最佳控制與特徵值問題

1. Linear quadratic optimal Control (H_2-Control) Problems (time-invariant, continuous-time) 1.1 Equivalent conditions of optimal control problems and continuous-time algebraic Riccati equation (CAREs) 1.2 Controllability/observability and stabilizability/Detectability 1.3 Pole assignment problems 1.4 Continuous-time AREs 1.5 Hamiltonian eigenvalue problems 2. Linear quadratic optimal Control problems (Time-invariant, discrete-time) 2.1 Equivalent conditions of optimal control problems and discrete-time algebraic Riccati equations (DAREs) 2.2 Controllability/observability and stabilizability/Detectability 2.3 Discrete-time AREs 2.4 Symplectic generalized eigenvalue problems 3. Structure-preserving doubling algorithms (SDAs) 3.1 Two doubling algorithms for SF1/SF2 3.2 Palindromic matrix pairs/symplextic matrix pairs 3.3 Convergence analysis of doubling algorithms for regular case and critical case. 3.4 M-matrix algebraic Riccati equations (MAREs) 3.5 A two-phase doubling algorithm for critical singular MAREs 4. H_∞-controls (time-invariant, continuous-time) 4.1 Bounded real Lemma 4.2 Stabilizing solution and Riccati operators 4.3 How to design a H_∞-controller 4.4 State feedback central H_∞-controller 4.5 Full-information H_∞-cotroller 4.6 Messeasurement output feedback H_∞-controller 5. H_∞-controls(time-invariant, discrete-time) 5.1 Z-transform and its H_∞-norm 5.2 Bounded real Lemma 5.3 State feedback/output feedback H_∞-controllers 6. Applications of SOA algorithms 6.1 vibration of fast trains 6.2 Green’s function approach for nano research 6.3 Surface acoustic wave filtering problems 6.4 MARE from transportation theory and Markov modulated fluid queue theory 7. Lanczos Method 8. Arnoldi Method 9. Jacobi-Davidson Method

Calculus, Linear Algebra, Introduction to Computers and Programming, Numerical Analysis

作業 40%、期末報告40%、出席20%

Textbook: Lecture Notes of Matrix Computations, edited by Wen-Wei Lin. (http://jupiter.math.nctu.edu.tw/~wwlin/2010_lecture_note.pdf) References: (1) Scientific Computing: An Introductory Survey, Michael T. Heath, 2nd edition (2) Scientific Computing with Case Studies, Dianne P. O'Leary

地點

SA316