arXiv subjects

Gioele Zardini

Publications and source records attributed to Gioele Zardini.

69 records · Page 4Linked to original sources

arXiv2024

Diagrammatic Negative Information

The flow of information through a complex system can be readily understood with category theory. However, negative information (e.g., what is not possible) does not have an immediately evident categorical representation. The formalization of nategories using unconventional composition addresses this issue, and lets imposed limitations on categories be considered. However, traditional nategories abandon core categorical constructs and rely on extensive mathematical development. This creates a divide between the consideration of positive and negative information composition. In this work, we show that negative information can be considered in a natural categorical manner. This is aided by functor string diagrams, a novel flexible diagrammatic approach that can intuitively show the operation of hom-functors and natural transformations in expressions. This insight reveals how to consider the composition of negative information with foundational categorical constructs without relying on enrichment. We present diagrammatic means to consider not only nategories, but preorders more broadly. This paper introduces diagrammatic methods for the consideration of triangle inequalities and co-designs $\mathbf{DP/Feas_{Bool}}$, showing how important cases of negative information composition can be categorically and diagrammatically approached. In particular, we develop systematic tools to rigorously consider imposed limitations on systems, advancing our mathematical understanding, and present intuitive diagrams which motivate widespread adoption and usage for various applications.

math.CT↗

arXiv2023

Reliability-aware Control of Power Converters in Mobility Applications

This paper introduces an automatic control method designed to enhance the operation of electric vehicles, besides the speed tracking objectives, by including reliability and lifetime requirements. The research considers an automotive power converter which supplies electric power to a permanent magnet synchronous motor (PMSM). The primary control objective is to mitigate the thermal stress on the power electronic Insulate Gate Bipolar Transistors (IGBTs), while simultaneously ensuring effective speed tracking performance. To achieve these goals, we propose an extended H-inf design framework, which includes reliability models. The method is tested in two distinct scenarios: reliability-aware, and reliability-free cases. Furthermore, the paper conducts a lifetime analysis of the IGBTs, leveraging the Rainflow algorithm and temperature data.

eess.SY↗

arXiv2023

Strategic Interactions in Multi-modal Mobility Systems: A Game-Theoretic Perspective

The evolution of existing transportation systems,mainly driven by urbanization and increased availability of mobility options, such as private, profit-maximizing ride-hailing companies, calls for tools to reason about their design and regulation. To study this complex socio-technical problem, one needs to account for the strategic interactions of the heterogeneous stakeholders involved in the mobility ecosystem and analyze how they influence the system. In this paper, we focus on the interactions between citizens who compete for the limited resources of a mobility system to complete their desired trip. Specifically, we present a game-theoretic framework for multi-modal mobility systems, where citizens, characterized by heterogeneous preferences, have access to various mobility options and seek individually-optimal decisions. We study the arising game and prove the existence of an equilibrium, which can be efficiently computed via a convex optimization problem. Through both an analytical and a numerical case study for the classic scenario of Sioux Falls, USA, we illustrate the capabilities of our model and perform sensitivity analyses. Importantly, we show how to embed our framework into a "larger" game among stakeholders of the mobility ecosystem (e.g., municipality, Mobility Service Providers, and citizens), effectively giving rise to tools to inform strategic interventions and policy-making in the mobility ecosystem.

cs.MA↗

arXiv2023

Categorification of Negative Information using Enrichment

In many engineering applications it is useful to reason about "negative information". For example, in planning problems, providing an optimal solution is the same as giving a feasible solution (the "positive" information) together with a proof of the fact that there cannot be feasible solutions better than the one given (the "negative" information). We model negative information by introducing the concept of "norphisms", as opposed to the positive information of morphisms. A "nategory" is a category that has "nom"-sets in addition to hom-sets, and specifies the interaction between norphisms and morphisms. In particular, we have composition rules of the form morphism + norphism $\to$ norphism. Norphisms do not compose by themselves; rather, they use morphisms as catalysts. After providing several applied examples, we connect nategories to enriched category theory. Specifically, we prove that categories enriched in de Paiva's dialectica categories GC, in the case C = Set and equipped with a modified monoidal product, define nategories which satisfy additional regularity properties. This formalizes negative information categorically in a way that makes negative and positive morphisms equal citizens.

