| 1. |
- Falkeborn, Rikard, et al.
(författare)
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Low-Rank Exploitation in Semidefinite Programming for Control
- 2010
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Ingår i: Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design. - Linköping : Linköping University Electronic Press. - 9781424453542 - 9781424453559 ; , s. 24-28
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Konferensbidrag (refereegranskat)abstract
- Many control related problems can be cast as semidefinite programs but, even though there exist polynomial time algorithms and good publicly available solvers, the time it takes to solve these problems can be long. Something many of these problems have in common, is that some of the variables enter as matrix valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this paper, we describe how this can be done, and show how our code can be used when using SDPT3. The idea behind this is old and is implemented in LMI Lab, but we show that when using a modern algorithm, the computational time can be reduced. Finally, we describe how the modeling language YALMIP is changed in such a way that our code can be interfaced using standard YALMIP commands, which greatly simplifies for the user.
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| 2. |
- Löfberg, Johan, 1974-
(författare)
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A Convex Relaxation of a Minimax MPC Controller
- 2001
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Ingår i: Proceedings of the Third Conference on Computer Science and Systems Engineering. - Linköping : Linköping University Electronic Press.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Model predictive control (MPC) for systems with bounded disturbances is studied. A minimax formulation with optimization of the worst-case scenario is defined and conservatively approximated using a relaxation (the S-procedure), yielding a semidefinite optimization problem. Possible extensions are discussed and it is argued that the approach constitutes a promising framework for minimax MPC.
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| 3. |
- Löfberg, Johan, 1974-
(författare)
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A Stabilizing MPC Algorithm using Performance Bounds from Saturated Linear Feedback
- 2001
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We present a method to increase feasibility in MPC algorithms that use ellipsoidal terminal state constraints and performance bounds from nominal controllers. The method is based on estimating a bound on the achievable performance with a saturated nominal controller and using this bound in the MPC algorithm. The resulting MPC controller can be implemented efficiently with Second Order Cone Programming.
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| 4. |
- Löfberg, Johan, 1974-
(författare)
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Approximations of Closed-Loop Minimax MPC
- 2003
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Ingår i: Proceedings of the 42nd IEEE Conference on Decicion and Control. - Linköping : Linköping University Electronic Press. - 0780379241 ; , s. 1438-1442 vol.2
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Konferensbidrag (refereegranskat)abstract
- Minimax or worst-case approaches have been used frequently recently in model predictive control (MPC) to obtain control laws that are less sensitive to uncertainty. The problem with minimax MPC is that the controller can become overly conservative. An extension to minimax MPC that can resolve this problem is closed-loop minimax MPC. Unfortunately, closed-loop minimax MPC is essentially an intractable problem. In this paper, we introduce a novel approach to approximate the solution to anumber of closed-loop minimax MPC problems. The result is convex optimization problems with size growing polynomially in system dimension and prediction horizon.
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| 5. |
- Löfberg, Johan, 1974-
(författare)
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Block Diagonalization of Matrix-Valued Sum-of-Squares Programs
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Checking non-negativity of polynomials using sum-of-squares has recently been popularized and found many applications in control. Although the method is based on convex programming, the optimization problems rapidly grow and result in huge semidefinite programs. The paper [4] describes how symmetry is exploited in sum-of-squares problems in the MATLAB toolbox YALMIP, but concentrates on the scalar case. This report serves as an addendum, and extends the strategy to matrix-valued sum-of-squares problems.
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| 6. |
- Löfberg, Johan, 1974-
(författare)
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Feasibility Analysis of MPC with Ellipsoidal Terminal State Constraints
- 2000
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Ingår i: Proceedings of Reglermöte 2000. - Linköping : Linköping University Electronic Press. ; , s. 223-227
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We present two methods to estimate the initial feasible region in MPC with ellipsoidal terminal constraints. As a part of the analysis, it shown that the feasible set is the union of a polytope and a finite number of ellipsoids.
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| 7. |
- Löfberg, Johan, 1974-
(författare)
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Improved Matrix Dilations for Robust Semidefinite Programming
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Simple improvements to an approach for robust semidefinite programming are proposed. The matrix dilation reformulation used as the core idea in a work by Oishi 2006 is improved in terms of computational complexity by applying standard sum-of-squares methods, and by introducing less conservative uncertainty dependent parameterizations of the dilation matrix.
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| 8. |
- Löfberg, Johan, 1974-
(författare)
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Minimax MPC for Systems with Uncertain Input Gain - Revisited
- 2001
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Robust synthesis is one of the remaining challenges in model predictive control (MPC). One way to robustify an MPC controller is to formulate a minimax problem, i.e., optimize a worst-case performance measure. For systems modeled with an uncertain gain, there are many results available. Typically, the minimax formulations have given intractable problems, or unorthodox performance measures have been used to obtain tractable problems. In this paper, we show how the standard quadratic performance measure can be used in a computationally tractable minimax MPC controller. The controller is developed in a linear matrix inequality framework that easily allows extensions and generalizations.
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| 9. |
- Löfberg, Johan, 1974-
(författare)
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MPC for Nonlinear Systems using Trajectory Linearizations
- 1999
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This report presents a simple method to extend linear MPC to nonlinear continuous-time systems. The method is based on an approximation of the underlying optimal control problem. Experiments have been carried out and show that the control algorithm manages to control various nonlinear systems.
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| 10. |
- Löfberg, Johan, 1974-
(författare)
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Nonlinear Receding Horizon Control : Stability without Stabilizing Constraints
- 2001
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Ingår i: Proceedings of the 2001 European Control Conference. - Linköping : Linköping University Electronic Press.
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Konferensbidrag (refereegranskat)abstract
- Almost all proposed approaches to nonlinear receding horizon control with guaranteed stability are based on adding stabilizing constraints, using linearizations of the system, or knowing an upperbound on the value function of an infinite horizon optimal control problem. In this contribution, we present a new approach using none of these ingredients. The idea is to use a dynamic receding horizon controller, where the dynamic part is introduced to tune emphasis between short-range optimality and stability. The result is a design procedure applicable to a nontrivial class of unconstrained nonlinear systems.
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