| 1. |
- Axehill, Daniel, et al.
(författare)
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A Preprocessing Algorithm for MIQP Solvers with Applications to MPC
- 2004
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Ingår i: Proceeding of Reglermöte 2004. - Linköping : Linköping University Electronic Press. ; , s. 2497-2502
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this paper a preprocessing algorithm for unconstrained mixed integer quadratic programming problems and binary quadratic programming problems is presented. The algorithm applies to problems with certain properties, which are further described in the paper. When the algorithm is applied to a problem with these properties, the optimal value for some or all integer variables can be computed without approximations in polynomial time. The algorithm is first derived for the binary quadratic programming problem and the result is then extended to the mixed integer quadratic programming problem by transforming the latter problem into the first problem. Both mentioned quadratic programming problems have several important applications. In this paper, the focus is on model predictive control problems with both real-valued and binary control signals. As an illustration of the method, the algorithm is applied to two different problems of this type.
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| 2. |
- Enqvist, Martin, 1976-, et al.
(författare)
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The CDIO Initiative from an Automatic Control Project Course Perspective
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The CDIO (Conceive Design Implement Operate) Initiative is explained, and some of the results at the Applied Physics and Electrical Engineering program at Linköping University, Sweden, are presented. A project course in Automatic Control is used as an example. The projects within the course are carried out using the LIPS (Linköping interactive project steering) model. An example of a project, the golf playing industrial robot, and the results from this project are also covered.
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| 3. |
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| 4. |
- Hansson, Anders, et al.
(författare)
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A Primal-Dual Potential Reduction Method for Integral Quadratic Constraints
- 2001
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Ingår i: Proceedings of the 2001 American Control Conference. - : IEEE. - 0780364953 ; , s. 3013-3018
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Konferensbidrag (refereegranskat)abstract
- We discuss how to implement an efficient interior-point algorithm for semi-definite programs that result from integral quadratic constraints. The algorithm is a primal-dual potential reduction method, and the computational effort is dominated by a least-squares system that has to be solved in each iteration. The key to an efficient implementation is to utilize iterative methods and the specific structure of integral quadratic constraints. The algorithm has been implemented in Matlab. To give a rough idea of the efficiencies obtained, it is possible to solve problems resulting in a linear matrix inequality of dimension 130 × 130 with approximately 5000 variables in about 5 minutes on a lap-top. Problems with approximately 20000 variable and a linear matrix inequality of dimension 230 × 230 are solved in about 45 minutes. It is not assumed that the system matrix has no eigenvalues on the imaginary axis, nor is it assumed that it is Hurwitz.
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| 5. |
- 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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| 6. |
- Hansson, Anders, et al.
(författare)
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Continuous-time blind channel deconvolution using Laguerre shifts
- 2000
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Ingår i: Mathematics of Control, Signals, and Systems. - 0932-4194 .- 1435-568X. ; 13:4, s. 333-346
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Tidskriftsartikel (refereegranskat)abstract
- The objective of this paper is to study the problem of continuous-time blind deconvolution of a pulse amplitude modulated signal propagated over an unknown channel and perturbed by additive noise. The main idea is to use so-called Laguerre filters to estimate a continuous-time model of the channel. Laguerre-filter-based models can be viewed as an extension of finite-impulse-response (FIR) models to the continuous-time case, and lead to compact and parsimonious linear-in-the-parameters models. Given an estimate of the channel, different symbol estimation techniques are possible. Here, the shift property of Laguerre filters is used to derive a minimum mean square error estimator to recover the transmitted symbols. This is done in a way that closely resembles recent FIR-based schemes for the corresponding discrete-time case. The advantage of this concept is that physical a priori information can be incorporated in the model structure, like the transmitter pulse shape.
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| 7. |
- 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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| 8. |
- Hansson, Anders, et al.
(författare)
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Efficient Solution of Second Order Cone Program for Model Predictive Control
- 2002
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Ingår i: Proceedings of the 15th IFAC World Congress. - Linköping : Linköping University Electronic Press. - 9783902661746 ; , s. 296-296
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Konferensbidrag (refereegranskat)abstract
- In this paper it is shown how to efficiently solve an optimal control problem with applications to model predictive control. The objective is quadratic and the constraints can be both linear and quadratic. The key to an efficient implementation is to rewrite the optimization problem as a second order cone program. This can be done in many different ways. However, done carefully, it is possible to use both very efficient scalings as well as Riccati recursions for computing the search directions.
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| 9. |
- Hansson, Anders, et al.
(författare)
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On Methods for Gradient Estimation in IFT for MIMO Systems
- 2002
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Ingår i: Proceedings of 15th IFAC World Congress. - 9783902661746 ; , s. 1047-1047
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Konferensbidrag (refereegranskat)abstract
- Iterative feedback tuning (IFT) is a model free control tuning method using closed loop experiments. For single-input single-output (SISO) systems only 2 or 3, depending on the controller structure, closed loop experiments are required. However for multivariable systems the number of experiments increase to a maximum of 1 + m times p, where m times p is the dimension of the controller. In this contribution several methods are proposed to reduce the experimental time by approximating the gradient of the cost function. The local convergence for a method which uses the same technique as in IFT for SISO systems is analyzed. It is shown that even if there are commutation errors due to the approximation method, the numerical optimization may still converge to the true optimum.
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| 10. |
- Hansson, Anders, et al.
(författare)
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Polynomial Complexity for a Nesterov-Todd Potential-Reduction Method with Inexact Search Directions
- 2003
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Ingår i: Proceedings of the 42nd IEEE Conference on Decision and Control. - 0780379241 ; , s. 3824-3829 vol.4
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Konferensbidrag (refereegranskat)abstract
- In this paper is discussed how to efficiently solve semidefinite programs related to the Kalman-Yakubovich-Popov lemma. We consider a potential-reduction method where Nesterov-Todd search directions are computed inexactly by applying a preconditioned conjugate gradient method to the Schur complement equation. An efficient preconditioner based on Lyapunov equations is derived. We give a proof of polynomial convergence for this interior point method.
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