Numerical Methods for Large-Scale Linear Time-Varying Control Systems and Related Differential Matrix Equations.

Numerical Methods for Large-Scale Linear Time-Varying Control Systems and Related Differential Matrix Equations.

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Bibliographic Details
Main Author: Lang, Norman
Format: Electronic eBook
Language:English
Published: Berlin : Logos Verlag Berlin, 2018.
Subjects:
Differential equations, Linear.
Online Access: Full text (Wentworth users only)
Local Note:ProQuest Ebook Central
Table of Contents:
  • Intro; 1 Introduction; 1.1 Motivation; 1.2 Outline of the Thesis; 1.3 Related own publications; 1.4 Used Software and Hardware; 2 Mathematical Basics; 2.1 Linear Systems and Optimal Control; 2.1.1 Basic Properties; 2.1.2 Related Matrix Equations; 2.1.3 Solution of the Algebraic Riccati Equation; 2.1.4 Solution of the Algebraic Lyapunov Equation; 2.1.5 Hamilton-Jacobi Theory; 2.2 Model Order Reduction of Linear Systems; 2.2.1 Balanced Truncation; 2.2.2 Interpolation-Based Model Order Reduction; 3 Optimal Control and Inverse Problems; 3.1 Inverse Problems.
  • 3.2 Finite-Time Tracking-Type Optimal Control3.2.1 Model Problem and LQR Design; 3.2.2 Solution of the Inhomogeneous Tracking Problem; 3.3 Numerical Experiments; 3.3.1 A Diffusion Problem on the Unit Square; 3.3.2 RealWorld Hollow Cylinder; 3.4 Summary and Conclusion; 4 Model Order Reduction of Linear Time-Varying Systems; 4.1 Model Order Reduction using LTI Model Approximations; 4.1.1 MOR for Switched Linear Systems; 4.1.2 MOR for Parametric LTI Systems; 4.2 Balanced Truncation for Linear Time-Varying Systems; 4.3 Numerical Experiments.
  • 4.3.1 Moving Load Problem: Machine Stand-Slide Structure4.3.2 BT for LTV Systems; 4.3.3 Time-Varying Rail Example; 4.4 Summary and Conclusion; 5 Time Integration Methods for Differential Matrix Equations; 5.1 Backward Differentiation Formulas; 5.2 Rosenbrock Methods; 5.3 Other Implicit Methods; 5.3.1 Midpoint Rule; 5.3.2 Trapezoidal Rule; 5.4 Peer Methods; 5.4.1 Implicit Peer Methods; 5.4.2 Rosenbrock-Type Peer Methods; 6 Efficient Solution of Large-Scale Differential Matrix Equations; 6.1 Classical Low-Rank Factorization; 6.1.1 Backward Differentiation Formulas; 6.1.2 Rosenbrock Methods.
  • 6.1.3 Midpoint Rule6.1.4 Trapezoidal Rule; 6.1.5 Peer Methods; 6.1.6 Limitation of the Classical Low-Rank Factorization; 6.2 Symmetric Indefinite Low-Rank Factorization; 6.2.1 Backward Differentiation Formulas; 6.2.2 Rosenbrock Methods; 6.2.3 Midpoint Rule; 6.2.4 Trapezoidal Rule; 6.2.5 Peer Methods; 6.3 Column Compression; 6.3.1 Classical Low-Rank Compression; 6.3.2 Classical Low-Rank Compression for Complex Data; 6.3.3 Symmetric Indefinite Compression; 6.4 Numerical Experiments; 6.4.1 Autonomous Control Systems; 6.4.2 Non-Autonomous Control Systems; 6.5 Summary and Conclusions.
  • 7 Conclusions and Outlook7.1 Summary and Conclusions; 7.2 Future Research Perspectives; A Fourth-Order Rosenbrock Method; Theses; Bibliography.

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