Giovanni Russo

Michael Dumbser, Walter Boscheri, Matteo Semplice et al.

We present a novel arbitrary high order accurate central WENO spatial reconstruction procedure (CWENO) for the solution of nonlinear systems of hyperbolic conservation laws on fixed and moving unstructured simplex meshes in two and three space dimensions. Starting from the given cell averages of a function on a triangular or tetrahedral control volume and its neighbors, the nonlinear CWENO reconstruction yields a high order accurate and essentially non-oscillatory polynomial that is defined everywhere in the cell. Compared to other WENO schemes on unstructured meshes, the total stencil size is the minimum possible one, as in classical point-wise WENO schemes of Jiang and Shu. However, the linear weights can be chosen arbitrarily, which makes the practical implementation on general unstructured meshes particularly simple. We make use of the piecewise polynomials generated by the CWENO reconstruction operator inside the framework of fully discrete and high order accurate one-step ADER finite volume schemes on fixed Eulerian grids as well as on moving Arbitrary-Lagrangian-Eulerian (ALE) meshes. The computational efficiency of the high order finite volume schemes based on the new CWENO reconstruction is tested on several two- and three-dimensional systems of hyperbolic conservation laws and is found to be more efficient in terms of memory consumption and computational efficiency with respect to classical WENO reconstruction schemes on unstructured meshes. We also provide evidence that the new algorithm is suitable for implementation on massively parallel distributed memory supercomputers, showing two numerical examples run with more than one billion degrees of freedom in space. To our knowledge, at present these are the largest simulations ever run with unstructured WENO finite volume schemes.

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.

Giovanni Russo, Pietro Santagati, Seok-Bae Yun

Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced [8, 17, 18]. These methods work in a satisfactory way either in rarefied or fluid regime. Moreover, because of the semi-Lagrangian feature, the stability property is not restricted by the CFL condition. These aspects make them very attractive for practical applications. In this paper, we investigate the convergence properties of the method and prove that the discrete solution of the scheme converges in a weighted L1 norm to the unique smooth solution by deriving an explicit error estimate.

Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini et al.

We review recent results and present new ones on a deterministic follow-the-leader particle approximation of first and second order models for traffic flow and pedestrian movements. We start by constructing the particle scheme for the first order Lighthill-Whitham-Richards (LWR) model for traffic flow. The approximation is performed by a set of ODEs following the position of discretised vehicles seen as moving particles. The convergence of the scheme in the many particle limit towards the unique entropy solution of the LWR equation is proven in the case of the Cauchy problem on the real line. We then extend our approach to the Initial-Boundary Value Problem (IBVP) with time-varying Dirichlet data on a bounded interval. In this case we prove that our scheme is convergent strongly in $L^1$ up to a subsequence. We then review extensions of this approach to the Hughes model for pedestrian movements and to the second order Aw-Rascle-Zhang (ARZ) model for vehicular traffic. Finally, we complement our results with numerical simulations. In particular, the simulations performed on the IBVP and the ARZ model suggest the consistency of the corresponding schemes, which is easy to prove rigorously in some simple cases.

Jing-Mei Qiu, Giovanni Russo

In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear advection problems, see {\em Cheng and Knorr, Journal of Computational Physics, 22(1976)}. However, such splitting is subject to the splitting error. If we consider multi-dimensional problems without splitting, difficulty arises in tracing characteristics with high order accuracy. Specifically, the evolution of characteristics is subject to the electric field which is determined globally from the distribution of particle densities via the Poisson's equation. In this paper, we propose a novel strategy of tracing characteristics high order in time via a two-stage multi-derivative prediction-correction approach and by using moment equations of the VP system. With the foot of characteristics being accurately located, we proposed to use weighted essentially non-oscillatory (WENO) interpolation to recover function values between grid points, therefore to update solutions at the next time level. The proposed algorithm does not have time step restriction as Eulerian approach and enjoys high order spatial and temporal accuracy. However, such finite difference algorithm does not enjoy mass conservation; we discuss one possible way of resolving such issue and its potential challenge in numerical stability. The performance of the proposed schemes are numerically demonstrated via classical test problems such as Landau damping and two stream instabilities.

