No Arabic abstract
We consider a control problem involving several agents coupled through multiple unit-demand resources. Such resources are indivisible, and each agents 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.
We consider the problem of dispatching a fleet of distributed energy reserve devices to collectively meet a sequence of power requests over time. Under the restriction that reserves cannot be replenished, we aim to maximise the survival time of an energy-constrained islanded electrical system; and we discuss realistic scenarios in which this might be the ultimate goal of the grid operator. We present a policy that achieves this optimality, and generalise this into a set-theoretic result that implies there is no better policy available, regardless of the realised energy requirement scenario.
Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -- including structural properties, such as monotonicity, that enable tractability and scalability -- over the specific applications, connections to well-established road traffic flow models are made.
This paper presents a stochastic, model predictive control (MPC) algorithm that leverages short-term probabilistic forecasts for dispatching and rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of self-driving vehicles). We first present the core stochastic optimization problem in terms of a time-expanded network flow model. Then, to ameliorate its tractability, we present two key relaxations. First, we replace the original stochastic problem with a Sample Average Approximation (SAA), and characterize the performance guarantees. Second, we separate the controller into two separate parts to address the task of assigning vehicles to the outstanding customers separate from that of rebalancing. This enables the problem to be solved as two totally unimodular linear programs, and thus easily scalable to large problem sizes. Finally, we test the proposed algorithm in two scenarios based on real data and show that it outperforms prior state-of-the-art algorithms. In particular, in a simulation using customer data from DiDi Chuxing, the algorithm presented here exhibits a 62.3 percent reduction in customer waiting time compared to state of the art non-stochastic algorithms.
The output of renewable energy fluctuates significantly depending on weather conditions. We develop a unit commitment model to analyze requirements of the forecast output and its error for renewable energies. Our model obtains the time series for the operational state of thermal power plants that would maximize the profits of an electric power utility by taking into account both the forecast of output its error for renewable energies and the demand response of consumers. We consider a power system consisting of thermal power plants, photovoltaic systems (PV), and wind farms and analyze the effect of the forecast error on the operation cost and reserves. We confirm that the operation cost was increases with the forecast error. The effect of a sudden decrease in wind power is also analyzed. More thermal power plants need to be operated to generate power to absorb this sudden decrease in wind power. The increase in the number of operating thermal power plants within a short period does not affect the total operation cost significantly; however the substitution of thermal power plants by wind farms or PV systems is not expected to be very high. Finally, the effects of the demand response in the case of a sudden decrease in wind power are analyzed. We confirm that the number of operating thermal power plants is reduced by the demand response. A power utility has to continue thermal power plants for ensuring supply-demand balance; some of these plants can be decommissioned after installing a large number of wind farms or PV systems, if the demand response is applied using an appropriate price structure.
This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our approach differs from well-known structural controllability conditions for linear systems or consensus networks, where controllability conditions are based on edge connectivity (i.e., zero or nonzero edges). Our results first provide a process for merging controllable graphs into a larger controllable graph. Then, based on this process, we provide a graph decomposition process for evaluating the topological controllability of a given network.