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  • 1.
    Garulli, Andrea
    et al.
    University of Siena, Italy.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Khoshfetrat Pakazad, Sina
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Masi, Alfio
    University of Siena, Italy.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust Finite-Frequency H2 Analysis of Uncertain Systems2011Report (Other academic)
    Abstract [en]

    In many applications, design or analysis is performed over a finite frequency range of interest. The importance of the H2/robust H2 norm highlights the necessity of computing this norm accordingly. This paper provides different methods for computing upper bounds on the robust finite-frequency H2 norm for systems with structured uncertainties. An application of the robust finite-frequency H2 norm for a comfort analysis problem of an aero-elastic model of an aircraft is also presented.

  • 2.
    Garulli, Andrea
    et al.
    Dipartimento di Ingegneria dell'Informazione Universita' degli Studi di Siena, Italy.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Khoshfetrat Pakazad, Sina
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Masi, Alfio
    Dipartimento di Ingegneria dell'Informazione Universita' degli Studi di Siena, Italy.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust finite-frequency H2 analysis of uncertain systems with application to flight comfort analysis2013In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 21, no 6, p. 887-897Article in journal (Refereed)
    Abstract [en]

    In many applications, design or analysis is performed over a finite-frequency range of interest. The importance of the H2 norm highlights the necessity of computing this norm accordingly. This paper provides different methods for computing upper bounds of the robust finite-frequency H2 norm for systems with structured uncertainties. An application of the robust finite-frequency H2 norm for a comfort analysis problem of an aero-elastic model of an aircraft is also presented.

  • 3.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Efficient Implementations of Interior-Point Methods for Integral Quadratic Constraints2001In: Proceedings of the Fourth SIAM Conference on Linear Algebra in Signals, Systems and Control, 2001Conference paper (Refereed)
    Abstract [en]

    We describe two strategies for exploiting structure in implementations of interior-point methods for the semidefinite programs (SDPs) that result from integral quadratic constraints. The first approach uses inexact search directions computed by the conjugate gradient algorithm. In the second approach we solve the problem via the dual. Simplifying the dual problem results in an SDP that has fewer variables (O(n)) than the primal SDP (O(n2) variables), and that can be solved efficiently using standard methods.

  • 4.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Maximum Likelihood Estimation of Gaussian Models with Missing Data: Eight Equivalent Formulations2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 9, p. 1955-1962Article in journal (Refereed)
    Abstract [en]

    In this paper we derive the maximum likelihood problem for missing data from a Gaussian model. We present in total eight different equivalent formulations of the resulting optimization problem, four out of which are nonlinear least squares formulations. Among these formulations are also formulations based on the expectation-maximization algorithm. Expressions for the derivatives needed in order to solve the optimization problems are presented. We also present numerical comparisons for two of the formulations for an ARMAX model.

  • 5.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Vandenberghe, Lieven
    University of California, CA, USA.
    Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints2003In: Proceedings of the 4th IFAC symposium on Robust Control Design, 2003Conference paper (Refereed)
    Abstract [en]

    As the semidefinite programs that result from integral quadratic contstraints are usually large it is important to implement efficient algorithms. The interior-point algorithms in this paper are primal-dual potential reduction methods and handle multiple constraints. Two approaches are made. For the first approach the computational cost is dominated by a least-squares problem that has to be solved in each iteration. The least squares problem is solved using an iterative method, namely the conjugate gradient method. The computational effort for the second approach is dominated by forming a linear system of equations. This systems of equations is used to compute the search direction in each iteration. If the number of variables are reduced by solving a smaller subproblem the resulting system has a very nice structure and can be solved efficiently. The first approach is more efficient for larger problems but is not as numerically stable.

  • 6.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Vandenberghe, Lieven
    University of California, CA, USA.
    Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints2003Report (Other academic)
    Abstract [en]

    As the semidefinite programs that result from integral quadratic contstraints are usually large it is important to implement efficient algorithms. The interior-point algorithms in this paper are primal-dual potential reduction methods and handle multiple constraints. Two approaches are made. For the first approach the computational cost is dominated by a least-squares problem that has to be solved in each iteration. The least squares problem is solved using an iterative method, namely the conjugate gradient method. The computational effort for the second approach is dominated by forming a linear system of equations. This systems of equations is used to compute the search direction in each iteration. If the number of variables are reduced by solving a smaller subproblem the resulting system has a very nice structure and can be solved efficiently. The first approach is more efficient for larger problems but is not as numerically stable.

