is designed and analyzed.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP13

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