We consider multi-agent systems interacting over directed network topologies where a subset of agents is adversary/faulty and where the non-faulty agents have the goal of reaching consensus, while fulfilling a differential privacy requirement on their initial conditions. To address this problem, we develop an update law for the non-faulty agents. Specifically, we propose a modification of the so-called Mean-Subsequence-Reduced (MSR) algorithm, the Differentially Private MSR (DP-MSR) algorithm, and characterize three important properties of the algorithm: correctness, accuracy and differential privacy. We show that if the network topology is (2f + 1)-robust, then the algorithm allows the non-faulty agents to reach consensus despite the presence of up to f faulty agents and we characterize the accuracy of the algorithm. Furthermore, we also show in two important cases that our distributed algorithm can be tuned to guarantees differential privacy of the initial conditions and the differential privacy requirement is related to the maximum network degree. The results are illustrated via simulations.

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application

In this letter, we analyze a genetic toggle switch recently studied in the literature where the expression of two repressor proteins can be tuned by controlling two different inputs, namely the concentration of two inducer molecules in the growth medium of the cells. Specifically, we investigate the dynamics of this system when subject to pulse-width modulated (PWM) input. We provide an analytical model that captures qualitatively the experimental observations reported in the literature and approximates its asymptotic behavior. We also discuss the effect that the system parameters have on the prediction accuracy of the model. Moreover, we propose a possible external control strategy to regulate the mean value of the fluorescence of the reporter proteins when the cells are subject to such periodic forcing.

We consider the problem of regulating by means of external control inputs the ratio of two cell populations. Specifically, we assume that these two cellular populations are composed of cells belonging to the same strain which embeds some bistable memory mechanism, e.g. a genetic toggle switch, allowing them to switch role from one population to another in response to some inputs. We present three control strategies to regulate the populations' ratio to arbitrary desired values which take also into account realistic physical and technological constraints occurring in experimental microfluidic platforms. The designed controllers are then validated in-silico using stochastic agent-based simulations.

We describe a multicellular approach to control a target cell population endowed with a bistable toggle-switch. The idea is to engineer a synthetic microbial consortium consisting of three different cell populations. In such a consortium, two populations, the Controllers, responding to some reference input, can induce the switch of a bistable memory mechanism in a third population, the Targets, so as to activate or deactivate some additional functionalities in the cells. Communication among the three populations is established by orthogonal quorum sensing molecules that are used to close a feedback control loop across the populations. The control design is validated via in-silico experiments in BSim, a realistic agentbased simulator of bacterial populations.

Controlling cells endowed with the genetic toggle switch has been suggested as a benchmark problem in synthetic biology. It has been shown that a carefully selected periodic forcing can balance a population of such cells in an undifferentiated state.The effectiveness of these control strategies, however, can be mined by the presence of stochastic perturbations and uncertainties typically observed in biological systems and is therefore not robust. Here, we propose the use of feedback control strategies to enhance robustness and performance of the balancing action by selecting in realtime both the amplitude and the duty-cycle of the inducer molecular signals affecting the toggle switch behavior. We show, via in-silico experiments and realistic agent-based simulations, the effectiveness of the proposed strategies even in presence of uncertainties and stochastic effects. In so doing, we confirm previous observations made in the literature about coherence of the population when pulsatile forcing inputs are used but, contrary to what proposed in the past, we leverage feedback control techniques to endow . CC-BY-NC-ND 4.

We address the problem of controlling the dilution rate in a chemostat to regulate the ratio between the concentrations of two microbial populations growing in continuous culture. After analyzing the open-loop dynamics of this multicellular system, we present two alternative feedback control strategies, one based on a gain-scheduled state feedback controller, the other on a switching control strategy. We show that both strategies are effective in solving the problem and illustrate the results by a set of representative numerical simulation.

We describe two multicellular implementations of the classical P and PI feedback controllers for the regulation of gene expression in a target cell population. Specifically, we propose to distribute the proportional and integral actions over two different cellular populations in a microbial consortium comprising a third target population whose output needs to be regulated. By engineering communication among the different cellular populations via appropriate orthogonal quorum sensing molecules, we are able to close the feedback loop across the consortium. We derive analytical conditions on the biological parameters guaranteeing the regulation of the output of the target population and we validate the robustness and modularity of proposed control schemes via in silico experiments in BSim, a realistic agent-based simulator of bacterial populations.