Giovanni Russo, Seok-Bae Yun

The ellipsoidal BGK model is a generalized version of the original BGK model designed to reproduce the physical Prandtl number in the Navier-Stokes limit. In this paper, we propose a new implicit semi-Lagrangian scheme for the ellipsoidal BGK model, which, by exploiting special structures of the ellipsoidal Gaussian, can be transformed into a semi-explicit form, guaranteeing the stability of the implicit methods and the efficiency of the explicit methods at the same time. We then derive an error estimate of this scheme in a weighted $L^{\infty}$ norm. Our convergence estimate holds uniformly in the whole range of relaxation parameter $ν$ including $ν=0$, which corresponds to the original BGK model.

Yingqi Gu, Mingming Liu, Joe Naoum-Sawaya et al.

Electric Vehicles (EVs) and Plug-in Hybrid Electric Vehicles (PHEVs) are increasingly being seen as a means of mitigating the pressing concerns of traffic-related pollution. While hybrid vehicles are usually designed with the objective of minimising fuel consumption, in this paper we propose engine management strategies that also take into account environmental effects of the vehicles to pedestrians outside of the vehicles. Specifically, we present optimisation based engine energy management strategies for PHEVs, that attempt to minimise the environmental impact of pedestrians along the route of the vehicle, while taking account of route dependent uncertainties. We implement the proposed approach in a real PHEV, and evaluate the performance in a hardware-in-the-loop platform. A variety of simulation results are given to illustrate the efficacy of our proposed approach.

Armando Coco, Giovanni Russo

In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is based on the Ghost Fluid Method, making use of ghost points on which the value is defined by suitable interface conditions. The multi-domain formulation is adopted, where the problem is split in two sub-problems and interface conditions will be enforced to close the problem. Interface conditions are relaxed together with the internal equations, leading to an iterative method on all the set of grid values (inside points and ghost points). A multigrid approach with a suitable definition of the restriction operator is provided. The restriction of the defect is performed separately for both sub-problems, providing a convergence factor close to the one measured in the case of smooth coefficient and independent on the magnitude of the jump in the coefficient. Numerical tests will confirm the second order accuracy. Although the method is proposed in one dimension, the extension in higher dimension is currently underway.

Pietro Santagati, Giovanni Russo

This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a Lagrangian formulation of the problem: information is stored on a fixed grid in space and velocity, and the equation is integrated along the characteristics. The source term is treated implicitly by using a DIRK (Diagonally Implicit Runge Kutta) scheme in order to avoid the time step restriction due to the stiff relaxation. In particular some L-stable schemes are tested by smooth and Riemann problems, both in rarefied and fully fluid regimes. Numerical results show good accuracy and efficiency of the method.

Emiland Garrabe, Hozefa Jesawada, Carmen Del Vecchio et al.

This paper is concerned with a finite-horizon inverse control problem, which has the goal of reconstructing, from observations, the possibly non-convex and non-stationary cost driving the actions of an agent. In this context, we present a result enabling cost reconstruction by solving an optimization problem that is convex even when the agent cost is not and when the underlying dynamics is nonlinear, non-stationary and stochastic. To obtain this result, we also study a finite-horizon forward control problem that has randomized policies as decision variables. We turn our findings into algorithmic procedures and show the effectiveness of our approach via in-silico and hardware validations. All experiments confirm the effectiveness of our approach.

Shaun Sweeney, Rodrigo Ordonez-Hurtado, Francesco Pilla et al.

