| 1. |
- Ohlsson, Henrik, 1981-, et al.
(author)
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Segmentation of ARX-Models using Sum-of-Norms Regularization
- 2010
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In: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 46:6, s. 1107-1111
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Journal article (peer-reviewed)abstract
- Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. Here it is formulated as a least-squares problem with sum-of-norms regularization over the state parameter jumps. a generalization of L1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade-off fit and the number of segments.
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| 2. |
- Ohlsson, Henrik, 1981-, et al.
(author)
-
Smoothed State Estimates under Abrupt Changes using Sum-of-Norms Regularization
- 2012
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In: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 48:4, s. 595-605
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Journal article (peer-reviewed)abstract
- The presence of abrupt changes, such as impulsive and load disturbances, commonly occur in applications, but make the state estimation problem considerably more difficult than in the standard setting with Gaussian process disturbance. Abrupt changes often introduce a jump in the state, and the problem is therefore readily and often treated by change detection techniques. In this paper, we take a different approach. The state smoothing problem for linear state space models is here formulated as a constrained least-squares problem with sum-of-norms regularization, a generalization of l1-regularization. This novel formulation can be seen as a convex relaxation of the well known generalized likelihood ratio method by Willsky and Jones. Another nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps. Good practical choices of this parameter along with an extension to nonlinear state space models are given.
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| 3. |
- Ohlsson, Henrik, 1981-, et al.
(author)
-
State Smoothing by Sum-of-Norms Regularization
- 2010
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In: Proceedings of the 49th Conference on Decision and Control. - 9781424477456 ; , s. 2880-2885
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Conference paper (peer-reviewed)abstract
- The presence of abrupt changes, such as impulsive disturbances and load disturbances, make state estimation considerably more difficult than the standard setting with Gaussian process noise. Nevertheless, this type of disturbances is commonly occurring in applications which makes it an important problem. An abrupt change often introduces a jump in the state and the problem is therefore readily treated by change detection techniques. In this paper, we take a rather different approach. The state smoothing problem for linear state space models is here formulated as a least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps.
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| 4. |
- Ohlsson, Henrik, 1981-, et al.
(author)
-
Trajectory Generation Using Sum-of-Norms Regularization
- 2010
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In: Proceedings of the 49th IEEE Conference on Decision and Control. - 9781424477456 ; , s. 540-545
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Conference paper (peer-reviewed)abstract
- Many tracking problems are split into two sub-problems, first a smooth reference trajectory is generated that meet the control design objectives, and then a closed loop control system is designed to follow this reference trajectory as well as possible. Applications of this kind include (autonomous) vehicle navigation systems and robotics. Typically, a spline model is used for trajectory generation and another physical and dynamical model is used for the control design. Here we propose a direct approach where the dynamical model is used to generate a control signal that takes the state trajectory through the waypoints specified in the design goals. The strength of the proposed formulation is the methodology to obtain a control signal with compact representation and that changes only when needed, something often wanted in tracking. The formulation takes the shape of a constrained least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. The formulation also gives a tool to, e.g. in model predictive control, prevent chatter in the input signal, and also select the most suitable instances for applying the control inputs.
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