The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is no constraint on the mutual coherence, making it difficult to handle sparse estimation. This article aims to tackle this issue for fixed denominator models, which include Laguerre, Kautz, and generalized orthonormal basis function expansion models, for example. The article proposes an optimal input design method where the achieved Fisher information matrix (FIM) is fitted to the desired Fisher matrix, together with a coordinate transformation designed to make the regressors in the transformed coordinates have low mutual coherence. The method can be used together with any sparse estimation method and any desired Fisher matrix. A numerical study shows its potential for alleviating the problem of model order selection when used in conjunction with, for example, classical methods such as the Akaike information criterion.

In this paper, we propose a new kernel-based method for compensating latent nonlinear dynamics for consensus control in multiagent systems. Although kernel regression is a well-known and thoroughly studied technique, recent research has shown its significant non-asymptotic potential. Under general conditions, we show the convergence of the proposed approach by stability analysis and show that applying kernel regression compensation for consensus control leads to synchronization of the agents within high probability error bounds.

When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system. Traditional linear system identification may not consider the most parsimonious model when relying solely on unfactored transfer functions, which typically result from standard direct approaches. This paper presents a novel identification method that delivers additive models for both open and closed-loop setups. The estimators that are derived are shown to be generically consistent, and can admit the identification of marginally stable additive systems. Numerical simulations show the efficacy of the proposed approach, and its performance in identifying a modal representation of a flexible beam is verified using experimental data.

In this technical communique, we present a sim2real approach for data-driven controller tuning, utilizing a digital twin to generate input–output data and suitable controllers around nominal parameter values. We establish a direct inverse supervised learning framework using advanced neural network architectures, including the WaveNet sequence model, to learn a tuning rule that maps input–output data to controller parameters. This approach automates controller re-calibration by meta-learning the tuning rule through inverse supervised learning, effectively avoiding human intervention via a machine learning model. The advantages of this methodology are demonstrated through numerical simulations across various neural network architectures.

The probability density function of the input plays a crucial role in the process of identifying nonlinear systems, with a finite representation commonly employed in the process. However, input design for nonlinear models is a challenging task because it usually involves optimizing a problem with a large number of free variables, which is computationally heavy. The first contribution of this paper is to demonstrate that the majority of these free variables are zero. Consequently, there is no necessity to optimize all of them. The second contribution is to identify the non-zero variables within this set of free variables associated with input design. To address this, we propose an alternating minimization approach. In the first step, we compute the per-sample Fisher Information Matrix (FIM). Then, in the second phase, we estimate the positions of the non-zero elements within the vector of free variables using the previously derived per-sample FIM. Additionally, in the later phase, we calculate the Lagrangian multipliers in our optimization problem using the Karush–Kuhn–Tucker conditions and derive an upper bound for the hyperparameter, which promotes sparsity. This bound ensures the maximum required number of non-zero variables to represent the per-sample FIM. Following this, the original input design problem is streamlined to optimize the cost function only with respect to the non-zero elements, resulting in a significant reduction in computational time. To assess the effectiveness of our proposed method, we conduct a comprehensive numerical performance evaluation by comparing it to state-of-the-art input design algorithms.

Appropriate excitation conditions are essential for reliably identifying sparse models. In regression problems, these conditions are often characterized by properties of the regressor matrix, with mutual coherence, the maximum correlation between regressors, playing a central role in enabling sparse recovery. However, obtaining sparse estimates is rarely the sole objective, as estimation accuracy is also important. When a model is used in an application, e.g. control design, acceptable performance with high probability can be (approximately) ensured by requiring the confidence ellipsoid to be contained in a certain ellipsoid which depends on the performance specifications in the application. However, it is well known that experiments fulfilling such requirements using minimal excitation energy (least-costly experiments) tend to generate highly correlated regressors, in conflict with the requirements for sparsity. Adhering to this setting and focusing on the popular orthogonal matching pursuit algorithm (OMP), we derive conditions for simultaneously ensuring sparsity and having the confidence ellipsoid contained in a pre-specified ellipsoid. We extend this result to a recently proposed two stage sparse estimation method where a linear transformation is used in a pre-processing step before OMP to reduce mutual coherence. A final contribution is to show that our theoretical results are of importance in optimal input design for sparse models. Specifically, we show that the choice of hyperparameters in a recently proposed input design method can be guided by our contributions and we show explicitly how this can be done in this two-stage method.

Data-driven control, the task of designing a controller based on process data, finds application in a wide range of disciplines and the topic has been intensively studied over more than half a century. The main purpose of this contribution is to elucidate on the commonalities between data-driven control and parameter estimation. In particular, we discuss the bias-variance trade-off, i.e. rather than aiming for the optimal controller one should aim for a constrained version, that may be characterized by tunable parameters, corresponding to hyperparameters in parameter estimation. As a result we shift attention from indirect vs direct data driven control by highlighting the important role played by (complete) minimal sufficient statistics. To keep technicalities at a minimum, still capturing the essential features of the problem, we consider the problem of minimizing the expected control cost for a quadratic open loop control problem applied to a finite impulse response system. In a Gaussian white noise setting, the maximum-likelihood parameter estimate constitutes a complete minimal sufficient statistic which allows us to focus on controllers that are functions of this model estimate without loss of statistical accuracy. We make a systematic study of three different controller structures and two different tuning techniques and illustrate their behaviours numerically.

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step least-squares algorithms, such as Weighted Null-Space Fitting. Recently, there has been an increasing interest in non-asymptotic analysis of estimation algorithms. In this contribution we identify the Markov parameters using weighted least-squares and present non-asymptotic analysis for such estimator. To cover both stable and unstable systems, multiple trajectories are collected. We show that with the optimal weighting matrix, weighted least-squares gives a tighter error bound than ordinary least-squares for the case of non-uniformly distributed measurement errors. Moreover, as the optimal weighting matrix depends on the system's true parameters, we introduce two methods to consistently estimate the optimal weighting matrix, where the convergence rate of these estimates is also provided. Numerical experiments demonstrate improvements of weighted least-squares over ordinary least-squares in finite sample settings.

Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.

We study the problem of diffusion-based network learning of a nonlinear phenomenon, m, from local agents' measurements collected in a noisy environment. For a decentralized network and information spreading merely between directly neighboring nodes, we propose a non-parametric learning algorithm, that avoids raw data exchange and requires only mild a priori knowledge about m. Non-asymptotic estimation error bounds are derived for the proposed method. Its potential applications are illustrated through simulation experiments.