The effect of transport-related pollution on human health is fast becoming recognised as a major issue in cities worldwide. Cyclists, in particular, face great risks, as they typically are most exposed to tail-pipe emissions. Three avenues are being explored worldwide in the fight against urban pollution: (i) outright bans on polluting vehicles and embracing zero tailpipe emission vehicles; (ii) measuring air-quality as a means to better informing citizens of zones of higher pollution; and (iii) developing smart mobility devices that seek to minimize the effect of polluting devices on citizens as they transport goods and individuals in our cities. Following this latter direction, in this paper we present a new way to protect cyclists from the effect of urban pollution. Namely, by exploiting the actuation possibilities afforded by pedelecs or e-bikes (electric bikes), we design a cyber-physical system that mitigates the effect of urban pollution by indirectly controlling the breathing rate of cyclists in polluted areas. Results from a real device are presented to illustrate the efficacy of our system.

Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini et al.

We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely, we introduce deterministic particle schemes for the Hughes model for pedestrian movements and for two vehicular traffic models, that are the scalar Lighthill-Whitham-Richards model (LWR) and the $2\times2$ system Aw-Rascle-Zhang model (ARZ). Their approximation is performed by a set of ODEs, determining the motion of platoons of possible fractional vehicles or pedestrians seen as particles. Convergence results of the schemes in the many particle limit are stated. The numerical simulations suggest the consistency of the schemes.

Zhennan Zhou, Giovanni Russo

In this paper, we reformulate the semi-classical Schrödinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schrödinger equation is equivalently transformed into another Schrödinger type wave equation, the $w$ equation, which is essentially not oscillatory and thus requires much less computational effort. We propose two numerical methods to solve the $w$ equation, where the Hamiltonian is either divided into the kinetic, the potential and the convection part, or into the kinetic and the potential-convection part. The convection, or the potential-convection part is treated by a semi-Lagrangian method, while the kinetic part is solved by the Fourier spectral method. The numerical methods are proved to be unconditionally stable, spectrally accurate in space and second order accurate in time, and in principle they can be extended to higher order schemes in time. Various one dimensional and multidimensional numerical tests are provided to justify the properties of the proposed methods.

Francesco De Lellis, Marco Coraggio, Giovanni Russo et al.

One of the major challenges in Deep Reinforcement Learning for control is the need for extensive training to learn the policy. Motivated by this, we present the design of the Control-Tutored Deep Q-Networks (CT-DQN) algorithm, a Deep Reinforcement Learning algorithm that leverages a control tutor, i.e., an exogenous control law, to reduce learning time. The tutor can be designed using an approximate model of the system, without any assumption about the knowledge of the system's dynamics. There is no expectation that it will be able to achieve the control objective if used stand-alone. During learning, the tutor occasionally suggests an action, thus partially guiding exploration. We validate our approach on three scenarios from OpenAI Gym: the inverted pendulum, lunar lander, and car racing. We demonstrate that CT-DQN is able to achieve better or equivalent data efficiency with respect to the classic function approximation solutions.

Antonio Baeza, Sebastiano Boscarino, Pep Mulet et al.

In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method for the numerical solution of ODEs is presented. This methods can be regarded as an approximate formulation of the Taylor methods and it follows an approach that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their high order derivatives, are needed. In this reference, the absolute stability region of the new methods is conjectured to be coincident with that of their exact counterparts. There is also a conjecture about their relationship with Runge-Kutta methods. In this work we answer positively both conjectures.

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

We investigate the problem of using a learning-based strategy to stabilize a synthetic toggle switch via an external control approach. To overcome the data efficiency problem that would render the algorithm unfeasible for practical use in synthetic biology, we adopt a sim-to-real paradigm where the policy is learnt via training on a simplified model of the toggle switch and it is then subsequently exploited to control a more realistic model of the switch parameterized from in-vivo experiments. Our in-silico experiments confirm the viability of the approach suggesting its potential use for in-vivo control implementations.

Armando Coco, Giovanni Russo

In this paper we present a multigrid approach to solve the Poisson equation in arbitrary domain (identified by a level set function) and mixed boundary conditions. The discretization is based on finite difference scheme and ghost-cell method. This multigrid strategy can be applied also to more general problems where a non-eliminated boundary condition approach is used. Arbitrary domain make the definition of the restriction operator for boundary conditions hard to find. A suitable restriction operator is provided in this work, together with a proper treatment of the boundary smoothing, in order to avoid degradation of the convergence factor of the multigrid due to boundary effects. Several numerical tests confirm the good convergence property of the new method.

