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In this contribution we consider sparse linear regression problems. It is well known that the mutual coherence, i.e. the maximum correlation of the regressors, is important for the ability of any algorithm to recover the sparsity pattern of an unknown parameter vector from data. A low mutual coherence improves the ability of recovery. In optimal experiment design this requirement may be in conflict with other objectives encoded by the desired Fisher matrix. In this contribution we alleviate this issue by combining optimal input design with a recently proposed approach to achieve low mutual coherence by way of a linear coordinate transformation. The resulting optimization problem is solved using cyclic minimization. Via simulations we demonstrate that the resulting algorithm is able to achieve a Fisher matrix which results in a performance close to the performance if the sparsity would have been known, while at the same time being able to recover the sparsity pattern., Part of proceedings; ISBN 978-3-907144-07-7QC 20221031

The problem of estimating the largest gain of an unknown linear and time-invariant filter is studied, known as the H-infinity -norm estimation problem. The approach presented in this paper is iterative and corresponds to the combination of two state-of-the-art methods: Power Iterations and Weighted Thompson Sampling. The combination is done by means of a well-known technique in communications known as a cyclic prefix, in which the last points of a signal are prepended to it. This allows to take considerably more exact measurements of the frequency response of the system at a set of equispaced frequencies. The discussion is complemented with a simulation study, showing that the proposed algorithm has an increased speed of convergence to the quantity of interest., QC 20220121

We consider fixed-interval smoothing problems for counter-adversarial autonomous systems. An adversary deploys an autonomous filtering and control system that i) measures our current state via a noisy sensor, ii) computes a posterior estimate (belief) and iii) takes an action that we can observe. Based on such observed actions and our knowledge of our state sequence, we aim to estimate the adversary's past and current beliefs - this forms a foundation for predicting, and counteracting against, future actions. We derive the optimal smoother for the adversary's beliefs (we treat the problem in a Bayesian framework). Moreover, we demonstrate how the smoother can be computed for discrete systems even though the corresponding backward variables do not admit a finite-dimensional characterization. Finally, we illustrate our results in numerical simulations., QC 20210414

We consider the control design problem of optimizing the H-2 performance of a closed-loop system despite the presence of a malicious covert attacker. It is assumed that the attacker has incomplete knowledge on the true process we are controlling. To account for this uncertainty, we employ different measures of risk from the so called family of coherent measures of risk. In particular, we compare the closed-loop performance when a nominal value is used, with three different measures of risk: average risk, worst-case scenario and conditional valueat- risk (CVaR). Additionally, applying the approach from a previous work, we derive a convex formulation for the control design problem when CVaR is employed to quantify the risk. A numerical example illustrates the advantages of our approach., QC 20190305, CERCES

This paper deals with robust experiment design for the Virtual Reference Feedback Tuning (VRFT) approach, a non-iterative control design method aimed to tune fixed-order controllers directly from experimental data, without the need for a model of the plant. In a previous contribution, it has been shown that the spectrum of the optimal input depends on the frequency response of the controller achieving the desired performance. In this work, a robust input design procedure is proposed, which requires only mild prior knowledge about the optimal controller. The solution is obtained analytically via constrained min-max optimization. Simulation results on a benchmark case study for digital control systems show the effectiveness of the proposed approach., QC 20190305

The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree 1, independent of the relative degree of the strictly proper real system. In this paper, a refinement of these methods is developed. Inspired by the indirect prediction error method, we propose an estimator that enforces a fixed relative degree in the continuous-time transfer function estimate, and show that the estimator is consistent and asymptotically efficient. Extensive numerical simulations are put forward to show the performance of this estimator when contrasted with other indirect and direct methods for continuous-time system identification., QC 20190305

A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification., QC 20190211

In this paper, we explore the problem of input design for systems with quantized measurements. For the input design problem, we calculate and optimize a function of the Fisher Information Matrix (FIM). The calculation of the FIM is greatly simplified by using known relationships of the derivative of the likelihood function, and the auxiliary function arising from the Expectation Maximization (EM) algorithm. To optimize the FIM, we design an experiment using a recently published method based on graph theory. A numerical example shows that the proposed experiment can be successfully used in quantized systems.

While the topic has a long history in research, model structure selection is still one of the more challenging problems in system identification. In this tutorial we focus on impulse response modelling, and link classical techniques such as hypothesis testing and information criteria (e.g. AIC) to recent model estimation approaches, including regularisation. We discuss the problem from minimum mean-square error and maximum-likelihood perspectives., QC 20150408

In this paper, the problem of experiment design for the task of channel identification in cyclic prefixed orthogonal frequency division multiplexing (CP-OFDM) systems is revisited. So far, the optimal input sequences for least squares (LS) channel identification with respect to minimizing the channel mean square error (MSE) under an input energy constraint have been derived. Here, we investigate the same problem for the LS channel estimator, but when the design takes into account an end performance metric of interest, namely, the symbol estimate MSE. Based on some convex approximations, we verify that optimal sparse preambles, i.e, input vectors employing as many pilots as the channel length, for LS channel estimation in its classical context are near optimal in the aforementioned application-oriented context for the symbol estimate MSE., QC 20150408