arXiv subjects

Italo Napolitano

Publications and source records attributed to Italo Napolitano.

9 recordsLinked to original sources

arXiv2026

Second-Order Mean-Field Schrödinger Bridges with Partial State Information

Motivated by scenarios in control systems where decision making is informed by only partial information about the states, we introduce a novel formulation of the Schrödinger bridge problem for inertial interacting-agent systems. Within our setting, the agent ensemble is steered to match partial specifications of the collective configuration. Our analysis pertains to a mean-field framework in which the collective dynamics are described by a nonlinear Vlasov--Fokker--Planck integro-PDE with nonlocal interactions. We assume that only distributions over positions are specified at the endpoints of a finite time horizon, representing aggregate population snapshots, while the corresponding velocity degrees of freedom remain unspecified. We derive the associated optimality system, identifying the optimal controlled evolution as jointly informed by the initial and terminal specifications through forward and backward propagation in time. We also show that the partial endpoint specifications bring about distinct conditions on the optimal control and the consistent evolution. Subsequently, to compute solutions to the optimality system, we develop a nested fixed-point algorithm inspired by the classical Fortet--Sinkhorn iteration, but extended to handle the nonlinearities arising from nonlocal interactions and temporal coupling.

math.OC↗

arXiv2026

Entropy-Regularized Optimal Transport for Time-Varying Multi-Agent Coverage Control

This paper addresses time-varying coverage control for multi-agent systems, formulated as the tracking of an evolving target density via entropy-regularized semi-discrete optimal transport. Unlike the hard Laguerre partition of the unregularized formulation, entropic regularization assigns fractions of the mass at each point to all agents, simplifying the design and numerical implementation of the control law. We derive a feedback-feedforward controller that tracks the evolving first-order optimality conditions with exponential convergence, and we investigate the role of the regularization parameter, which, above a critical threshold, renders the fully collapsed configuration locally optimal. Numerical experiments validate the theory: for moderate regularization, the proposed approach has performance comparable to the unregularized formulation and outperforms the corresponding Voronoi-based coverage baseline.

eess.SY↗

arXiv2026

Semi-discrete Optimal Transport for Time-Varying Multi-Agent Coverage Control

Coverage control algorithms have traditionally focused on static target densities, where agents optimally cover a fixed spatial distribution. However, many applications, such as environmental monitoring, surveillance, and adaptive sensing, involve time-varying densities. While time-varying coverage has been studied in Voronoi-based frameworks, extending recent optimal transport formulations of static coverage control to time-varying target densities remains an open problem. This paper presents a semi-discrete optimal transport framework for time-varying coverage control, in which agents track the first-order optimality conditions associated with minimizing the instantaneous Wasserstein distance from an evolving target density. The proposed approach is based on a coupled system of differential equations governing agent positions and the dual variables defining Laguerre regions. The resulting optimality residuals converge exponentially to zero, with global convergence established for one-dimensional domains. We also derive decentralized approximations and numerical simulations demonstrate improved tracking performance over quasi-static and Voronoi-based methods.

eess.SY↗

arXiv2026

Schrödinger Bridges over Kinetic Swarming Models

Paradigmatic interaction models explain how collective behaviors can emerge in complex systems from interactions among the constituent agents. In bio-inspired swarms, however, interactions alone may not suffice to bring the population to a desired aggregate configuration within a prescribed time horizon, as needed in applications ranging from targeted therapy to collective transport and emergency evacuation. In the present work, we consider finite-horizon minimum-energy collective steering for inertial swarms that are subject to stochastic disturbances. We focus on the mean-field representations of these multi-agent systems driven by Cucker--Smale alignment or Morse attraction--repulsion interactions. Our objective is to steer the swarm between prescribed endpoint distributions using a state-feedback control, where the endpoint specifications can be full phase-space distributions (positions and velocities) or position marginals alone. Our formalism is rooted in the theory of Schrödinger bridges, which has inspired contemporary developments spanning statistical inference, biological modeling, stochastic control, and generative learning. Within the bridges framework, the uncontrolled interacting stochastic dynamics are viewed as a prior model, and the optimal control as the minimum-energy corrective drift needed to realize the prescribed distributions. We derive nonlinear, coupled necessary optimality systems with a time-symmetric structure reminiscent of classical Schrödinger bridges, and propose nested fixed-point schemes to numerically solve them. Numerical examples show that the obtained optimal control (corrective drift) can dynamically exploit or counteract the interaction forces, depending on whether the latter are favorable or adversarial to the steering task.