Francesco De Lellis, Marco Coraggio, Giovanni Russo et al.

In addressing control problems such as regulation and tracking through reinforcement learning, it is often required to guarantee that the acquired policy meets essential performance and stability criteria such as a desired settling time and steady-state error prior to deployment. Motivated by this necessity, we present a set of results and a systematic reward shaping procedure that (i) ensures the optimal policy generates trajectories that align with specified control requirements and (ii) allows to assess whether any given policy satisfies them. We validate our approach through comprehensive numerical experiments conducted in two representative environments from OpenAI Gym: the Inverted Pendulum swing-up problem and the Lunar Lander. Utilizing both tabular and deep reinforcement learning methods, our experiments consistently affirm the efficacy of our proposed framework, highlighting its effectiveness in ensuring policy adherence to the prescribed control requirements.

Klaas Willems, Axel Klar, Giovanni Russo et al.

We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in which grid points move with the local mean velocity of the gas. The main advantage of the moving grid is that the algorithm can deal well with cases where the domain boundaries are time-dependent and the simulation domain contains rigid objects. Due to the irregular nature of the grid, we use a novel meshless MUSCL-like Moving Least Squares Method (MLS) for spatial discretisation coupled with a higher-order Implicit-Explicit Runge-Kutta method. To avoid spurious oscillations at discontinuities, we use the so-called Multi-dimensional Optimal Order Detection (MOOD) method with an adapted criterion to relax the discrete maximum property. Finally, we employ a new implementation of the boundary conditions that requires no iterative or extrapolation procedure. The method achieves fourth-order in 1D and second-order in 2D for simulations with moving boundaries. We demonstrate the method's effectiveness on classical test cases such as the driven square cavity, shear layer, and shock tube.

Julien Monteil, Giovanni Russo, Robert Shorten

This paper is concerned with the study of bidirectionally coupled platoon systems. The case considered is when the vehicles are heterogeneous and the coupling can be nonlinear and asymmetric. For such systems, a sufficient condition for $\mathcal{L}_{\infty}$ string stability is presented. The effectiveness of our approach is illustrated via a numerical example, where it is shown how our result can be recast as an optimization problem, allowing to design the control protocol for each vehicle independently on the other vehicles and hence leading to a bottom-up approach for the design of string stable systems able to track a time-varying reference speed.

Rodrigo Ordóñez-Hurtado, Giovanni Russo, Sam Sinnott et al.

Vehicles are becoming connected entities. As a result, a likely scenario is that such entities might be literally bombarded with information from a multitude of devices. In this context, a key challenging requirement for both connected and autonomous vehicles is that they will need to become cognitive bodies, able to parse information and use only the pieces of information that are relevant to the vehicle in the context of a given journey. In order to address this fundamental requirement, a decision engine is presented in this paper. The engine makes it possible for the vehicle to understand which pieces of information are really relevant, and subsequently to process only those pieces of information. In order to illustrate the key features of our system, we show that it is possible to build upon the engine to develop a distributed traffic management system, and then we validate such a system via both conventional (numerical and SUMO-based) simulations and a Hardware-in-the-Loop (HIL) platform. Both the conventional simulations and the HIL validation showed that the engine can be effectively used to design a distributed traffic management system.

Giovanni Russo, Rovert Shorten

This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide conditions for synchronization and consensus for networks of nonlinear, diffusively coupled nodes, where noise diffusion is not just additive but it depends on the nodes' state. The sufficient condition we provide, wich links together network topology, coupling strength and noise diffusion, offers two interesting interpretations. First, as suggested by {\em intuition}, in order for a network to achieve synchronization/consensus, its nodes need to be sufficiently well connected together. The second implication might seem, instead, counter-intuitive: if noise diffusion is {\em properly} designed, then it can drive an unsynchronized network towards synchronization/consensus. Motivated by our current research in Smart Cities and Internet of Things, we illustrate the effectiveness of our approach by showing how our results can be used to control certain collective decision processes.

