Necessary Condition for Near Optimal Control of Linear Forward-backward Stochastic Differential Equations

This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex. In the previous work (Theorem 3.1) of the second and third authors [\textit{% Automatica} \textbf{46} (2010) 397-404], some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it. The necessary condition of the near-optimality is established within the framework of optimality variational principle developed by Yong [\textit{SIAM J. Control Optim.} \textbf{48} (2010) 4119--4156] and obtained by the convergence technique to treat the optimal control of FBSDEs in unbounded control domains by Wu [% \textit{Automatica} \textbf{49} (2013) 1473--1480]. Some new estimates are given here to handle the near optimality. In addition, an illustrating example is discussed as well.Comment: To appear in International Journal of Contro

Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case

Discontinuities and hysteresis in quantized average consensus

We consider continuous-time average consensus dynamics in which the agents' states are communicated through uniform quantizers. Solutions to the resulting system are defined in the Krasowskii sense and are proven to converge to conditions of "practical consensus". To cope with undesired chattering phenomena we introduce a hysteretic quantizer, and we study the convergence properties of the resulting dynamics by a hybrid system approach.Comment: 26 pages, 7 figures. Accepted for publication in Automatica. v4 is minor revision of v

On the complexity of switching linear regression

This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we show that, on the one hand the problem is NP-hard, but on the other hand, it admits a polynomial-time algorithm with respect to the number of data points for any fixed data dimension and number of modes.Comment: Automatica, Elsevier, 201

Integrating Deep Contextualized Word Embeddings into Text Summarization Systems

In questa tesi saranno usate tecniche di deep learning per affrontare unodei problemi più difficili dell’elaborazione automatica del linguaggio naturale:la generazione automatica di riassunti. Dato un corpus di testo, l’obiettivoè quello di generare un riassunto che sia in grado di distillare e comprimerel’informazione dall’intero testo di partenza. Con i primi approcci si é provatoa catturare il significato del testo attraverso l’uso di regole scritte dagliumani. Dopo questa era simbolica basata su regole, gli approcchi statistici hanno preso il sopravvento. Negli ultimi anni il deep learning ha impattato positivamente ogni area dell’elaborazione automatica del linguaggionaturale, incluso la generazione automatica dei riassunti. In questo lavoroi modelli pointer-generator [See et al., 2017] sono utilizzati in combinazionea pre-trained deep contextualized word embeddings [Peters et al., 2018]. Sivaluta l’approccio sui due più grossi dataset per la generazione automaticadei riassunti disponibili ora: il dataset CNN/Daily Mail e il dataset Newsroom. Il dataset CNN/Daily Mail è stato generato partendo dal dataset diQuestion Answering pubblicato da DeepMind [Hermann et al., 2015], concatenando le frasi di highlight delle news e formando cosı̀ dei riassunti multifrase. Il dataset Newsroom [Grusky et al., 2018] è, invece, il primo datasetesplicitamente costruito per la generazione automatica di riassunti. Comprende un milione di coppie articolo-riassunto con diversi gradi di estrattività/astrattività a diversi ratio di compressione.L’approccio è valutato sui test-set con l’uso della metrica Recall-Oriented Understudy for Gisting Evaluation (ROUGE). Questo approccio causa un sostanzioso aumento nelle performance per il dataset Newsroom raggiungendo lo stato dell’arte sul valore di ROUGE-1 e valori competitivi per ROUGE-2 e ROUGE-L