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Norms have been extensively proposed as coordination mechanisms for both agent and human societies. Nevertheless, choosing the norms to regulate a society is by no means straightforward. The reasons are twofold. First, the norms to choose…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to…

This paper introduces a two-level robust approach to estimate the unknown states of a large-scale power system while the measurements and network parameters are subjected to uncertainties. The bounded data uncertainty (BDU) considered in…

Latent force models, a class of hybrid modeling approaches, integrate physical knowledge of system dynamics with a latent force - an unknown, unmeasurable input modeled as a Gaussian process. In this work, we introduce two optimal state…

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…

We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a…

Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…

The increasing complexity of power grid management, driven by the emergence of prosumers and the demand for cleaner energy solutions, has needed innovative approaches to ensure stability and efficiency. This paper presents a novel approach…

An aggregated method of nonparametric estimators based on time-domain and state-domain estimators is proposed and studied. To attenuate the curse of dimensionality, we propose a factor modeling strategy. We first investigate the asymptotic…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically…

Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…

The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…

Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…

We introduce optimal energy shaping as an enhancement of classical passivity-based control methods. A promising feature of passivity theory, alongside stability, has traditionally been claimed to be intuitive performance tuning along the…

The optimal placement of measurement devices in electrical power systems is commonly modeled through the power dominating set problem. However, in real-world applications, these devices have limited capacities, leading to a capacitated…

The ability to learn and execute optimal control policies safely is critical to realization of complex autonomy, especially where task restarts are not available and/or the systems are safety-critical. Safety requirements are often…

In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is…

Recent developments in linear system identification have proposed the use of non-parameteric methods, relying on regularization strategies, to handle the so-called bias/variance trade-off. This paper introduces an impulse response estimator…