# Fabian Wirth's research while affiliated with Universität Passau and other places

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## Publications (256)

In power systems, one wishes to regulate the aggregate demand of an ensemble of distributed energy resources (DERs), such as controllable loads and battery energy storage systems. We propose a notion of predictability and fairness, which suggests that the long-term averages of prices or incentives offered should be independent of the initial states...

The AIMD algorithm, which underpins the Transmission Control Protocol (TCP) for transporting data packets in communication networks, is perhaps the most successful control algorithm ever deployed. Recently, its use has been extended beyond communication networks, and successful applications of the AIMD algorithm have been reported in transportation...

We study input-to-state stability (ISS) of discrete-time networks of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for ISS with respect to a closed set and show the necessity of the proposed small-gain condition in case of exponentially ISS infinite networks. Moreover, we study the well-posedness o...

We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified on which the order is total, but it is shown that already for the set of distributions with compactly supporte...

In power systems, one wishes to regulate the aggregate demand of an ensemble of distributed energy resources (DERs), such as controllable loads and battery energy storage systems. We suggest a notion of predictability and fairness, which suggests that the long-term averages of prices or incentives offered should be independent of the initial states...

We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the particular model of the hyperreals, specifically the underlying ultrafilter. Hence, our distribution family is const...

In a federated setting, agents coordinate with a central agent or a server to solve an optimization problem in which agents do not share their information with each other. Wirth and his co-authors, in a recent paper, describe how the basic additive-increase multiplicative-decrease (AIMD) algorithm can be modified in a straightforward manner to solv...

We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified on which the order is total, but it is shown that already for the set of distributions with compactly supporte...

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study both linear and nonlinear dynamical systems on time scales. Specifically, we start with considering linear time...

Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a closed set and show that every exponentially input-to-state stable system necessarily satisfies the proposed...

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study both linear and nonlinear dynamical systems on time scales. Specifically, we start with considering linear time...

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop...

In many sharing economy scenarios, agents both produce as well as consume a resource; we call them prosumers. A community of prosumers agrees to sell excess resource to another community in a prosumer market. In this chapter, we propose a control theoretic approach to regulate the number of prosumers in a prosumer community, where each prosumer has...

In several social choice problems, agents collectively make decisions over the allocation of multiple divisible and heterogeneous resources with capacity constraints to maximize utilitarian social welfare. The agents are constrained through computational or communication resources or privacy considerations. In this paper, we analyze the convergence...

We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class, the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies integral-to-integral input-to-state stability. Assuming further regularity it is possible to conclude input-to-state st...

In this paper we consider countable couplings of finite-dimensional input-to-state stable systems. We consider the whole interconnection as an infinite-dimensional system on the ∞ state space. We develop stability conditions of the small-gain type to guarantee that the whole system remains ISS and highlight the differences between finite and infini...

Across smart-grid and smart-city application domains, there are many problems where an ensemble of agents is to be controlled such that both the aggregate behaviour and individual-level perception of the system’s performance are acceptable. In many applications, traditional PI control is used to regulate aggregate ensemble performance. Our principa...

In this work, we establish different control design approaches for discrete-time systems, which build upon the notion of finite-step control Lyapunov functions (fs-CLFs). The design approaches are formulated as optimization problems and solved in a model predictive control (MPC) fashion. In particular, we establish contractive multi-step MPC with a...

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume Lyapunov stability of the uncontrolled system, and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop sys...

We investigate integral input-to-state stability (iISS) of nonlinear networked control systems (NCSs). The controller is designed by emulation, i.e. it is constructed to ensure iISS for the closed-loop system in the absence of the network. Afterwards, the latter is taken into account and explicit conditions are provided on the scheduling protocol a...

A stochastic algorithm is presented for a class of optimisation problems that arise when a group of agents compete to share a single constrained resource in an optimal manner. The approach uses intermittent single-bit feedback, which indicates a constraint violation and does not require inter-agent communication. The algorithm is based on a positiv...

In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic s...

In this paper we consider countable couplings of finite-dimensional input-to-state stable systems. We consider the whole interconnection as an infinite-dimensional system on the ℓ∞ state space. We develop stability conditions of the small-gain type to guarantee that the whole system remains ISS and highlight the differences between finite and infin...

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume Lyapunov stability of the uncontrolled system, and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop sys...

We study a class of distributed optimization problems for multiple shared resource allocation in Internet-connected devices. We propose a derandomized version of an existing stochastic additive-increase and multiplicative-decrease (AIMD) algorithm. The proposed solution uses one bit feedback signal for each resource between the system and the Inter...

Internet-of-Things (IoT) enables the development of sharing economy applications. In many sharing economy scenarios, agents both produce as well as consume a resource; we call them prosumers. A community of prosumers agrees to sell excess resource to another community in a prosumer market. In this chapter, we propose a control theoretic approach to...

Internet-of-Things (IoT) enables the development of sharing economy applications. In many sharing economy scenarios, agents both produce as well as consume a resource; we call them prosumers. A community of prosumers agrees to sell excess resource to another community in a prosumer market. In this chapter, we propose a control theoretic approach to...

We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies integral input-to-integral state stability. Assuming further regularity it is possible to conclude input-to-state stabil...

We study a class of distributed optimization problems for multiple shared resource allocation in Internet-connected devices. We propose a derandomized version of an existing stochastic additive-increase and multiplicative-decrease (AIMD) algorithm. The proposed solution uses one bit feedback signal for each resource between the system and the Inter...