  • 7.
    Hansson, Jörgen
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ståhl-Gunnarsson, Karin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Karlsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Clearance of Flight Control Laws for Time-Varying Parameters2003Report (Other academic)
    Abstract [en]

    In this article exponential stability of the closed loop for the Saab AB VEGAS model controlled by a gain-scheduled linear fractional transformation controller is investigated for time-varying Mach-number. The analysis is based on parameter-dependent Lyapunov-functions which are obtained by investigating feasibility of linear matrix inequalities.

  • 8.
    Harju, Janne
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Utilizing low rank properties when solving KYP-SDPs2006Report (Other academic)
    Abstract [en]

    Semidefinite programs and especially those derived from the Kalman-Yakubovich- Popov lemma are quite common in control applications. KYPD is a dedicated solver for KYP-SDPs. It solves the optimization problem via the dual SDP. The solver is iterative. In each step a Hessian is formed and a linear system of equations is solved. The calculations can be performed much faster if we utilize sparsity and low rank structure. We show how to transform a dense optimization problem into a sparse one with low rank structure. A customized calculation of the Hessian is presented and investigated

  • 9.
    Harju, Janne
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Utilizing Low Rank Properties when Solving KYP-SDPs2006In: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, p. 5150-5155Conference paper (Refereed)
    Abstract [en]

    Semidefinite programs and especially those derived from the Kalman-Yakubovich-Popov lemma are quite common in control applications. KYPD is a dedicated solver for KYP-SDPs. It solves the optimization problem via the dual SDP. The solver is iterative. In each step a Hessian is formed and a linear system of equations is solved. The calculations can be performed much faster if we utilize sparsity and low rank structure. We show how to transform a dense optimization problem into a sparse one with low rank structure. A customized calculation of the Hessian is presented and investigated.

  • 10.
    Henrion, Didier
    et al.
    Czech Technical University, Czech Republic.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Reduced LMIs for Fixed-Order Polynomial Controller Design2004In: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, 2004Conference paper (Refereed)
    Abstract [en]

    A reduction procedure based on semidefinite programming duality is applied to LMI conditions for fixed-order scalar linear controller design in the polynomial framework. It is namely shown that the number of variables in the reduced design LMI is equal to the difference between the open-loop plant order and the desired controller order. A standard linear system of equations must then be solved to retrieve the controller parameters. Therefore high computational load is not necessarily expected when the number of controller parameters is large, but rather when a large number of plant parameters are to be controlled with a small number of controller paramters. Tailored interior-point algorithms dealing with the specific structure of the reduced design LMI are also discussed.

  • 11.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Isaksson, Alf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An Iterative Method for Identification of ARX Models from Incomplete Data2000In: Proceedings of the 39th IEEE Conference on Decision and Control, IEEE , 2000, p. 203-208 vol.1Conference paper (Refereed)
    Abstract [en]

    This paper describes a very simple and intuitive algorithm to estimate parameters of ARX models from incomplete data sets. An iterative scheme involving two least squares steps and a bias correction is all that is needed.

  • 12.
    Ståhl Gunnarsson, Karin
    et al.
    Saab AB, Sweden.
    Hansson, Jörgen
    Saab AB, Sweden.
    Karlsson, Fredrik
    Saab AB, Sweden.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Clearance of Flight Control Laws using Linear Fractional Transformations2004In: Proceedings of the 2004 AIAA Guidance, Navigation and Control Conference and Exhibit, 2004Conference paper (Refereed)
    Abstract [en]

    The problem of flight clearance of linear stability requirements in the complete flight evelope is studied. The approach is to use mu-analysis of linear fractional transformations description of the system dynamics augmented with an uncertainty model of the clearance criteria. Two methods to derive the linear fractional transformations are used and compared: the Trends and Bands method and rational approximations. The two approaches are applied to a UAV demostrator model. The resulting models are analyzed by mu-sensitivites in order to demonstrate how this can be used to reduce the order of the linear fractional transformations description. A number of algorithms to compute upper and lower bounds on mu are also compared. Results from applying the clearance criteria to the UAV demonstrator model are given.

  • 13.
    Vandenberghe, Lieven
    et al.
    University of California, Los Angeles, USA.
    Balakrishnan, Venkataramanan
    Purdue University, Richmond, IN, USA.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Roh, Tae
    University of California, Los Angeles, USA.
    Interior-Point Algorithms for Semidefinite Programming Problems Derived from the KYP Lemma2005In: Positive Polynomials in Control / [ed] Henrion, Didier, Garulli, Andrea, Springer Berlin/Heidelberg, 2005, p. 195-238Chapter in book (Refereed)
    Abstract [en]

    We discuss fast implementations of primal-dual interior-point methods for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, a class of problems that are widely encountered in control and signal processing applications. By exploiting problem structure we achieve a reduction of the complexity by several orders of magnitude compared to general-purpose semidefinite programming solvers.

