arXiv subjects

Luca Deori

Publications and source records attributed to Luca Deori.

3 recordsLinked to original sources

arXiv2018

Price of anarchy in electric vehicle charging control games: When Nash equilibria achieve social welfare

We consider the problem of optimal charging of plug-in electric vehicles (PEVs). We treat this problem as a multi-agent game, where vehicles/agents are heterogeneous since they are subject to possibly different constraints. Under the assumption that electricity price is affine in total demand, we show that, for any finite number of heterogeneous agents, the PEV charging control game admits a unique Nash equilibrium, which is the optimizer of an auxiliary minimization program. We are also able to quantify the asymptotic behaviour of the price of anarchy for this class of games. More precisely, we prove that if the parameters defining the constraints of each vehicle are drawn randomly from a given distribution, then, the value of the game converges almost surely to the optimum of the cooperative problem counterpart as the number of agents tends to infinity. In the case of a discrete probability distribution, we provide a systematic way to abstract agents in homogeneous groups and show that, as the number of agents tends to infinity, the value of the game tends to a deterministic quantity.

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arXiv2017

Regularized Jacobi iteration for decentralized convex optimization with separable constraints

We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common objective function. We focus on a regularized variant of the so called Jacobi algorithm for decentralized computation in such problems. We first consider the case where the objective function is quadratic, and provide a fixed-point theoretic analysis showing that the algorithm converges to a minimizer of the centralized problem. Moreover, we quantify the potential benefits of such an iterative scheme by comparing it against a scaled projected gradient algorithm. We then consider the general case and show that all limit points of the proposed iteration are optimal solutions of the centralized problem. The efficacy of the proposed algorithm is illustrated by applying it to the problem of optimal charging of electric vehicles, where, as opposed to earlier approaches, we show convergence to an optimal charging scheme for a finite, possibly large, number of vehicles.

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arXiv2016

A relaxation technique to ensure feasibility in stochastic control with input and state constraints

We consider a stochastic linear system and address the design of a finite horizon control policy that is optimal according to some average cost criterion and accounts also for probabilistic constraints on both the input and state variables. This finite horizon control problem formulation is quite common in the literature and has potential for being implemented in a receding horizon fashion according to the model predictive control strategy. Such a possibility, however, is hampered by the fact that, if the disturbance has unbounded support, a feasibility issue may arise. In this paper, we address this issue by introducing a constraint relaxation that is effective only when the original problem turns out to be unfeasible and, in that case, recovers feasibility as quickly as possible. This is obtained via a cascade of two probabilistically-constrained optimization problems, which are solved here through a computationally tractable scenario-based scheme, providing an approximate solution that satisfies the original probabilistic constraints of the cascade, with high confidence. A simulation example showing the effectiveness of the proposed approach concludes the paper.

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