非线性系统课程简介(麻省理工学院)

非线性系统课程简介(麻省理工学院) 課程描述 本課程主要講授的內容是非線性動力系統建模、 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 和設計等方面的現有方法，以及這些方法在控制方面 的實際應用。課程的主題包括: , 非線性現象 , 對非線性現象建模的數學語言 o 離散時間狀態空間方程組 o 基於流形的微分方程組 o 模型的輸入和輸出 o 有限自動機和混合系統 , 線性化 o 軌跡線附近的線性化 o 奇異攝動 o 諧波平衡 o 模型的降維 o 迴授的線性化 , 系統不變數 o 能量函數和李雅普諾夫函數 o 隱式定義的能量函數 o 李雅普諾夫函數的確定 , 微分方程組的局部特性 o 局部穩定性 o 中心流形定理 o 分岔 , 非線性微分方程組的可控性 o 弗洛比尼斯定理 o 迴授線性化的存在性 o 非線性系統的局部可控性 , 非線性迴授設計技術 o 李雅普諾夫函數的控制 o 迴授線性化:後退法，逆向動態法等 o 自適應控制 o 不變數概率密度函數 o 優化控制和動態規劃 預備知識:課程6.241或內容接近的課程 資訊資源和文獻 本年度不要求有課本，所有的資訊都會在講義中提供。 參考書包括由Prentice Hall出版社出版，Hassan K. Khalil著的《非線性系統》(Nonlinear Systems)， 以及另一本更深入的著作，即Springer出版社出版，Shankar Satry著的《非線性系統:分析，穩定性及 控制》(Nonlinear Systems: Analysis, Stability, and Control )。這兩本書均可以作為本課程的參考資料，包括了課程中沒有涉及的一些內容。 指導教師 Alexandre Megretski教授 課程安排 授課: 每週2節 每節1.5小時 作業 通常在星期三留作業，下一個星期三的上課時間收作業。授課教師將儘快對作業進行修改、打分和發回。在發回修改過的作業時將給出作業的答案。 我們非常鼓勵在做作業時結成不同的小組來討論，以得到盡可能好的答案。然而每個人必須獨立完成作業的文本(必要時還包括獨立完成的程式碼) MATLAB? 在某些作業中可能需用到MATLAB，即所謂「工程計算語言」。我們可能用到其中的Simulink，控制系統工具箱以及LMI控制工具箱。對於一些通用的資訊以及對系統進行仿真和分析時的具體命令，可以從線上幫助中獲得答案。 考核 在授課過程中包括兩次課外測驗，均需在24小時內完成和遞交，但沒有期末考試。這些測驗將涵蓋課程6.243J的所有知識(將盡可能地讓每次測驗占同樣的比重)。至少在測驗前兩周就將講到測驗內容所涉及的問題和解題思路。在這兩周的星期三不會交代作業。在課外測驗時不允許互相合作。 評分 在學期末將根據數位評分N給出學生的字母評分，N從如下公式中計算出: N=0.5*H+0.25*Q1+0.25*Q2 其中H是作業的平均分，Q1、Q2是兩次測驗的得分(H、Q1和Q2均在0和100之間取值)。根據全班同學得分N的分佈劃分恰當的等級來給出字母評分。對於那些接近不同等級間邊界的同學，將根據其他的因素(如努力程度、課堂 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 現等)來給出具體的分數。 Course Description This course studies state-of-the-art methods for modeling, analysis, and design of nonlinear dynamical systems with applications in control. Topics include: , Nonlinear Behavior , Mathematical Language for Modeling Nonlinear Behavior o Discrete Time State Space Equations o Differential Equations on Manifolds o Input/Output Models o Finite State Automata and Hybrid Systems , Linearization o Linearization Around a Trajectory o Singular Perturbations o Harmonic Balance o Model Reduction o Feedback Linearization , System Invariants o Storage Functions and Lyapunov Functions o Implicitly Defined Storage Functions o Search for Lyapunov Functions , Local Behavior of Differential Equations o Local Stability o Center Manifold Theorems o Bifurcations , Controllability of Nonlinear Differential Equations o Frobenius Theorem o Existence of Feedback Linearization o Local Controllability of Nonlinear Systems , Nonlinear Feedback Design Techniques o Control Lyapunov Functions o Feedback Linearization: Backstepping, Dynamic Inversion, etc. o Adaptive Control o Invariant Probability Density Functions o Optimal Control and Dynamic Programming Prerequisite: 6.241 or an equivalent course. Information Resources and Literature This year, there will be no required textbook. All necessary information will be supplied in the lecture notes. The books Nonlinear Systems by Hassan K. Khalil, published by Prentice Hall, and the more advanced Nonlinear Systems: Analysis, Stability, and Control by Shankar Sastry, published by Springer, can both serve as basic references on Nonlinear Systems Theory, frequently covering the topics skipped in the lectures. Instructor Prof. Alexandre Megretski Class Schedule Lectures: Two sessions / week 1.5 hours / session Homework Homework assignments are usually given on Wednesdays. Homework papers are to be submitted during the lecture hours on the following Wednesday. The homework will be corrected, graded, and returned as soon as possible. Solutions to the homework will be distributed when the corrected homework is returned. Team work on home assignments is strictly encouraged, as far as generating ideas and arriving at the best possible solution is concerned. However, you have to write your own solution texts (and your own code, when needed). MATLAB? MATLAB?, the "language of technical computing'', will be used in some assignments. We will need Simulink?, Control Systems, and LMI Control Toolboxes. You may wish to consult its online help for general information and for specific commands for simulating and analysing systems. Examinations There will be two take-home quizzes, to be completed and returned within 24 hours, but no final exam. The quizzes will cover the theory of 6.243J (divided as equally as possible). The questions will be based on the ideas used in the problem set solutions made available at least a week before the test. No homework will be given on the last Wednesdays before the quizzes. No cooperation is allowed on take-home quizzes. Grading The letter grade will be determined at the end of the semester from a numerical grade N, obtained from the formula N=0.5*H+0.25*Q1+0.25*Q2 where H is the average homework grade, and Q1, Q2 are quiz grades (H, Q1, Q2 are numbers between 0 and 100). From the distribution of N for the entire class, boundaries will be chosen to define letter grades. For students near the boundariesrades. For students near the boundaries, other factors may be taken into account to determine the letter grade, such as effort, classroom activity, etc.