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|2 23/ger/20230216
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|a Lang, Norman.
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|a Numerical Methods for Large-Scale Linear Time-Varying Control Systems and Related Differential Matrix Equations.
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|a Berlin :
|b Logos Verlag Berlin,
|c 2018.
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|a 1 online resource (232 pages)
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|a text
|b txt
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|a 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.
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|a 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.
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|a 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.
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|a 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.
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|a 7 Conclusions and Outlook7.1 Summary and Conclusions; 7.2 Future Research Perspectives; A Fourth-Order Rosenbrock Method; Theses; Bibliography.
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|a Print version record.
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| 590 |
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|a ProQuest Ebook Central
|b Ebook Central Academic Complete
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|a Differential equations, Linear.
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|a Numerical methods for large-scale linear time-varying control systems and related differential Matrix equations (Text)
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|a Lang, Norman.
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|d Berlin : Logos Verlag Berlin, ©2018
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Wentworth
Institute of Technology