本文選題：非線性隨機(jī)控制系統(tǒng)　切入點：泊松過程　出處：《哈爾濱工業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來,基于伊藤型隨機(jī)微分或隨機(jī)差分方程建模的離散隨機(jī)動力系統(tǒng)一直都倍受人們的廣泛關(guān)注�，F(xiàn)實中,很多隨機(jī)現(xiàn)象和時間延遲都會不可避免的存在,而隨機(jī)干擾和延遲的出現(xiàn)對系統(tǒng)的穩(wěn)定性有很大的影響,因此,研究隨機(jī)延遲動力系統(tǒng)的穩(wěn)定性受到了越來越多學(xué)者的青睞。注意到,泊松過程能夠很好的描述跳躍隨機(jī)現(xiàn)象,于是,帶有泊松跳的離散延遲非線性隨機(jī)控制系統(tǒng)的穩(wěn)定性分析是一項值得深入研究的課題。本文主要研究幾類帶有泊松跳的離散延遲非線性隨機(jī)控制系統(tǒng)的穩(wěn)定性。值得注意的是,為了縮小計算成本,本文給出了一種新的有效處理泊松過程的方法,即補(bǔ)償法。文章具體研究內(nèi)容如下:首先研究了帶有泊松過程和離散時間延遲的非線性隨機(jī)控制系統(tǒng)的穩(wěn)定性。基于Lyapunov-Krasovskii泛函和線性矩陣不等式技巧,得出一些均方意義下的全局漸近穩(wěn)定性準(zhǔn)則。同時,給出了反饋控制矩陣的具體求解公式。數(shù)值算例驗證了理論結(jié)果的有效性。其次,考慮到系統(tǒng)的歷史會對現(xiàn)在的狀態(tài)產(chǎn)生影響,引入了另一種時間延遲—分布延遲。給出了帶有泊松過程和混合時間延遲離散非線性隨機(jī)控制系統(tǒng)的均方意義下的全局漸近穩(wěn)定性定理和求解反饋控制矩陣的公式。最后,由于隨機(jī)擾動的多樣性,在離散非線性隨機(jī)系統(tǒng)帶有泊松過程和混合延遲的基礎(chǔ)上,加入了布朗運(yùn)動。通過分析,證明了帶有混合時間延遲、泊松過程和布朗運(yùn)動兩種隨機(jī)擾動的離散非線性隨機(jī)系統(tǒng)的可控性,并用數(shù)值模擬加以說明了理論的有效性。
[Abstract]:In recent years, discrete stochastic dynamical systems based on Ito stochastic differential equations or stochastic difference equations have attracted much attention. In reality, many stochastic phenomena and time delays will inevitably exist. But the emergence of stochastic disturbance and delay have great influence on the stability of the system. Therefore, the study of the stability of stochastic delay dynamical system has attracted more and more scholars. It is noted that the Poisson process can well describe the jump stochastic phenomenon. So, The stability analysis of discrete delay nonlinear stochastic control systems with Poisson jump is a subject worth further study. This paper mainly studies the stability of some discrete delay nonlinear stochastic control systems with Poisson jump. In order to reduce the computational cost, a new and effective method for dealing with Poisson process is presented in this paper. The main contents of this paper are as follows: firstly, the stability of nonlinear stochastic control systems with Poisson process and discrete time delay is studied. Based on Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique, the stability of nonlinear stochastic control system with Poisson process and discrete time delay is studied. Some global asymptotic stability criteria in the mean square sense are obtained. At the same time, the concrete solution formulas of the feedback control matrix are given. Numerical examples verify the validity of the theoretical results. Considering that the history of the system will have an impact on the current state, Another time-delay distributed delay is introduced. The global asymptotic stability theorem for discrete nonlinear stochastic control systems with Poisson process and mixed time delay in the sense of mean square and the formula for solving the feedback control matrix are given. Because of the diversity of stochastic disturbances, the Brownian motion is added to the discrete nonlinear stochastic system with Poisson process and mixed delay. The controllability of discrete nonlinear stochastic systems with two stochastic perturbations of Poisson process and Brownian motion is demonstrated by numerical simulation.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O231

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