  • 14.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    User's Guide to Kypd_Solver2003Report (Other academic)
    Abstract [en]

    This package contains software for solving semidefinite programs (SDPs) originating from the Kalman-Yakubovich-Popov lemma. A presentation of the software is given and the options included are presented and described.

  • 15.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Efficient Solution of Semidefinite Programs for Analysis of Gain Scheduled Controllers2002In: Proceedings of the 2002 SIAM Conference on Optimization, 2002Conference paper (Refereed)
    Abstract [en]

    Gain scheduling is a very powerful control methodology for systems with time varying parameters. The only requirement is that the process dynamics can be predicted. Often, analysis of a system controlled by again scheduled controller results in solving extremely large optimization problems involving linear matrix inequalities (LMIs) as constraints. Standard algorithms for solving these so called semidefinite programs (SDPs) cannot handle problems of the size commonly encountered in applications. However, the LMIs have a very special structure. If this structure is exploited and is combined with an interior-point method for solving the SDP a very efficient algorithm results.

  • 16.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    KYPD: A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma2004In: Proceedings of the 2004 IEEE International Symposium on Computer Aided Control System Design, 2004, p. 1-6Conference paper (Refereed)
    Abstract [en]

    Semidenite programs derived from the Kalman-Yakubovich-Popov lemma are quite common in control and signal processing applications. The programs are often of high dimension making them hard or impossible to solve with general-purpose solvers. KYPD is a customized solver for KYP-SDPs that utilizes the inherent structure of the optimization problem thus improving efficiency signicantly.

  • 17.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    KYPD: A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma2004Report (Other academic)
    Abstract [en]

    Semidenite programs derived from the Kalman-Yakubovich-Popov lemma are quite common in control and signal processing applications. The programs are often of high dimension making them hard or impossible to solve with general-purpose solvers. KYPD is a customized solver for KYP-SDPs that utilizes the inherent structure of the optimization problem thus improving efficiency signicantly.

  • 18.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Maximum likelihood estimation of linear SISO models subject to missing output data and missing input data2014In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 87, no 11, p. 2354-2364Article in journal (Refereed)
    Abstract [en]

    In this paper we describe an approach to maximum likelihood estimation of linear single input single output (SISO) models when both input and output data are missing. The criterion minimised in the algorithms is the Euclidean norm of the prediction error vector scaled by a particular function of the covariance matrix of the observed output data. We also provide insight into when simpler and in general sub-optimal schemes are indeed optimal. The algorithm has been prototyped in MATLAB, and we report numerical results that support the theory.

  • 19.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Decomposition Approach for Solving KYP-SDPs2004Report (Other academic)
    Abstract [en]

    Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm is applied to the problem to improve efficiency.

  • 20.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Harju Johansson, Janne
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Structure Exploiting Preprocessor for Semidefinite Programs Derived From the Kalman-Yakubovich-Popov Lemma2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 4, p. 697-704Article in journal (Refereed)
    Abstract [en]

    Semidefinite programs derived from the Kalman-Yakubovich-Popov (KYP) lemma are quite common in control and signal processing applications. The programs are often of high dimension which makes them hard or impossible to solve with general-purpose solvers. Here we present a customized preprocessor, KYPD, that utilizes the inherent structure of this particular optimization problem. The key to an efficient implementation is to transform the optimization problem into an equivalent semidefinite program. This equivalent problem has much fewer variables and the matrices in the linear matrix inequality constraints are of low rank. KYPD can use any primal-dual solver for semidefinite programs as an underlying solver.

  • 21.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Vandenberghe, Lieven
    University of California, CA, USA.
    Efficiently Solving Semidefinite Programs Originating from the KYP Lemma using Standard Primal-Dual Solvers2003Report (Other academic)
    Abstract [en]

    Semidefinite programs (SDPs) originating from the Kalman-Yakubovich-Popov lemma often have a large number of variables. Standard solvers for semidefinite programs cannot handle problems of this size. Much research has been invested in developing customized solvers for such problems. In this paper we show that it is possible to use standard primal-dual SDP solvers if we reduce the number of variables in the dual SDP. The interesting variables in the primal SDP can be recovered from the solution.

