1,720,997 research outputs found
Optimal intervention in transportation networks
Full text linkWe study a network design problem (NDP) where the planner aims at selecting
the optimal single-link intervention on a transportation network to minimize
the travel time under Wardrop equilibrium flows. Our first result is that, if
the delay functions are affine and the support of the equilibrium is not
modified with interventions, the NDP may be formulated in terms of electrical
quantities computed on a related resistor network. In particular, we show that
the travel time variation corresponding to an intervention on a given link
depends on the effective resistance between the endpoints of the link. We
suggest an approach to approximate such an effective resistance by performing
only local computation, and exploit it to design an efficient algorithm to
solve the NDP. We discuss the optimality of this procedure in the limit of
infinitely large networks, and provide a sufficient condition for its
optimality. We then provide numerical simulations, showing that our algorithm
achieves good performance even if the equilibrium support varies and the delay
functions are non-linear.Comment: 40 pages, 12 figure
Optimal intervention in transportation networks
Full text linkWe study a network design problem (NDP) where the planner aims at selecting the optimal single-link intervention on a transportation network to minimize the travel time under Wardrop equilibrium flows. Our first result is that, if the delay functions are affine and the support of the equilibrium is not modified with interventions, the NDP may be formulated in terms of electrical quantities computed on a related resistor network. In particular, we show that the travel time variation corresponding to an intervention on a given link depends on the effective resistance between the endpoints of the link. We suggest an approach to approximate such an effective resistance by performing only local computation and exploit it to design an efficient algorithm to solve the NDP. We discuss the optimality of this procedure in the limit of infinitely large networks and provide a sufficient condition for its optimality. We then provide numerical simulations, showing that our algorithm achieves good performance even if the equilibrium support varies and the delay functions are nonlinear
Constrained deterministic leader-follower mean field control
No full textWe consider a mean field game among a large population of noncooperative agents divided into two categories: leaders and followers. Each agent is subject to heterogeneous convex constraints and minimizes a quadratic cost function; the cost of each leader is affected by the leaders' aggregate strategy, while the cost of each follower is affected by both the leaders' and followers' aggregate strategy. We propose a decentralized scheme in which the agents update their strategies optimally with respect to a global incentive signal, possibly different for leaders and followers, broadcast by a central coordinator. We propose several incentive update rules that, under different conditions on the problem data, are guaranteed to steer the population to an ε-Nash equilibrium, with ε decreasing linearly to zero as the number of players increases. We illustrate our theoretical results on a demand-response program between electricity consumers and producers in the day-ahead market
Reachability analysis for switched affine systems and its application to controlled stochastic biochemical reaction networks
No full textUnder suitable assumptions, the moments of a controlled stochastic biochemical reaction network can be computed as the solution of a switched affine system. Motivated by this application, we propose a new method to approximate projections of the reachable set of a switched affine system onto a plane of interest. Our method does not require the computation of the full reachable set, thus allowing us to efficiently analyze the moments of a species of interest in arbitrarily large biochemical networks. To illustrate the benefits of the proposed method we consider a controlled gene expression model involving two species: the mRNA and the corresponding protein. The proposed approach can be used to estimate the reachable set of the protein mean and variance, under less stringent assumptions than those adopted in the literature. Specifically, we address the cases of multiple controlled reactions and heterogeneous population
On the use of hyperplane methods to compute the reachable set of controlled stochastic biochemical reaction networks
No full textOn constrained mean field control for large populations of heterogeneous agents: Decentralized convergence to Nash equilibria
No full textWe consider mean field games in a large population of heterogeneous agents subject to convex constraints and coupled by a quadratic cost, which depends on the average population behavior. The problem of steering such population to a Nash equilibrium is usually addressed in the (mean field control) literature by formulating an iterative game between the agents and a central coordinator, that broadcasts at every step the average population behavior. Here we generalize this approach by allowing the central operator to filter such signal using a feedback mapping. We propose different classes of feedback mappings and we derive sufficient conditions guaranteeing convergence to a ε-Nash equilibrium, even for cases when the standard approach fails. We show that the deviation ε of each agent from its optimal cost, decreases at least linearly to zero with the increase of the population size. Contrary to the state of the art, the proposed approach guarantees convergence in the presence of heterogeneous convex constraints for the agents. Finally, we show how these results can be applied to regulate in a decentralized fashion the charging process of a large population of plug-in electric vehicles. Our findings give theoretical support and extend previous literature results
Computing the Projected Reachable Set of Stochastic Biochemical Reaction Networks Modelled by Switched Affine Systems
No full textA fundamental question in systems biology is what
combinations of mean and variance of the species present in
a stochastic biochemical reaction network are attainable by
perturbing the system with an external signal. To address this
question, we show that the moments evolution in any generic network
can be either approximated or, under suitable assumptions,
computed exactly as the solution of a switched affine system.
We then propose a new method to approximate the reachable
set of such switched affine system. A remarkable feature of our
approach is that it allows one to easily compute projections of the
reachable set for pairs of moments of interest, without requiring
the computation of the full reachable set, which can be prohibitive
for large networks. As a second contribution, we also show how to
select the external signal in order to maximize the probability of
reaching a target set. To illustrate the method we study a renown
model of controlled gene expression and we derive estimates of
the reachable set, for the protein mean and variance, that are
more accurate than those available in the literature and consistent
with experimental data
Decentralized convergence to Nash equilibria in constrained deterministic mean field games
No full textThis paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem
Mean field constrained charging policy for large populations of Plug-in Electric Vehicles
No full textConstrained charging control of large populations of Plug-in Electric Vehicles (PEVs) is addressed using mean field game theory. We consider PEVs as heterogeneous agents, with different charging constraints (plug-in times and deadlines). The agents minimize their own charging cost, but are weakly coupled by the common electricity price. We propose an iterative algorithm that, in the case of an infinite population, converges to the Nash equilibrium associated with a related decentralized optimization problem. In this way we approximate the centralized optimal solution, which in the unconstrained case fills the overnight power demand valley, via a decentralized procedure. The benefits of the proposed formulation in terms of convergence behavior and overall charging cost are illustrated through numerical simulations
A Mean Field control approach for demand side management of large populations of Thermostatically Controlled Loads
No full textThis paper presents a Mean Field (MF) control approach for demand side management of large populations of flexible electric loads, such as electrical cooling/heating appliances, called Thermostatically Controlled Loads (TCLs). We model the switching dynamics of each individual TCL as the solution of a local optimization problem, characterized by individual cost function, comfort constraints, cooling/heating rates and external temperature. We consider that a central utility company broadcasts macroscopic incentives to steer the overall TCL population towards a convenient equilibrium, to avoid power demand peaks due to possible synchronization of the TCL duty cycles. To find such pricing schemes we propose an iterative algorithm where, at every step, a simple model-free feedback law is used to update the incentives, given the current aggregate demand of the TCL population only. The convergence of such algorithm is ensured for any population size, even in the presence of heterogeneous convex constraints. We illustrate our MF control approach via numerical analysis
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