| 1. |
- Hansson, Anders, et al.
(författare)
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Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
- 2003
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Ingår i: Proceedings of the 4th IFAC symposium on Robust Control Design. - Linköping : Linköping University Electronic Press. - 9780080440125
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 2. |
- Hansson, Anders, et al.
(författare)
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Efficient Implementations of Interior-Point Methods for Integral Quadratic Constraints
- 2001
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Ingår i: Proceedings of the Fourth SIAM Conference on Linear Algebra in Signals, Systems and Control.
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 3. |
- Hansson, Jörgen, et al.
(författare)
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Clearance of Flight Control Laws for Time-Varying Parameters
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 4. |
- Henrion, Didier, et al.
(författare)
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Reduced LMIs for Fixed-Order Polynomial Controller Design
- 2004
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Ingår i: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems. - 9056825178
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 5. |
- Ljung, Lennart, 1946-, et al.
(författare)
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An Iterative Method for Identification of ARX Models from Incomplete Data
- 2000
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Ingår i: Proceedings of the 39th IEEE Conference on Decision and Control. - Linköping : IEEE. - 0780366387 ; , s. 203-208 vol.1
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 6. |
- Ståhl Gunnarsson, Karin, et al.
(författare)
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Clearance of Flight Control Laws using Linear Fractional Transformations
- 2004
-
Ingår i: Proceedings of the 2004 AIAA Guidance, Navigation and Control Conference and Exhibit. - Reston, Virigina : American Institute of Aeronautics and Astronautics. - 9781624100734
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 7. |
- Wallin, Ragnar, et al.
(författare)
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A Decomposition Approach for Solving KYP-SDPs
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 8. |
- Wallin, Ragnar, et al.
(författare)
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Efficient Solution of Semidefinite Programs for Analysis of Gain Scheduled Controllers
- 2002
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Ingår i: Proceedings of the 2002 SIAM Conference on Optimization.
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 9. |
- Wallin, Ragnar, et al.
(författare)
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Efficiently Solving Semidefinite Programs Originating from the KYP Lemma using Standard Primal-Dual Solvers
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 10. |
- Wallin, Ragnar, 1962-, et al.
(författare)
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KYPD : A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma
- 2004
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Ingår i: Proceedings of the 2004 IEEE International Symposium on Computer Aided Control System Design. - Linköping : Linköping University Electronic Press. - 0780386361 ; , s. 1-6
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Konferensbidrag (refereegranskat)abstract
- 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.
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