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

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 Control -- 3.2.1 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 Structure -- 4.3.2 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 Rule -- 6.1.4 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 Outlook -- 7.1 Summary and Conclusions -- 7.2 Future Research Perspectives -- A Fourth-Order Rosenbrock Method -- Theses -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.