Clarissa Astuto, Giovanni Russo

In this paper, we propose and validate a two-species Multiscale model for a Poisson-Nernst-Planck (PNP) system, focusing on the correlated motion of positive and negative ions under the influence of a trap. Specifically, we aim to model surface traps whose attraction range, of length $δ$, is much smaller then the scale of the problem. The physical setup we refer to is an anchored gas drop (bubble) surrounded by a flow of charged surfactants {(composed by positive and negative ions) that diffuses in water. When the diffusing surfactants reach the surface of the trap, the negative ions are adsorbed because of their hydrophobic tail that is attracted by the air bubble}. As in our previous works, the effect of the attractive potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The novelty of this work is the extension of the model proposed in \cite{astuto2023multiscale}, now incorporating the influence of both carriers -- positive and negative ions -- simultaneously, which is often neglected in traditional approaches that treat ion species independently. The two carriers interact through the Coulomb potential, that is computed by a Poisson equation. [...]

Veronica Centorrino, Francesca Rossi, Francesco Bullo et al.

This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications. To tackle these optimization problems, inspired by recent results, we introduce the \emph{proportional--integral proximal gradient dynamics} (PI--PGD): a closed-loop system where the Lagrange multipliers are control inputs and states are the problem decision variables. First, we establish the equivalence between the stationary points of the minimization problem and the equilibria of the PI--PGD. Then for the case of affine constraints, by leveraging tools from contraction theory we give a comprehensive convergence analysis for the dynamics, showing linear--exponential convergence towards the equilibrium. That is, the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. Our findings are illustrated numerically on a set of representative examples, which include an exploratory application to nonlinear equality constraints.

Vyacheslav Kungurtsev, Giovanni Russo

Fully Probabilistic design (FPD) is a powerful framework offering an elegant and unifying account of stochastic control, learning and decision-making. Here we introduce a generalized FPD framework, which we term as Tsallis FPD. Tsallis FPD uses Tsallis divergence in place of the Kullback-Leibler divergence that defines the standard FPD cost term. Tsallis divergence is a natural generalization of the KL divergence, rooted in non-extensive statistical mechanics and providing flexibility towards modeling stochastic processes with non-Gaussian tail behavior. After formulating Tsallis FPD, we develop a constructive proof of convergence by formulating a fixed point iteration. The construction takes the form of a double iteration scheme that performs a sequence of backwards inductions, rather than a single pass down the stages that constitutes the proven approach for classical FPD. We prove that this construction asymptotically converges to a fixed point and that this fixed point is an optimal solution to Tsallis FPD.

Hridya Dilip, Clarissa Astuto, Armando Coco et al.

We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set function. The proposed approach relies on a space discretization based on the ghost finite element method (ghost-FEM), which allows computations on unfitted meshes and avoids costly remeshing as the domain evolves in time. Time integration is performed using an IMplicit-EXplicit (IMEX) scheme to address the nonlinearity of the convective term, ensuring high-order accuracy for incompressible flows. The error introduced by the geometrical approximation is handled using the Shifted Boundary Method, which allows higher order approximations of boundary conditions on unfitted meshes. Dirichlet boundary conditions are imposed weakly by means of Nitsche's method. The associated stabilization parameter is chosen by solving a generalized eigenvalue problem, ensuring stability and accuracy of the numerical scheme. We present a series of numerical experiments designed to validate the accuracy of the proposed method, as well as comparisons with established benchmark problems involving moving boundaries.

Francesca Rossi, Veronica Centorrino, Francesco Bullo et al.