In several smart city applications, multiple resources must be allocated among competing agents that are coupled through such shared resources and are constrained --- either through limitations of communication
infrastructure or privacy considerations. We propose a distributed algorithm to solve such distributed multi-resource allocation problems w...

In several smart city applications, multiple resources must be allocated among competing agents that are coupled through such shared resources and are constrained --- either through limitations of communication infrastructure or privacy considerations. We propose a distributed algorithm to solve such distributed multi-resource allocation problems w...

Across smart-grid and smart-city applications, there are problems where an ensemble of agents is to be controlled such that both the aggregate behaviour and individual-level perception of the system's performance are acceptable. In many applications, traditional PI control is used to regulate aggregate ensemble performance. Our principal contributi...

In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic s...

In this paper we present a generalization of a recent result on the almost sure consensus for networks affected by relative-state-dependent measurement noise. Specifically, we give two sufficient conditions for the synchronization of networks of diffusively coupled nonlinear nodes affected by certain state-dependent noise diffusion processes. We us...

We consider a control problem involving several agents coupled through multiple unit-demand resources. Such resources are indivisible, and each agent's consumption is modeled as a Bernoulli random variable. Controlling the number of such agents in a probabilistic manner, subject to capacity constraints, is ubiquitous in smart cities. For instance,...

We consider a control problem involving several agents coupled through multiple unit-demand resources. Such resources are indivisible, and each agent’s consumption is modeled as a Bernoulli random variable. Controlling the number of such agents in a probabilistic manner, subject to capacity constraints, is ubiquitous in smart cities. For instance,...

In this paper a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite-and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic sta...

We propose a distributed algorithm to solve a special distributed multi-resource allocation problem with no direct inter-agent communication. We do so by extending a recently introduced additive-increase multiplicative-decrease (AIMD) algorithm, which only uses very little communication between the system and agents. Namely, a control unit broadcas...

We consider a class of consensus systems driven by a nonlinear input. Such systems arise in a class of
Internet of Things (IOT) applications. Our objective in this paper is to determine conditions under which a
certain partially distributed system converges to a Lur’e-like scalar system, and to provide a rigorous proof
of its stability. Conditions...

We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that ISS is equivalent to existence of a non-coercive ISS Lyapunov function and provide two simpler constructions o...

This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of the existing small-gain theorems. In particular, we introduce small-gain conditions that are necessary and sufficient to ensure input-to-state stability (ISS) with respect to closed sets. Toward this end, we first develop a Lyapunov characteriz...

We investigate integral input-to-state stability (iISS) of networked control systems (NCSs). In particular, we establish that the bound for the maximum allowable transfer interval (MATI) developed in [Carnevale et al., 2007] also allows for iISS of NCS with an emulated controller. It is also established that our results subsume existing work on inp...

We present several results describing the interplay between the max algebraic joint spectral radius (JSR) for compact sets of matrices and suitably defined matrix norms. In particular, we extend a classical result for the conventional algebra, showing that the JSR can be described in terms of induced norms of the matrices in the set. We also show t...

We first recall and describe some recently published results giving sufficient conditions for persistence and the existence of periodic solutions for switched SIS epidemiological models. We extend the result on the existence of persistent switching signals in two ways. We establish uniform strong persistence where previous work only guaranteed weak...

We discuss the applicability of classical control theory to problems in smart grids and smart cities. We use tools from iterated function systems to identify controllers with desirable properties. In particular, controllers are identified that can be used to design not only stable closed-loop systems, but also to regulate large-scale populations of...

It is known that the stability of a Metzler matrix can be characterised in a Routh-Hurwitz like fashion based on a recursive application of scalar Schur complements [1]. Our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result, and can be deduced directly therefrom using only e...

We prove characterizations of ISS for a large class of infinite-dimensional control systems, including differential equations in Banach spaces, time-delay systems, ordinary differential equations, switched systems. These characterizations generalize well-known criteria of ISS, proved by Sontag and Wang in \cite{SoW96} for ODE systems. For the speci...

We show that existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided an additional mild assumption is fulfilled. For UGAS infinite-dimensional systems with external disturbances we derive a novel ‘integral’ construction of non-coer...

We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied. For evolution equations in Banach spaces with...

This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of the existing small-gain theorems. In particular, we introduce small-gain conditions that are necessary and sufficient to ensure input-to-state stability (ISS) with respect to not-necessarily compact sets. Toward this end, we first develop a Lya...

The recent radical progress in the fields of future Internet and Smart City related technology innovation are transforming society. Describes theupcoming society as a sociotechnical urban superorganismc. One of the main drivers of this transformation is digital technology, whose impact on the structure and on the dynamics of social networks is also...

We show that existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided an additional mild assumption is fulfilled. For UGAS infinite-dimensional systems with external disturbances we derive a novel 'integral' construction of non-coer...

We show by means of counterexamples that many characterizations of input-to-state stability (ISS) known for ODE systems are not valid for general differential equations in Banach spaces. Moreover, these notions or combinations of notions are not equivalent to each other, and can be classified into several groups according to the type and grade of n...

Water network optimization problemsrequiremodeling the progression of flow and pressure over time. The time discretization step for the resulting differential algebraic equation must be chosen carefully; a large time step can result in a solution that bears little relevance to the physical system, and small time steps impact a problem’s tractabilit...