Segmentation of ARX systems through SDP-relaxation techniques

Segmentation of ARX models can be formulated as a combinato- rial minimization problem in terms of the ℓ0-norm of the param- eter variations and the ℓ2-loss of the prediction error. A typical approach to compute an approximate solution to such a prob- lem is based on ℓ1-relaxation. Unfortunately, evaluation of the level of accuracy of the ℓ1-relaxation in approximating the opti- mal solution of the original combinatorial problem is not easy to accomplish. In this poster, an alternative approach is proposed which provides an attractive solution for the ℓ0-norm minimiza- tion problem associated with segmentation of ARX models

An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multi-period portfolio optimization with transaction costs. In each iteration of our method, the first step involves separately optimizing over each variable block, which can be carried out in parallel. The second step is not separable in the variables, but can be carried out very efficiently. We apply the algorithm to segmentation of data based on changes inmean (l_1 mean filtering) or changes in variance (l_1 variance filtering). In a numerical example, we show that our implementation is around 10000 times faster compared with the generic optimization solver SDPT3

Sparse Iterative Learning Control with Application to a Wafer Stage: Achieving Performance, Resource Efficiency, and Task Flexibility

Trial-varying disturbances are a key concern in Iterative Learning Control (ILC) and may lead to inefficient and expensive implementations and severe performance deterioration. The aim of this paper is to develop a general framework for optimization-based ILC that allows for enforcing additional structure, including sparsity. The proposed method enforces sparsity in a generalized setting through convex relaxations using $\ell_1$ norms. The proposed ILC framework is applied to the optimization of sampling sequences for resource efficient implementation, trial-varying disturbance attenuation, and basis function selection. The framework has a large potential in control applications such as mechatronics, as is confirmed through an application on a wafer stage.Comment: 12 pages, 14 figure

Dynamic network identification from non-stationary vector autoregressive time series

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