Self triggered controller co-design using LASSO regression

In this work, we consider the control of a linear time-invariant system with self-triggered sampling. This study leads us to the resolution of the co-design problem. We address it by jointly computing the controller and the future sampling scheduled as a sparse optimization problem. Accordingly, we show that a relaxation of the optimal self trigger co-design can be formulated as a LASSO (Least Absolute Shrinkage and Selection Operator) regression. Thus, we give some results on the possibility to obtain a controller ensuring practical or asymptotic stability while reducing sampling of the control action, by using the properties of the solutions of the LASSO regression.