math.CT↗

arXiv2022

Co-Design to Enable User-Friendly Tools to Assess the Impact of Future Mobility Solutions

The design of future mobility solutions and the design of the mobility systems they enable are closely coupled. Indeed, knowledge about the intended service of novel mobility solutions would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management policies. This requires tools to study such a coupling and co-design mobility systems in terms of different objectives. We present a framework to address such co-design problems, leveraging a mathematical theory of co-design to frame and solve the problem of designing and deploying an intermodal mobility system, whereby autonomous vehicles service travel demands jointly with micromobility solutions and public transit, in terms of fleets sizing, vehicle characteristics, and public transit service frequency. Our framework is modular and compositional, allowing one to describe the design as the interconnection of simple components and to tackle it from a systemic perspective. Moreover, it requires general monotonicity assumptions and naturally handles multiple objectives, delivering rational, actionable solutions for policy makers. We showcase our methodology in a case study of Washington D.C., USA. Our work suggests the possibility to create user-friendly optimization tools to systematically assess costs and benefits of interventions, and to inform policy-making in the future.

eess.SY↗

arXiv2022

Limits and Colimits in a Category of Lenses

Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.

math.CT↗

arXiv2022

Task-driven Modular Co-design of Vehicle Control Systems

When designing autonomous systems, we need to consider multiple trade-offs at various abstraction levels, and the choices of single (hardware and software) components need to be studied jointly. In this work we consider the problem of designing the control algorithm as well as the platform on which it is executed. In particular, we focus on vehicle control systems, and formalize state-of-the-art control schemes as monotone feasibility relations. We then show how, leveraging a monotone theory of co-design, we can study the embedding of control synthesis problems into the task-driven co-design problem of a robotic platform. The properties of the proposed approach are illustrated by considering urban driving scenarios. We show how, given a particular task, we can efficiently compute Pareto optimal design solutions.

eess.SY↗

arXiv2021

Analysis and Control of Autonomous Mobility-on-Demand Systems

Challenged by urbanization and increasing travel needs, existing transportation systems need new mobility paradigms. In this article, we present the emerging concept of autonomous mobility-on-demand, whereby centrally orchestrated fleets of autonomous vehicles provide mobility service to customers. We provide a comprehensive review of methods and tools to model and solve problems related to autonomous mobility-on-demand systems. Specifically, we first identify problem settings for their analysis and control, from both operational and planning perspectives. We then review modeling aspects, including transportation networks, transportation demand, congestion, operational constraints, and interactions with existing infrastructure. Thereafter, we provide a systematic analysis of existing solution methods and performance metrics, highlighting trends and trade-offs. Finally, we present various directions for further research.

eess.SY↗

arXiv2021

Posetal Games: Efficiency, Existence, and Refinement of Equilibria in Games with Prioritized Metrics

Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a partially ordered set of metrics. This allows one to combine hierarchical priorities of each player with the interactive nature of the environment. By contextualizing standard game theoretical notions, we provide two sufficient conditions on the preference of the players to prove existence of pure Nash Equilibria in finite action sets. Moreover, we define formal operations on the preference structures and link them to a refinement of the game solutions, showing how the set of equilibria can be systematically shrunk. The presented results are showcased in a driving game where autonomous vehicles select from a finite set of trajectories. The results demonstrate the interpretability of results in terms of minimum-rank-violation for each player.

cs.MA↗

arXiv2021

Game Theory to Study Interactions between Mobility Stakeholders

Increasing urbanization and exacerbation of sustainability goals threaten the operational efficiency of current transportation systems and confront cities with complex choices with huge impact on future generations. At the same time, the rise of private, profit-maximizing Mobility Service Providers leveraging public resources, such as ride-hailing companies, entangles current regulation schemes. This calls for tools to study such complex socio-technical problems. In this paper, we provide a game-theoretic framework to study interactions between stakeholders of the mobility ecosystem, modeling regulatory aspects such as taxes and public transport prices, as well as operational matters for Mobility Service Providers such as pricing strategy, fleet sizing, and vehicle design. Our framework is modular and can readily accommodate different types of Mobility Service Providers, actions of municipalities, and low-level models of customers choices in the mobility system. Through both an analytical and a numerical case study for the city of Berlin, Germany, we showcase the ability of our framework to compute equilibria of the problem, to study fundamental tradeoffs, and to inform stakeholders and policy makers on the effects of interventions. Among others, we show tradeoffs between customers satisfaction, environmental impact, and public revenue, as well as the impact of strategic decisions on these metrics.

