9,553 research outputs found

    Contraction analysis of nonlinear systems and its application

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    The thesis addresses various issues concerning the convergence properties of switched systems and differential algebraic equation (DAE) systems. Specifically, we focus on contraction analysis problem, as well as tackling problems related to stabilization and synchronization. We consider the contraction analysis of switched systems and DAE systems. To address this, a transformation is employed to convert the contraction analysis problem into a stabilization analysis problem. This transformation involves the introduction of virtual systems, which exhibit a strong connection with the Jacobian matrix of the vector field. Analyzing these systems poses a significant challenge due to the distinctive structure of their Jacobian matrices. Regarding the switched systems, a time-dependent switching law is established to guarantee uniform global exponential stability (UGES). As for the DAE system, we begin by embedding it into an ODE system. Subsequently, the UGES property is ensured by analyzing its matrix measure. As our first application, we utilize our approach to stabilize time-invariant switched systems and time-invariant DAE systems, respectively. This involves designing control laws to achieve system contractivity, thereby ensuring that the trajectory set encompasses the equilibrium point. In oursecond application, we propose the design of a time-varying observer by treating the system’s output as an algebraic equation of the DAE system. In our study on synchronization problems, we investigate two types of synchronization issues: the trajectory tracking of switched oscillators and the pinning state synchronization. In the case of switched oscillators, we devise a time-dependent switching law to ensure that these oscillators effectively follow the trajectory of a time-varying system. As for the pinning synchronization problem, we define solvable conditions and, building upon these conditions, we utilize contraction theory to design dynamic controllers that guarantee synchronization is achieved among the agents

    Choreographing tragedy into the twenty-first century

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    What makes a tragedy? In the fifth century BCE this question found an answer through the conjoined forms of song and dance. Since the mid-twentieth century, and the work of the Tanztheater Wuppertal Pina Bausch, tragedy has been variously articulated as form coming apart at the seams. This thesis approaches tragedy through the work of five major choreographers and a director who each, in some way, turn back to Bausch. After exploring the Tanztheater Wuppertal’s techniques for choreographing tragedy in chapter one, I dedicate a chapter each to Dimitris Papaioannou, Akram Khan, Trajal Harrell, Ivo van Hove with Wim Vandekeybus, and Gisèle Vienne. Bringing together work in Queer and Trans* studies, Performance studies, Classics, Dance, and Classical Reception studies I work towards an understanding of the ways in which these choreographers articulate tragedy through embodiment and relation. I consider how tragedy transforms into the twenty-first century, how it shapes what it might mean to live and die with(out) one another. This includes tragic acts of mythic construction, attempts to describe a sense of the world as it collapses, colonial claims to ownership over the earth, and decolonial moves to enact new ways of being human. By developing an expanded sense of both choreography and the tragic one of my main contributions is a re-theorisation of tragedy that brings together two major pre-existing schools, to understand tragedy not as an event, but as a process. Under these conditions, and the shifting conditions of the world around us, I argue that the choreography of tragedy has and might continue to allow us to think about, name, and embody ourselves outside of the ongoing catastrophes we face

    A heuristic with a performance guarantee for the Commodity constrained Split Delivery Vehicle Routing Problem

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    The Commodity constrained Split Delivery Vehicle Routing Problem (C-SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C-SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially-many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. Several new (best-known) solutions are found in reasonable computational time. The comparison with the state of the art heuristics for solving C-SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality

    Optimising heating and cooling of smart buildings

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    This thesis is concerned with optimization techniques to improve the efficiency of heating and cooling of both existing and new buildings. We focus on the thermal demand-side and we make novel contributions to the optimality of both design and operational questions. We demonstrate that our four novel contributions can reduce operations cost and consumption, optimize retrofit and estimate relevant parameters of the built environment. The ultimate objective of this work is to provide affordable and cost-effective solutions that take advantage of local existing resources. This work addresses four gaps in the state-of-the-art. First, we contribute to current building practice that is mostly based on human experience and simulations, which often leads to oversized heating systems and low efficiency. The results in this thesis show the advantages of using optimization approaches for thermal aspects in buildings. We propose models that seek optimal decisions for one specific design day, as well as an approach that optimizes multiple day-scenarios to more accurately represent a whole year. Second, we study the full potential of buildings’ thermal mass and design. This has not been fully explored due to two factors: the complexity of the mathematics involved, and the fast developing and variety of emerging technologies and approaches. We tackle the mathematical challenge by solving non-linear non-convex models with integer decisions and by estimating building’s thermal mass. We support rapid architectural development by studying flexible models able to adapt to the latest building technologies such as passive house design, smart façades, and dynamic shadings. Third, we consider flexibility provision to significantly reduce total energy costs. Flexibility studies often only focus on flexible building loads but do not consider heating, which is often the largest load of a building and is less flexible. Because of that, we study and model a building’s heating demand and we propose optimization techniques to support greater flexibility of heating loads, allowing buildings to participate more efficiently in providing demand response. Fourth, we consider a building as an integrated system, unlike many other modelling approaches that focus on single aspects. We model a building as a complex system comprising the building’s structure, weather conditions and users’ requirements. Furthermore, we account for design decisions and for new and emerging technologies, such as heat pumps and thermal storage. Optimal decisions come from the joint analysis of all these interconnected factors. The thesis is structured in three parts: the introduction, the main body and the conclusions. The main body is made by five chapters, each of which focuses on one research project and has the following structure: overview, introduction, literature review, mathematical framework description, application and results section, conclusion and future works. The first two chapters discuss the optimization of operational aspects. The first focuses on a single thermal zone and the second in two connected ones. The third chapter is a continuation of the first two, and presents an approach to optimize both operations and design of buildings in a heat community. This approach integrates the use of an energy software already in the market. The fourth chapter discusses an approach to find the optimal refurbishment of an existing building at minimum cost. The fifth chapter shows an inferring model to represent a house of a building stock. We study the common case where the house’s data is lacking or inaccurate, and we present a model that is able to estimate the required thermal parameters for modelling the house using only heating demand

