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In this paper we propose an extended version of the Friedkin-Johnsen (FJ) model that accounts for the effects of homophily mechanisms on the agents' mutual appraisals. The proposed model consists of two difference equations. The first one describes the opinions' evolution, namely how agents modify their opinions taking into account both their personal beliefs and the influences of other agents, as in the standard FJ model. Meanwhile, the second equation models how the influence matrix involved in the opinion formation process updates according to a homophily mechanism, by allowing both positive and negative appraisals. We show that the proposed time-varying version of the classical FJ model always asymptotically converges to a constant solution. Moreover, in the case of a single discussion topic, the asymptotic behavior of the system is derived in closed form.

Dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive theory of semicontracting systems, we investigate seminorms on vector spaces and define two canonical notions: projection and distance semi-norms. We show that the well-known lp ergodic coefficients are induced matrix seminorms and play a central role in stability problems. In particular, we formulate a duality theorem that explains why the Markov-Dobrushin coefficient is the rate of contraction for both averaging and conservation flows in discrete time. Moreover, we obtain parallel results for induced matrix log seminorms. Finally, we propose comprehensive theorems for strong semicontractivity of linear and non-linear time-varying dynamical systems with invariance and conservation properties both in discrete and continuous time.

In this paper, we propose a mathematical model for a Transactive Memory System (TMS) involved in the cooperative process of learning a task. The model is based on an intertwined dynamics involving both the individuals level of expertise and the interaction network among the cooperators. The model shows that if all the agents are non-stubborn, then all of them are able to acquire the competence of the most expert members of the group, asymptotically reaching their level of proficiency. Conversely, when dealing with all stubborn agents, the capability to pass on the task depends on the connectedness properties of the interaction graph., Comment: Accepted for presentation at the European Control Conference (ECC 2022)

In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the(interior of the) positive orthant. Specifically, we investigate herdability for linear time-invariant systems, both from an algebraic perspective and based on the graph representing the systems interactions. In addition, we focus on linear state-space models corresponding to matrix pairs (A;B) in which the matrix B is a selection matrix that determines the leaders in the network, and we show that the weights that followers give to the leaders do not affect the herdability of the system. We then focus on the herdability problem for systems with a single leader in which interactions are symmetric and the network topology is acyclic, in which case an algorithm for the leader selection is provided. In this context, under some additional conditions on the mutual distances, necessary and sufficient conditions for the herdability of the overall system are given.

In this paper we investigate the problem of the sudden disconnection of an edge in a discrete-time multi-agent consensus network. If the graph remains strongly connected, the multi-agent system still achieves consensus, but in general, unless the information exchange between each pair of agents is symmetric, the agents' states converge to a drifted value of the original consensus value. Consequently the edge disconnection can go unnoticed. In this paper the problems of detecting an edge disconnection and of identifying in a finite number of steps the exact edge that got disconnected are investigated. Necessary and sufficient conditions for both problems to be solvable are presented, both in case all the agents' states are available and in case only a subset of the agents' states is measured. Finally, an example of a network of 7 agents is provided, to illustrate some of the theoretical results derived in the paper.

Context-Aware systems are becoming useful components in autonomic and monitoring applications and the assessment of their properties is an important step towards reliable implementation, especially in safety-critical applications. In this paper, using an avalanche/landslide alert system as a running example, we propose a technique, based on Boolean Control Networks, to verify that the system dynamics has stable equilibrium states, corresponding to constant inputs, and hence it does not exhibit oscillatory behaviors, and to establish other useful properties in order to implement a precise and timely alarm system.

A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this question, we show that the moments evolution in any generic network can be either approximated or, under suitable assumptions, computed exactly as the solution of a switched affine system. Motivated by this application, we propose a new method to approximate the reachable set of switched affine systems. A remarkable feature of our approach is that it allows one to easily compute projections of the reachable set for pairs of moments of interest, without requiring the computation of the full reachable set, which can be prohibitive for large networks. As a second contribution, we also show how to select the external signal in order to maximize the probability of reaching a target set. To illustrate the method we study a renown model of controlled gene expression and we derive estimates of the reachable set, for the protein mean and variance, that are more accurate than those available in the literature and consistent with experimental data.

In this paper, we consider a discrete-time consensus network, and assume that one of the agents acts as a leader and injects an input signal to improve the overall system performance, in particular to increase the speed of convergence to consensus or to achieve finite-time consensus. Two possible control protocols are proposed, and the characteristic polynomials of the resulting closed-loop systems are determined. These results allow us to investigate the consensus and finite-time consensus of the overall systems. Open problems and future research directions conclude this paper.