math.OC↗

arXiv2026

Sparse shepherding control of large-scale multi-agent systems via Reinforcement Learning

We propose a Reinforcement Learning framework for sparse indirect control of large-scale multi-agent systems, where few controlled agents shape the collective behavior of many uncontrolled agents. The approach addresses this multi-scale challenge by coupling ODEs (modeling controlled agents) with a PDE (describing the uncontrolled population density), capturing how microscopic control achieves macroscopic objectives. Our method combines model-free Reinforcement Learning with adaptive interaction strength compensation to overcome sparse actuation limitations. Numerical validation demonstrates effective density control, with the system achieving target distributions while maintaining robustness to disturbances and measurement noise, confirming that learning-based sparse control can replace computationally expensive online optimization.

eess.SY↗

arXiv2025

Decentralized Shepherding of Non-Cohesive Swarms Through Cluttered Environments via Deep Reinforcement Learning

This paper investigates decentralized shepherding in cluttered environments, where a limited number of herders must guide a larger group of non-cohesive, diffusive targets toward a goal region in the presence of static obstacles. A hierarchical control architecture is proposed, integrating a high-level target assignment rule, where each herder is paired with a selected target, with a learning-based low-level driving module that enables effective steering of the assigned target. The low-level policy is trained in a one-herder-one-target scenario with a rectangular obstacle using Proximal Policy Optimization and then directly extended to multi-agent settings with multiple obstacles without requiring retraining. Numerical simulations demonstrate smooth, collision-free trajectories and consistent convergence to the goal region, highlighting the potential of reinforcement learning for scalable, model-free shepherding in complex environments.

eess.SY↗

arXiv2025

Hierarchical Learning-Based Control for Multi-Agent Shepherding of Stochastic Autonomous Agents

Multi-agent shepherding represents a challenging distributed control problem where herder agents must coordinate to guide independently moving targets to desired spatial configurations. Most existing control strategies assume cohesive target behavior, which frequently fails in practical applications where targets exhibit stochastic autonomous behavior. This paper presents a hierarchical learning-based control architecture that decomposes the shepherding problem into a high-level decision-making module and a low-level motion control component. The proposed distributed control system synthesizes effective control policies directly from closed-loop experience without requiring explicit inter-agent communication or prior knowledge of target dynamics. The decentralized architecture achieves cooperative control behavior through emergent coordination without centralized supervision. Experimental validation demonstrates superior closed-loop performance compared to state-of-the-art heuristic control methods, achieving 100\% success rates with improved settling times and control efficiency. The control architecture scales beyond its design conditions, adapts to time-varying goal regions, and demonstrates practical implementation feasibility through real-time experiments on the Robotarium platform.

eess.SY↗

arXiv2025

Hierarchical Policy-Gradient Reinforcement Learning for Multi-Agent Shepherding Control of Non-Cohesive Targets

We propose a decentralized reinforcement learning solution for multi-agent shepherding of non-cohesive targets using policy-gradient methods. Our architecture integrates target-selection with target-driving through Proximal Policy Optimization, overcoming discrete-action constraints of previous Deep Q-Network approaches and enabling smoother agent trajectories. This model-free framework effectively solves the shepherding problem without prior dynamics knowledge. Experiments demonstrate our method's effectiveness and scalability with increased target numbers and limited sensing capabilities.

cs.LG↗

arXiv2024

Emergent Cooperative Strategies for Multi-Agent Shepherding via Reinforcement Learning

We present a decentralized reinforcement learning (RL) approach to address the multi-agent shepherding control problem, departing from the conventional assumption of cohesive target groups. Our two-layer control architecture consists of a low-level controller that guides each herder to contain a specific target within a goal region, while a high-level layer dynamically selects from multiple targets the one an herder should aim at corralling and containing. Cooperation emerges naturally, as herders autonomously choose distinct targets to expedite task completion. We further extend this approach to large-scale systems, where each herder applies a shared policy, trained with few agents, while managing a fixed subset of agents.

eess.SY↗