Abstract: The theory of rigidity originates from the study of the structural properties of multi-element geometries to characterize their stiffness and flexibility, positioning itself at the nexus of combinatorics, geometry, and algebra. In the last decade, this theory has extended towards the study of multi-agent systems, leveraging the mathematical descriptions of these dynamical systems through graph-based representation and its interplay with the related algebraic properties. As a result, rigidity theory naturally connects with networked, mobile, and parallel robotics, where heterogeneous agents operate in different spatial domains under actuation, sensing, and communication constraints. Interestingly, rigidity theory not only offers novel insights into classical problems such as localization and formation control, but also enables the design of control strategies for emerging applications, including cooperative transportation tasks and active sensing policies.

Abstract: Multi-robot task planning and control under temporal logic specifications has been gaining increasing attention in recent years due to its applicability among others in autonomous systems, manufacturing systems, service robotics and intelligent transportation. Initial approaches considered qualitative logics, such as Linear Temporal Logic, whose automata representation facilitates the direct use of model checking tools for correct-by-design control synthesis. In many real world applications however, there is a need to quantify spatial and temporal constraints, e.g., in order to include deadlines and separation assurance bounds. This led to the use of quantitative logics, such as Metric Interval and Signal Temporal Logic, to impose such spatiotemporal constraints. However, the lack of direct automata representations for such specifications hinders the use of standard verification tools from computer science, such as model checking. Motivated by this, the use of transient control methodologies that fulfil the aforementioned qualitative constraints becomes evident. In this talk, we review some of our recent results in applying transient control techniques, and in particular Model Predictive Control, Barrier Certificates based design and Prescribed Performance Control, to high level robot task planning under spatiotemporal specifications, treating both the case of a single and a multi-agent system. The results are supported by relevant experimental validations.

Abstract: In this talk we consider the problem of distributed estimation of the state of a discrete-time, linear and time-invariant (LTI) state space model affected by disturbances. A connected sensor network, in which each sensor has access only to part of the control inputs and provides its own output signal (that represents a partial indirect measure of the state), is deployed to reconstruct the state of a target system. Such sensors exchange information and implement a consensus strategy to compensate for the lack of information due to the distributed nature of the proposed scheme. Necessary and sufficient conditions for the existence of distributed unknown input observers with augmented states that achieve both consensus and asymptotic state estimation are derived. The problem solution exploits the theory of decentralized output feedback control, thus making it possible to inherit the algorithms available for the solution of that problem.

Abstract: This talk is divided into two parts. In the first part, we consider constraint-coupled optimization problems where agents in a network aim to cooperatively minimise the sum of local objective functions subject to individual constraints and a common linear coupling constraint. To solve this problem, we propose a solution that embeds a dynamic average consensus protocol in the parallel Alternating Direction Method of Multipliers (ADMM) to design a fully distributed scheme for the considered setup. Convergence to the optimal solution is proved using recent advanced results in the theory of time-scale separation in nonlinear systems. The rate of convergence is shown to be linear under standard assumptions on the local cost functions. Interestingly, the algorithm is amenable to direct implementation to deal with asynchronous communication scenarios that may be corrupted by other non-idealities such as packet loss. In the second part of the talk, we show how the considered optimization scenario often arises in the modelling and control of energy systems. In particular, we focus our attention on the optimal management of the distributed resources populating Energy Communities (ECs). The concept of ECs was introduced by the European Community in the Clean Energy for all Europeans (CEP) package in 2019, as a means to enable citizen-driven energy actions to support the clean energy transition. We envisage that the smart design and management of ECs could pave the way for significant actions to decarbonise our planet.

Abstract: Autonomous systems in a dynamic environment are requested to make decisions, ranging from the low-level control to the high-level planning. For instance, this is the case of self-driving cars and mobile robots. The ecosystem where they live incorporates a full spectrum of computing resources, from IoT devices to the cloud, and a capillary communication system, which is provided by 5G networks. This architecture readily allows autonomous systems to offload any decision process to different computing devices. Control algorithm offloading needs to be efficiently designed to trade-off between the computational power and the communication delay taking into account the underlying dynamic system. In this presentation, we will see when to offload a control algorithm, where to optimally execute it, and how to seamlessly switch from one controller to another through a suitable control design.

Abstract: The optimal mass transport (OMT) problem is a classical mathematical framework with historical roots in planning and logistics. Over the past two decades there has been a rapid development in the field, leading to a mature framework with computationally efficient tools for addressing a wide range of problems in applied mathematics. This talk will focus on multi-marginals OMT and its applications in control and estimation of multi-agent systems. The OMT framework enables a shift from the standard state space formalism, where an individual state evolve over time, to a setting where instead densities or entire multi-agent systems evolve over time. This perspective allows for modeling and solving a large set of problems, e.g., with dynamics of the underlying agents, multiple classes of agents, nonlocal interactions, as well as including constraints between different time points such as origin destination constraints. We will also discuss computational efficient methods for solving these problems, highlighting a dual coordinate ascent approach inspired by Sinkhorn's algorithm for the classical OMT problem.

Abstract: TBA

Abstract: Reinforcement Learning algorithms proved a promising solution to solve complex control problems in  robotics applications. Model-free RL  (MFRL) algorithms are particularly effective in settings where a large amount of data is available, such as virtual environments. As an example, MFRL algorithms reach super-human performance in playing Chess, Shogi, and Go. On the contrary, when dealing with physical systems, the number of samples available is limited, possibly compromising the effectiveness of these technologies. This motivates the interest in data-efficient RL algorithms for physical systems. Among the others, Model-Based RL (MBRL) algorithms are a promising solution: by learning and updating a mathematical model of the system based on interaction data, MBRL algorithms limit interaction time on the actual system. In this talk, we present MC-PILCO, a data-efficient MBRL  algorithm that relies on Gaussian Process Regression (GPR) to model the system dynamics.

Abstract: This talk presents control-theoretic approaches to online optimization in settings where the objective function is time-varying, noisy, and partially uncertain. To achieve this, we propose two algorithms tailored for quadratic objectives evolving according to a stochastic linear model. The first uses Kalman filtering techniques to estimate and adapt to changes in the cost, while the second draws from H$\infty$-control to maintain robustness under significant model uncertainty. Numerical results show that both methods outperform classical gradient-based schemes and deterministic internal model-based approaches. We aim to encourage discussion on how stochastic modeling and control can enhance the design of online optimization algorithms.