Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence of a solution and feasibility of a suitable, a priori known candidate solution. Subsequently, a Stochastic Model Predictive Control algorithm which unifies previous results is derived, leaving the designer the option to balance an increased feasible region against guaranteed bounds on the asymptotic average performance and convergence time. Besides typical performance bounds, under mild assumptions, we prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller. A numerical example, demonstrating the efficacy of the proposed approach in comparison with classical, recursively feasible Stochastic MPC and Robust MPC, is provided.

This paper presents a review of the literature on network traffic prediction, while also serving as a tutorial to the topic. We examine works based on autoregressive moving average models, like ARMA, ARIMA and SARIMA, as well as works based on Artifical Neural Networks approaches, such as RNN, LSTM, GRU, and CNN. In all cases, we provide a complete and self-contained presentation of the mathematical foundations of each technique, which allows the reader to get a full understanding of the operation of the different proposed methods. Further, we perform numerical experiments based on real data sets, which allows comparing the various approaches directly in terms of fitting quality and computational costs. We make our code publicly available, so that readers can readily access a wide range of forecasting tools, and possibly use them as benchmarks for more advanced solutions.

Aim of this paper is to propose a novel methodology for estimating the social influence among agents interacting in a sparse social network described by the Friedkin and Johnsen’s model. In this classical model, $n$ agents discuss $m \ll n$ topics, are influenced by the others’ opinions, but are not completely open-minded, being persistently driven by their prejudices. We reconstruct the social network topology and the strength of the interconnections starting from observations of the initial and final opinionsn profile only. The intrinsic sparsity of the graph is exploited via an $\ell_0/\ell_1$ minimization. Different from the techniques previously proposed in literature, no partial knowledge of the social graph is assumed, and there is no need of optimally placing external stubborn agents injecting prescribed inputs, thus changing the terminal behavior of the opinion dynamics. Under suitable assumptions, we derive theoretical conditions that guarantee that the problem is well posed and sufficient requirements on the number of topics under discussion that ensure perfect recovery. Extensive simulations on synthetic and real networks corroborate theoretical results.