    Conversations on Empathy

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    In the aftermath of a global pandemic, amidst new and ongoing wars, genocide, inequality, and staggering ecological collapse, some in the public and political arena have argued that we are in desperate need of greater empathy — be this with our neighbours, refugees, war victims, the vulnerable or disappearing animal and plant species. This interdisciplinary volume asks the crucial questions: How does a better understanding of empathy contribute, if at all, to our understanding of others? How is it implicated in the ways we perceive, understand and constitute others as subjects? Conversations on Empathy examines how empathy might be enacted and experienced either as a way to highlight forms of otherness or, instead, to overcome what might otherwise appear to be irreducible differences. It explores the ways in which empathy enables us to understand, imagine and create sameness and otherness in our everyday intersubjective encounters focusing on a varied range of "radical others" – others who are perceived as being dramatically different from oneself. With a focus on the importance of empathy to understand difference, the book contends that the role of empathy is critical, now more than ever, for thinking about local and global challenges of interconnectedness, care and justice

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    State-wise Constrained Policy Optimization

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    Reinforcement Learning (RL) algorithms have shown tremendous success in simulation environments, but their application to real-world problems faces significant challenges, with safety being a major concern. In particular, enforcing state-wise constraints is essential for many challenging tasks such as autonomous driving and robot manipulation. However, existing safe RL algorithms under the framework of Constrained Markov Decision Process (CMDP) do not consider state-wise constraints. To address this gap, we propose State-wise Constrained Policy Optimization (SCPO), the first general-purpose policy search algorithm for state-wise constrained reinforcement learning. SCPO provides guarantees for state-wise constraint satisfaction in expectation. In particular, we introduce the framework of Maximum Markov Decision Process, and prove that the worst-case safety violation is bounded under SCPO. We demonstrate the effectiveness of our approach on training neural network policies for extensive robot locomotion tasks, where the agent must satisfy a variety of state-wise safety constraints. Our results show that SCPO significantly outperforms existing methods and can handle state-wise constraints in high-dimensional robotics tasks.Comment: arXiv admin note: text overlap with arXiv:2305.1368

    Online Game with Time-Varying Coupled Inequality Constraints

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    In this paper, online game is studied, where at each time, a group of players aim at selfishly minimizing their own time-varying cost function simultaneously subject to time-varying coupled constraints and local feasible set constraints. Only local cost functions and local constraints are available to individual players, who can share limited information with their neighbors through a fixed and connected graph. In addition, players have no prior knowledge of future cost functions and future local constraint functions. In this setting, a novel decentralized online learning algorithm is devised based on mirror descent and a primal-dual strategy. The proposed algorithm can achieve sublinearly bounded regrets and constraint violation by appropriately choosing decaying stepsizes. Furthermore, it is shown that the generated sequence of play by the designed algorithm can converge to the variational GNE of a strongly monotone game, to which the online game converges. Additionally, a payoff-based case, i.e., in a bandit feedback setting, is also considered and a new payoff-based learning policy is devised to generate sublinear regrets and constraint violation. Finally, the obtained theoretical results are corroborated by numerical simulations.Comment: arXiv admin note: text overlap with arXiv:2105.0620

    RED WoLF Hybrid Energy Storage System: Algorithm Case Study and Green Competition Between Storage Heaters and Heat Pump

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    Green house gases reduction is critical in current climate emergency and was declared as major target by United Nations. This manuscript proposes the progressive adaptive recursive multi threshold control strategy for hybrid energy storage system that combines thermal storage reservoirs, heat pumps, storage heaters, photovoltaic array and a battery. The newest control strategy is tested in numerical experiment against primal dual simplex optimisation method as benchmark and previous iterations of RED WoLF threshold approaches. The proposed algorithm allows improvement in reduction of CO2 emissions by 9 % comparatively to RED WoLF double threshold approach and by 26 % comparatively to RED WoLF single threshold approach. Besides, the proposed technique is at least 100 times faster than linear optimisation, making the algorithm applicable to edge systems. The proposed method is later tested in numerical experiment on two measured datasets from Luxembourg school and office, equipped with batteries and ground source heat pumps. The system allows the reduction of CO2 emission and improvement of self-consumption, size reduction of the photovoltaic array installed at the facilities by at least by half as well as substituting battery storage by thermal storage, reducing the initial investment to the system. Intriguingly, despite 3.6 times difference in efficiency between heat pumps and storage heaters, the system equipped with latter have potential to achieve similar performance in carbon reduction, suggesting that energy storage have more prominent carbon reduction effect, than the power consumption, making cheaper systems with storage heaters a possible alternative to heat pumps
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