Davide Fiore

Davide Fiore, Giovanni Russo

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.

Davide Salzano, Davide Fiore, Mario di Bernardo

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.

Agostino Guarino, Davide Fiore, Mario di Bernardo

The synthetic toggle switch, first proposed by Gardner & Collins [1] is a MIMO control system that can be controlled by varying the concentrations of two inducer molecules, aTc and IPTG, to achieve a desired level of expression of the two genes it comprises. It has been shown [2] that this can be accomplished through an open-loop external control strategy where the two inputs are selected as mutually exclusive periodic pulse waves of appropriate amplitude and duty-cycle. In this paper, we use a recently derived average model of the genetic toggle switch subject to these inputs to synthesize new feedback control approaches that adjust the inputs duty-cycle in real-time via two different possible strategies, a model based hybrid PI-PWM approach and a so-called Zero-Average dynamics (ZAD) controller. The controllers are validated in-silico via both deterministic and stochastic simulations (SSA) illustrating the advantages and limitations of each strategy

Mario di Bernardo, Davide Fiore

In this paper we present a switching control strategy to incrementally stabilize a class of nonlinear dynamical systems. Exploiting recent results on contraction analysis of switched Filippov systems derived using regularization, sufficient conditions are presented to prove incremental stability of the closed-loop system. Furthermore, based on these sufficient conditions, a design procedure is proposed to design a switched control action that is active only where the open-loop system is not sufficiently incrementally stable in order to reduce the required control effort. The design procedure to either locally or globally incrementally stabilize a dynamical system is then illustrated by means of a representative example.

Davide Fiore, Marco Coraggio, Mario di Bernardo

The aim of this paper is to present the application of an approach to study contraction theory recently developed for piecewise smooth and switched systems. The approach that can be used to analyze incremental stability properties of so-called Filippov systems (or variable structure systems) is based on the use of regularization, a procedure to make the vector field of interest differentiable before analyzing its properties. We show that by using this extension of contraction theory to nondifferentiable vector fields, it is possible to design observers for a large class of piecewise smooth systems using not only Euclidean norms, as also done in previous literature, but also non-Euclidean norms. This allows greater flexibility in the design and encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear) systems. The theoretical methodology is illustrated via a set of representative examples.

Antonio Spallone, Davide Fiore, Fabrizio Cartenì et al.

Extracellular DNA accumulation in recirculating bioprocesses inhibits microbial growth and reduces productivity. We consider a continuous bioreactor with a recirculating loop and an electrophoretic filtration unit for selective DNA removal, and develop a feedback control framework combining online state and parameter estimation via an Unscented Kalman Filter with two control strategies: an adaptive Model Predictive Controller that jointly optimizes dilution rate and filtration activation, and a simpler bang--bang filtration policy with lookup-table dilution rate selection. Closed-loop simulations under nominal and perturbed conditions show that the MPC strategy achieves significantly higher cumulative profit while keeping DNA concentration below the inhibition threshold.

Sara Maria Brancato, Davide Salzano, Francesco De Lellis et al.

A key problem toward the use of microorganisms as bio-factories is reaching and maintaining cellular communities at a desired density and composition so that they can efficiently convert their biomass into useful compounds. Promising technological platforms for the real time, scalable control of cellular density are bioreactors. In this work, we developed a learning-based strategy to expand the toolbox of available control algorithms capable of regulating the density of a \textit{single} bacterial population in bioreactors. Specifically, we used a sim-to-real paradigm, where a simple mathematical model, calibrated using a few data, was adopted to generate synthetic data for the training of the controller. The resulting policy was then exhaustively tested in vivo using a low-cost bioreactor known as Chi.Bio, assessing performance and robustness. In addition, we compared the performance with more traditional controllers (namely, a PI and an MPC), confirming that the learning-based controller exhibits similar performance in vivo. Our work showcases the viability of learning-based strategies for the control of cellular density in bioreactors, making a step forward toward their use for the control of the composition of microbial consortia.

Davide Fiore, Agostino Guarino, Mario di Bernardo

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.

Mario di Bernardo, Davide Fiore, S. John Hogan

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.

Davide Fiore, Giovanni Russo, Mario di Bernardo

We present new conditions to obtain synchronization and consensus patterns in complex network systems. The key idea is to exploit symmetries of the nodes' vector fields to induce a desired synchronization/consensus pattern, where nodes are clustered in different groups each converging towards a different synchronized evolution. We show that the new conditions we present offer a systematic methodology to design a distributed network controller able to drive a network of interest towards a desired synchronization/consensus pattern.