The ability to compose acquired skills to plan and execute behaviors is a hallmark of natural intelligence. Yet, despite remarkable cross-disciplinary efforts, a principled account of how task structure shapes gating and how such computations could be delivered in neural circuits, remains elusive. Here we introduce GateMod, an interpretable theoretically grounded computational model linking the emergence of gating to the underlying decision-making task, and to a neural circuit architecture. We first develop GateFrame, a normative framework casting policy gating into the minimization of the free energy. This framework, relating gating rules to task, applies broadly across neuroscience, cognitive and computational sciences. We then derive GateFlow, a continuous-time energy based dynamics that provably converges to GateFrame optimal solution. Convergence, exponential and global, follows from a contractivity property that also yields robustness and other desirable properties. Finally, we derive a neural circuit from GateFlow, GateNet. This is a soft-competitive recurrent circuit whose components perform local and contextual computations consistent with known dendritic and neural processing motifs. We evaluate GateMod across two different settings: collective behaviors in multi-agent systems and human decision-making in multi-armed bandits. In all settings, GateMod provides interpretable mechanistic explanations of gating and quantitatively matches or outperforms established models. GateMod offers a unifying framework for neural policy gating, linking task objectives, dynamical computation, and circuit-level mechanisms. It provides a framework to understand gating in natural agents beyond current explanations and to equip machines with this ability.

Allahkaram Shafiei, Hozefa Jesawada, Karl Friston et al.

Despite their groundbreaking performance, state-of-the-art autonomous agents can misbehave when training and environmental conditions become inconsistent, with minor mismatches leading to undesirable behaviors or even catastrophic failures. Robustness towards these training/environment ambiguities is a core requirement for intelligent agents and its fulfillment is a long-standing challenge when deploying agents in the real world. Here, we introduce a Distributionally Robust Free Energy model (DR-FREE) that instills this core property by design. It directly wires robustness into the agent decision-making mechanisms via free energy minimization. By combining a robust extension of the free energy principle with a novel resolution engine, DR-FREE returns a policy that is optimal-yet-robust against ambiguity. The policy has an explicit, soft-max, structure that reveals the mechanistic role of ambiguity on optimal decisions and requisite Bayesian belief updating. We evaluate DR-FREE on an experimental testbed involving real rovers navigating an ambiguous environment filled with obstacles. Across all the experiments, DR-FREE enables robots to successfully navigate towards their goal even when, in contrast, state-of-the-art free energy models fail. In short, DR-FREE can tackle scenarios that elude previous methods: this milestone may inspire both deployment in multi-agent settings and, at a perhaps deeper level, the quest for a biologically plausible explanation of how natural agents -- with little or no training -- survive in capricious environments.

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.

Hozefa Jesawada, Antonio Acernese, Giovanni Russo et al.

Ensuring robustness against epistemic, possibly adversarial, perturbations is essential for reliable real-world decision-making. While the Probabilistic Ensembles with Trajectory Sampling (PETS) algorithm inherently handles uncertainty via ensemble-based probabilistic models, it lacks guarantees against structured adversarial or worst-case uncertainty distributions. To address this, we propose DR-PETS, a distributionally robust extension of PETS that certifies robustness against adversarial perturbations. We formalize uncertainty via a p-Wasserstein ambiguity set, enabling worst-case-aware planning through a min-max optimization framework. While PETS passively accounts for stochasticity, DR-PETS actively optimizes robustness via a tractable convex approximation integrated into PETS planning loop. Experiments on pendulum stabilization and cart-pole balancing show that DR-PETS certifies robustness against adversarial parameter perturbations, achieving consistent performance in worst-case scenarios where PETS deteriorates.

Enrico Ferrentino, Pasquale Chiacchio, Giovanni Russo

We present the principled design of a control pipeline for the synthesis of policies from examples data. The pipeline, based on a discretized design which we term as discrete fully probabilistic design, expounds an algorithm recently introduced in Gagliardi and Russo (2021) to synthesize policies from examples for constrained, stochastic and nonlinear systems. Contrary to other approaches, the pipeline we present: (i) does not need the constraints to be fulfilled in the possibly noisy example data; (ii) enables control synthesis even when the data are collected from an example system that is different from the one under control. The design is benchmarked numerically on an example that involves controlling an inverted pendulum with actuation constraints starting from data collected from a physically different pendulum that does not satisfy the system-specific actuation constraints. We also make our fully documented code openly available.

