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We propose a counter-example guided inductive synthesis (CEGIS) scheme for the design of control Lyapunov functions and associated state-feedback controllers for linear systems affected by parametric uncertainty with arbitrary shape. In the CEGIS framework, a learner iteratively proposes a candidate control Lyapunov function and a tailored controller by solving a linear matrix inequality (LMI) feasibility problem, while a verifier either falsifies the current candidate by producing a counter-example to be considered at the next iteration, or it certifies that the tentative control Lyapunov function actually enjoys such feature. We investigate the Lipschitz continuity of the objective function of the global optimization problem solved by the verifier, which is key to establish the convergence of our method in a finite number of iterations. Numerical simulations confirm the effectiveness of the proposed approach.

Modern socio-technical systems typically consist of many interconnected users and competing service providers, where notions like market equilibrium are tightly connected to the ``evolution'' of the network of users. In this paper, we model the users' dynamics as a linear dynamical system, and the service providers as agents taking part to a generalized Nash game, whose outcome coincides with the input of the users' dynamics. We thus characterize the notion of co-evolution of the market and the network dynamics and derive dissipativity-based conditions leading to a pertinent notion of equilibrium. We then focus on the control design and adopt the light-touch policy to incentivize or penalize the service providers as little as possible, while steering the networked system to a desirable outcome. We also provide a dimensionality-reduction procedure, which offers network-size independent conditions. Finally, we illustrate our novel notions and algorithms on a simulation setup stemming from digital market regulations for influencers, a topic of growing interest.

During an ongoing epidemic, especially in the case of a new agent, data are partial and sparse, also affected by external factors as for example climatic effects or preparedness and response capability of healthcare structures. Despite that we showed how, under some universality assumptions, it is possible to extract strategic insights by modelling the pandemic trough a probabilistic Polya urn scheme. In the Polya framework, we provide both the distribution of infected cases and the asymptotic estimation of the incidence rate, showing that data are consistent with a general underlying process at different scales. Using European confirmed cases and diagnostic test data on COVID-19 , we provided an extensive comparison among European countries and between Europe and Italy at regional scale, for both the two big waves of infection. We globally estimated an incidence rate in accordance with previous studies. On the other hand, this quantity could play a crucial role as a proxy variable for an unbiased estimation of the real incidence rate, including symptomatic and asymptomatic cases., Comment: 22 pages, 15 figures