  • 22.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Vandenberghe, Lieven
    UCLA, CA, USA.
    Balakrishnan, V. Ragu
    Purdue University, IN, USA.
    On the Implementation of Primal-Dual Interior-Point Methods for Semidefinite Programming Problems Derived from the KYP Lemma2003In: Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, p. 4658-4663 vol.5Conference paper (Refereed)
    Abstract [en]

    We discuss fast implementations of primal-dual interior-point methods for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, a class of problems that are widely encountered in control and signal processing applications. By exploiting problem structure we achieve a reduction of the complexity by several orders of magnitude compared to general-purpose semidefinite programming solvers.

  • 23.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Harju, Janne
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    User's Guide to Kypd_Solver2006Report (Other academic)
    Abstract [en]

    This package contains software for solving semidefinite programs (SDPs) originating from the Kalman-Yakubovich-Popov lemma. A presentation of the software is given and the options included are presented and described.

  • 24.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Isaksson, Alf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An Iterative Method for Identification of ARX Models from Incomplete Data2000Report (Other academic)
    Abstract [en]

    This paper describes a very simple and intuitive algorithm to estimate parameters of ARX models from incomplete data sets. An iterative scheme involving two least squares steps and a bias correction is all that is needed.

  • 25.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Kao, Chung-Yao
    University of Melbourne, Australia.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Cutting Plane Method for Solving KYP-SDPs2006Report (Other academic)
    Abstract [en]

    Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. To this end structure exploiting algorithms have been proposed, based on the dual formulation. In this paper a cutting plane algorithm is proposed. In a comparison with a general purpose solver and a structure exploiting solver it is shown that the cutting plane based solver can handle optimization problems of much higher dimension.

  • 26.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Kao, Chung-Yao
    University of Melbourne, Australia.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Cutting Plane Method for Solving KYP-SDPs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 2, p. 418-429Article in journal (Refereed)
    Abstract [en]

    Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. To this end structure exploiting algorithms have been proposed, based on the dual formulation. In this paper a cutting plane algorithm is proposed. In a comparison with a general purpose solver and a structure exploiting solver it is shown that the cutting plane based solver can handle optimization problems of much higher dimension.

  • 27.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Kao, Chung-Yao
    University of Melbourne, Australia.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Decomposition Approach for Solving KYP-SDPs2005In: Proceedings of the 16th IFAC World Congress, 2005, p. 1021-1021Conference paper (Refereed)
    Abstract [en]

    Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm is applied to the problem to improve efficiency.

  • 28.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Khoshfetrat Pakazad, Sina
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Garuli, Andrea
    Università di Siena, Italy.
    Masi, Alfio
    Università di Siena, Italy.
    Applications of IQC-Based Analysis Techniques for Clearance2012In: Optimization Based Clearance of Flight Control Laws: A Civil Aircraft Application / [ed] Andreas Varga, Anders Hansson and Guilhem Puyou, Springer Berlin/Heidelberg, 2012, p. 277-297Chapter in book (Refereed)
    Abstract [en]

    Results for stability analysis of the nonlinear rigid aircraft model and comfort and loads analysis of the integral aircraft model are presented in this chapter. The analysis is based on the theory for integral quadratic constraints and relies on linear fractional representations (LFRs) of the underlying closed-loop aircraft models. To alleviate the high computational demands associated with the usage of IQC based analysis to large order LFRs, two approaches have been employed aiming a trade-off between computational complexity and conservatism. First, the partitioning of the flight envelope in several smaller regions allows to use lower order LFRs in the analysis, and second, IQCs with lower computational demands have been used whenever possible. The obtained results illustrate the applicability of the IQCs based analysis techniques to solve highly complex analysis problems with an acceptable level of conservativeness.

  • 29.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Masi, Alfio
    University of Siena, Italy.
    Garulli, Andrea
    University of Siena, Italy.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust Finite-Frequency H2 Analysis2010In: Proceedings of the 49th IEEE Conference on Decision and Control, 2010, p. 6876-6881Conference paper (Refereed)
    Abstract [en]

    Finite-frequency H2 analysis is relevant to a number of problems in which a priori information is available on the frequency domain of interest. This paper addresses the problem of analyzing robust finite-frequency H2 performance of systems with structured uncertainties. An upper bound on this measure is provided by exploiting convex optimization tools for robustness analysis and the notion of finite-frequency Gramians. An application to a comfort analysis problem for an aircraft aeroelastic model is presented.

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