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In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse…
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
The problem of suboptimality under bounded disturbances for the adaptive systems based on speed-graadient approach is discussed. A formulation of the estimated optimality of nonlinear nonlinearly parametrized adaptive control systems is…
We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case $H_\infty$ norm over a pre-specified set of uncertain parameters. At the core of…
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, "$N$-convex functionals" (the simplest example being the maximum of several fractional-linear functions) of unknown "signal"…
The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Optimal design of experiments for correlated processes is an increasingly relevant and active research topic. Present methods have restricted possibilities to judge their quality. To fill this gap, we complement the virtual noise approach…
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…