Fabian Wirth

Claudio De Persis, Rudolf Sailer, Fabian Wirth

In this paper the problem of stabilizing large-scale systems by distributed controllers, where the controllers exchange information via a shared limited communication medium is addressed. Event-triggered sampling schemes are proposed, where each system decides when to transmit new information across the network based on the crossing of some error thresholds. Stability of the interconnected large-scale system is inferred by applying a generalized small-gain theorem. Two variations of the event-triggered controllers which prevent the occurrence of the Zeno phenomenon are also discussed.

Syed Eqbal Alam, Robert Shorten, Fabian Wirth et al.

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 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 broadcasts a one-bit signal to agents whenever one of the allocated resources exceeds capacity. Agents then respond to this signal in a probabilistic manner. In the proposed algorithm, each agent makes decision of its resource demand locally and an agent is unaware of the resource allocation of other agents. In empirical results, we observe that the average allocations converge over time to optimal allocations.

Syed Eqbal Alam, Robert Shorten, Fabian Wirth et al.

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 regulate the number of prosumers in a prosumer community, where each prosumer has a cost function that is coupled through its time-averaged production and consumption of the resource. Furthermore, each prosumer runs its distributed algorithm and takes only binary decisions in a probabilistic way, whether to produce one unit of the resource or not and to consume one unit of the resource or not. In the proposed approach, prosumers do not explicitly exchange information with each other due to privacy reasons, but little exchange of information is required for feedback signals, broadcast by a central agency. In the proposed approach, prosumers achieve the optimal values asymptotically. Furthermore, the proposed approach is suitable to implement in an IoT context with minimal demands on infrastructure. We describe two use cases; community-based car sharing and collaborative energy storage for prosumer markets. We also present simulation results to check the efficacy of the algorithms.

Syed Eqbal Alam, Robert Shorten, Fabian Wirth et al.

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 Internet-connected devices and does not require inter-device communication. Additionally, the Internet-connected devices do not compromise their privacy and the solution does not dependent on the number of participating devices. In the system, each Internet-connected device has private cost functions which are strictly convex, twice continuously differentiable and increasing. We show empirically that the long-term average allocations of multiple shared resources converge to optimal allocations and the system achieves minimum social cost. Furthermore, we show that the proposed derandomized AIMD algorithm converges faster than the stochastic AIMD algorithm and both the approaches provide approximately same solutions.

Andrii Mironchenko, Fabian Wirth, Antoine Chaillet et al.

We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state stability, provided that uniform global stability can also be ensured using the same LKF. To this end, we develop a stability theory, in which the behavior of solutions is not assessed through the classical norm but rather through a specific LKF, which may provide significantly tighter estimates. We discuss the advantages of our approach by means of an example.

Yingqing Chen, Anni Li, Christos G. Cassandras et al.

Dynamic pricing is commonly used to regulate congestion in shared service systems. This paper is motivated by the fact that when heterogeneaous user groups (in terms of price responsiveness) are present, conventional monotonic pricing can lead to unfair outcomes by disproportionately excluding price-elastic users, particularly under high or uncertain demand. The paper's contributions are twofold. First, we show that when fairness is imposed as a hard state constraint, the optimal (revenue maximizing) pricing policy is generally non-monotonic in demand. This structural result departs fundamentally from standard surge pricing rules and reveals that price reduction under heavy load may be necessary to maintain equitable access. Second, we address the problem that price elasticity among heterogeneous users is unobservable. To solve it, we develop a robust dynamic pricing and admission control framework that enforces resource capacity and fairness constraints for all user type distributions consistent with aggregate measurements. By integrating integral High Order Control Barrier Functions (iHOCBFs) with a worst case robust optimization framework, we obtain a controller that guarantees forward invariance of safety and fairness constraints while optimizing revenue. Numerical experiments demonstrate improved fairness and revenue performance relative to monotonic surge pricing policies.

Syed Eqbal Alam, Fabian Wirth, Jia Yuan Yu

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 solve a class of optimization problems for federated settings for a single shared resource with no inter-agent communication. The AIMD algorithm is one of the most successful distributed resource allocation algorithms currently deployed in practice. It is best known as the backbone of the Internet and is also widely explored in other application areas. We extend the single-resource algorithm to multiple heterogeneous shared resources that emerge in smart cities, sharing economy, and many other applications. Our main results show the convergence of the average allocations to the optimal values. We model the system as a non-homogeneous Markov chain with place-dependent probabilities. Furthermore, simulation results are presented to demonstrate the efficacy of the algorithms and to highlight the main features of our analysis.

Syed Eqbal Alam, Robert Shorten, Fabian Wirth et al.

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, such agents can be humans in a feedback loop---who respond to a price signal, or automated decision-support systems that strive toward system-level goals. In this paper, we consider both single feedback loop corresponding to a single resource and multiple coupled feedback loops corresponding to multiple resources consumed by the same population of agents. For example, when a network of devices allocates resources to deliver several services, these services are coupled through capacity constraints on the resources. We propose a new algorithm with fundamental guarantees of convergence and optimality, as well as present an example illustrating its performance.

Mingming Liu, Fabian Wirth, Martin Corless et al.

We consider a class of consensus systems driven by a nonlinear input. Such systems arise in a class of 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 are derived for the non-uniform convergence and stability of such a system and an example is given of a speed advisory system where such a system arises in real engineering practice.

Mingming Liu, Rodrigo H. Ordóñez-Hurtado, Fabian Wirth et al.

One of the key ideas to make Intelligent Transportation Systems (ITS) work effectively is to deploy advanced communication and cooperative control technologies among the vehicles and road infrastructures. In this spirit, we propose a consensus-based distributed speed advisory system that optimally determines a recommended common speed for a given area in order that the group emissions, or group battery consumptions, are minimised. Our algorithms achieve this in a privacy-aware manner; namely, individual vehicles do not reveal in-vehicle information to other vehicles or to infrastructure. A mobility simulator is used to illustrate the efficacy of the algorithm, and hardware-in-the-loop tests involving a real vehicle are given to illustrate user acceptability and ease of the deployment.