cs.MA↗

arXiv2021

Co-Design of Embodied Intelligence: A Structured Approach

We consider the problem of co-designing embodied intelligence as a whole in a structured way, from hardware components such as propulsion systems and sensors to software modules such as control and perception pipelines. We propose a principled approach to formulate and solve complex embodied intelligence co-design problems, leveraging a monotone co-design theory. The methods we propose are intuitive and integrate heterogeneous engineering disciplines, allowing analytical and simulation-based modeling techniques and enabling interdisciplinarity. We illustrate through a case study how, given a set of desired behaviors, our framework is able to compute Pareto efficient solutions for the entire hardware and software stack of a self-driving vehicle.

cs.RO↗

arXiv2021

Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Designing cyber-physical systems is a complex task which requires insights at multiple abstraction levels. The choices of single components are deeply interconnected and need to be jointly studied. In this work, we consider the problem of co-designing the control algorithm as well as the platform around it. In particular, we leverage a monotone theory of co-design to formalize variations of the LQG control problem as monotone feasibility relations. We then show how this enables the embedding of control co-design problems in the higher level co-design problem of a robotic platform. We illustrate the properties of our formalization by analyzing the co-design of an autonomous drone performing search-and-rescue tasks and show how, given a set of desired robot behaviors, we can compute Pareto efficient design solutions.

eess.SY↗

arXiv2021

On the Co-Design of AV-Enabled Mobility Systems

The design of autonomous vehicles (AVs) and the design of AV-enabled mobility systems are closely coupled. Indeed, knowledge about the intended service of AVs would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management decisions. This calls for tools to study such a coupling and co-design AVs and AV-enabled mobility systems in terms of different objectives. In this paper, we instantiate a framework to address such co-design problems. In particular, we leverage the recently developed theory of co-design to frame and solve the problem of designing and deploying an intermodal Autonomous Mobility-on-Demand system, whereby AVs service travel demands jointly with public transit, in terms of fleet sizing, vehicle autonomy, and public transit service frequency. Our framework is modular and compositional, allowing one to describe the design problem as the interconnection of its individual components and to tackle it from a system-level perspective. To showcase our methodology, we present a real-world case study for Washington D.C., USA. Our work suggests that it is possible to create user-friendly optimization tools to systematically assess costs and benefits of interventions, and that such analytical techniques might gain a momentous role in policy-making in the future.

eess.SY↗

arXiv2020

A Compositional Sheaf-Theoretic Framework for Event-Based Systems (Extended Version)

A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types, all within a unified, sheaf-theoretic formalism. We take robotic systems as an exemplar of complex systems and rigorously describe actuators, sensors, and algorithms using this framework.

eess.SY↗

arXiv2020

Towards a Co-Design Framework for Future Mobility Systems

The design of Autonomous Vehicles (AVs) and the design of AVs-enabled mobility systems are closely coupled. Indeed, knowledge about the intended service of AVs would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management decisions. This calls for tools to study such a coupling and co-design AVs and AVs-enabled mobility systems in terms of different objectives. In this paper, we instantiate a framework to address such co-design problems. In particular, we leverage the recently developed theory of co-design to frame and solve the problem of designing and deploying an intermodal Autonomous Mobility-on-Demand system, whereby AVs service travel demands jointly with public transit, in terms of fleet sizing, vehicle autonomy, and public transit service frequency. Our framework is modular and compositional, allowing to describe the design problem as the interconnection of its individual components and to tackle it from a system-level perspective. Moreover, it only requires very general monotonicity assumptions and it naturally handles multiple objectives, delivering the rational solutions on the Pareto front and thus enabling policy makers to select a solution through political criteria. To showcase our methodology, we present a real-world case study for Washington D.C., USA. Our work suggests that it is possible to create user-friendly optimization tools to systematically assess the costs and benefits of interventions, and that such analytical techniques might gain a momentous role in policy-making in the future.

eess.SY↗