| 1. |
- Jönsson, Ulf T., et al.
(författare)
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Analysis and computation of limit cycles for systems with separable nonlinearities
- 2008
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 69:12, s. 4674-4693
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Tidskriftsartikel (refereegranskat)abstract
- The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only a unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.
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| 2. |
- Kao, Chien-Ya, et al.
(författare)
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A New Barrier Function for IQC Optimization Problems
- 2003
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Ingår i: Proceedings of the American Control Conference. - 0743-1619. ; 5, s. 4281-4286
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a new barrier function for optimization problems with Integral Quadratic Constraints (IQCs). The new barrier function is used to construct an interior point algorithm which solves IQC optimization problems in a more efficient fashion. Numerical tests as well as worst-case computational complexity analysis are performed to evaluate the efficiency of the proposed algorithm.
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| 4. |
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| 7. |
- Megretski, Alexandre, et al.
(författare)
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Integral Quadratic Constraints
- 2010
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Ingår i: The Control Handbook, Second Edition. - 9781420073669 ; 1
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Bokkapitel (refereegranskat)
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| 12. |
- Sandberg, Henrik
(författare)
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Linear Time-Varying Systems: Modeling and Reduction
- 2002
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Linear time-invariant models are widely used in the control community. They often serve as approximations of nonlinear systems. For control purposes linear approximations are often good enough since feedback control systems are inherently robust to model errors. In this thesis some of the possibilities for linear time-varying modeling are studied. In the thesis it is shown that the balanced truncation procedure can be applied to reduce the order of linear time-varying systems. Many of the attractive properties of balanced truncation for time-invariant systems can be generalized into the time-varying framework. For example, it is shown that a truncated input-output stable system will be input-output stable, and computable simple worst-case error bounds are derived. The method is illustrated with model reduction of a nonlinear diesel exhaust catalyst model. It is also shown that linear time-periodic models can be used for analysis of systems with power converters. Power converters produce harmonics in the power grids and give frequency coupling that cannot be modeled with standard time-invariant linear models. With time-periodic models we can visualize the coupling and also use all the available tools for linear time-varying systems, such as balanced truncation. The method is illustrated on inverter locomotives.
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| 13. |
- Sou, Kin Cheong, et al.
(författare)
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A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction
- 2005
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Ingår i: 42nd Design Automation Conference, Proceedings 2005. ; , s. 933-938
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Konferensbidrag (refereegranskat)abstract
- In this paper an optimization based model order reduction (MOR) framework is proposed. The method involves setting up a quasiconvexprogram that explicitly minimizes a relaxation of the optimal H∞ norn MOR problem. The method generates guaranteedstable and passive reduced models and it is very flexible in imposingadditional constraints. The proposed optimization approach isalso extended to parameterized model reduction problem (PMOR).The proposed method is compared to existing moment matchingand optimization based MOR methods in several examples. APMOR model for a large RF inductor is also constructed.
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| 14. |
- Sou, Kin Cheong, et al.
(författare)
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A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction
- 2008
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Ingår i: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. - 0278-0070 .- 1937-4151. ; 27:3, s. 456-469
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, an optimization-based model orderreduction (MOR) framework is proposed. The method involvessetting up a quasi-convex program that solves a relaxation of theoptimal H∞ norm MOR problem. The method can generate guaranteedstable and passive reduced models and is very flexible inimposing additional constraints such as exact matching of specificfrequency response samples. The proposed optimization-basedapproach is also extended to solve the parameterized modelreductionproblem (PMOR). The proposed method is compared to existing moment matching and optimization-basedMOR methodsin several examples. PMOR models for large RF inductors oversubstrate and power-distribution grid are also constructed.
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| 15. |
- Sou, Kin Cheong, et al.
(författare)
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Bounding L2 Gain System Error Due to Approximations of the Nonlinear Vector Field
- 2007
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Ingår i: Proceedings of the IEEE Conference on Computer-Aided Design. ; , s. 879-886
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Konferensbidrag (refereegranskat)abstract
- Typical nonlinear model order reduction approachesneed to address two issues: reducing the order ofthe model, and approximating the vector field. In this paperwe focus exclusively on the second issue, and present resultscharacterizing the repercussions at the system level of vector fieldapproximations. The error assessment problem is formulatedas the L2 gain upper bounding problem of a scaled feedbackinterconnection. Applying the small gain theorem in the proposedsetup, we prove that the L2 gain of the error system is upperbounded by the L2 gain of the vector field approximationerror, provided it is small. In addition, the paper also presentsa numerical procedure, based on the IQC/LMI approach, toperform the error estimation task with less conservatism. Anumerical example is given in this paper to demonstrate thepractical implications of the presented results.
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| 16. |
- Sou, Kin Cheong, et al.
(författare)
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Convex Relaxation Approach to the Identification of the Wiener-Hammerstein Model
- 2008
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Ingår i: Proceedings of the 47th IEEE Conference on Decision and Control. ; , s. 1375-1382
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Konferensbidrag (refereegranskat)abstract
- In this paper, an input/output system identificationtechnique for the Wiener-Hammerstein model and its feedbackextension is proposed. In the proposed framework, the identificationof the nonlinearity is non-parametric. The identificationproblem can be formulated as a non-convex quadratic program(QP). A convex semidefinite programming (SDP) relaxation isthen formulated and solved to obtain a sub-optimal solution tothe original non-convex QP. The convex relaxation turns out tobe tight in most cases. Combined with the use of local search,high quality solutions to the Wiener-Hammerstein identificationcan frequently be found. As an application example, randomlygenerated Wiener-Hammerstein models are identified.
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