Mariette Annergren

Mariette Annergren, Anders Hansson, Bo Wahlberg

We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an l_1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem has applications in control, for example in l_1 regularized MPC. The ADMM algorithm is easy to implement, converges fast to a solution of moderate accuracy, and enables separation of the optimization problem into sub-problems that may be solved in parallel. We show that the most costly step of the proposed ADMM algorithm is equivalent to solving an LQ regulator problem with an extra linear term in the cost function, a problem that can be solved efficiently using a Riccati recursion. We apply the ADMM algorithm to an example of l_1 regularized MPC. The numerical examples confirm fast convergence to moderate accuracy and a linear complexity in the MPC prediction horizon.

Afrooz Ebadat, Mariette Annergren, Christian A. Larsson et al.

This contribution considers one central aspect of experiment design in system identification. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to errors in the estimated model is measured by an application cost function. In order to use an optimization based input design method, a convex approximation of the set of models that atisfies the control specification is required. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.

Bo Wahlberg, Stephen Boyd, Mariette Annergren et al.

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.