Francesco De Lellis, Giovanni Russo, Mario di Bernardo

We introduce a control-tutored reinforcement learning (CTRL) algorithm. The idea is to enhance tabular learning algorithms by means of a control strategy with limited knowledge of the system model. By tutoring the learning process, the learning rate can be substantially reduced. We use the classical problem of stabilizing an inverted pendulum as a benchmark to numerically illustrate the advantages and disadvantages of the approach.

Francesco De Lellis, Fabrizia Auletta, Giovanni Russo et al.

We introduce a control-tutored reinforcement learning (CTRL) algorithm. The idea is to enhance tabular learning algorithms so as to improve the exploration of the state-space, and substantially reduce learning times by leveraging some limited knowledge of the plant encoded into a tutoring model-based control strategy. We illustrate the benefits of our novel approach and its effectiveness by using the problem of controlling one or more agents to herd and contain within a goal region a set of target free-roving agents in the plane.

Francesco De Lellis, Fabrizia Auletta, Giovanni Russo et al.

In this extended abstract we introduce a novel control-tutored Q-learning approach (CTQL) as part of the ongoing effort in developing model-based and safe RL for continuous state spaces. We validate our approach by applying it to a challenging multi-agent herding control problem.

Meghana Rathi, Pietro Ferraro, Giovanni Russo

In this paper we propose a new approach to complement reinforcement learning (RL) with model-based control (in particular, Model Predictive Control - MPC). We introduce an algorithm, the MPC augmented RL (MPRL) that combines RL and MPC in a novel way so that they can augment each other's strengths. We demonstrate the effectiveness of the MPRL by letting it play against the Atari game Pong. For this task, the results highlight how MPRL is able to outperform both RL and MPC when these are used individually.

Sebastiano Boscarino, Seung-Yeon Cho, Giovanni Russo et al.

In this paper, we present a conservative semi-Lagrangian finite-difference scheme for the BGK model. Classical semi-Lagrangian finite difference schemes, coupled with an L-stable treatment of the collision term, allow large time steps, for all the range of Knudsen number. Unfortunately, however, such schemes are not conservative. There are two main sources of lack of conservation. First, when using classical continuous Maxwellian, conservation error is negligible only if velocity space is resolved with sufficiently large number of grid points. However, for a small number of grids in velocity space such error is not negligible, because the parameters of the Maxwellian do not coincide with the discrete moments. Secondly, the non-linear reconstruction used to prevent oscillations destroys the translation invariance which is at the basis of the conservation properties of the scheme. As a consequence the schemes show a wrong shock speed in the limit of small Knudsen number. To treat the first problem and ensure machine precision conservation of mass, momentum and energy with a relatively small number of velocity grid points, we replace the continuous Maxwellian with the discrete Maxwellian introduced by Mieussens. The second problem is treated by implementing a conservative correction procedure based on the flux difference form. In this way we can construct a conservative semi-Lagrangian scheme which is Asymptotic Preserving (AP) for the underlying Euler limit, as the Knudsen number vanishes. The effectiveness of the proposed scheme is demonstrated by extensive numerical tests.

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.

Tao Xiong, Giovanni Russo, Jing-Mei Qiu

In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid points, does not necessarily conserve the total mass. To ensure mass conservation, we propose a conservative correction procedure based on a flux difference form. Such procedure guarantees local mass conservation, while introducing time step constraints for stability. We theoretically investigate such stability constraints from an ODE point of view by assuming exact evaluation of spatial differential operators and from the Fourier analysis for linear PDEs. The scheme is tested by classical two dimensional linear passive-transport problems, such as linear advection, rotation and swirling deformation. The scheme is applied to solve the nonlinear Vlasov-Poisson system using a a high order tracing mechanism proposed in [Qiu and Russo, 2016]. Such high order characteristics tracing scheme is generalized to the nonlinear guiding center Vlasov model and incompressible Euler system. The effectiveness of the proposed conservative semi-Lagrangian scheme is demonstrated numerically by our extensive numerical tests.