Regularized Jacobi iteration for decentralized convex quadratic optimization with separable constraints

We consider multi-agent, convex quadratic 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 provide a fixed-point theoretic analysis showing that the algorithm converges to a minimizer of the centralized problem under more relaxed conditions on the regularization coefficient from those available in the literature, and in particular with respect to scaled projected gradient algorithms. The efficacy of the proposed algorithm is illustrated by applying it to the problem of optimal charging of electric vehicles

Explicit solutions for safety problems using control barrier functions

The control Barrier function approach has been widely used for safe controller synthesis. By solving an online convex quadratic programming problem, an optimal safe controller can be synthesized implicitly in state-space. Since the solution is unique, the mapping from state-space to control inputs is injective, thus enabling us to evaluate the underlying relationship. In this paper we aim at explicitly synthesizing a safe control law as a function of the state for nonlinear control-affine systems with limited control ability. We propose to transform the online quadratic programming problem into an offline parameterized optimisation problem which considers states as parameters. The obtained explicit safe controller is shown to be a piece-wise Lipschitz continuous function over the partitioned state space if the program is feasible. We address the infeasible cases by solving a parameterized adaptive control Barrier function-based quadratic programming problem. Extensive simulation results show the state-space partition and the controller properties

Probabilistic feasibility guarantees for convex scenario programs with an arbitrary number of discarded constraints

Discarding constraints in scenario optimization, a technique known as the sampling-and-discarding scheme, allows the decision maker to trade feasibility to performance. Recently, a removal scheme with a less conservative bound on the constraint violation probability of the final decision has been proposed. In this letter, we further contribute to the theoretical properties of such a scheme by extending the number of discarded scenarios to be arbitrary, as opposed to an integer multiple of the dimension of the decision space. There are two facets to the results of this paper. On the one hand, our feasibility guarantees outperform the standard “sampling-and-discarding” bound in the literature. On the other hand, we highlight an inherent property of the discarding mechanism, namely, the fact that removing a number of scenarios that is not an integer multiple of the dimension of the decision space is likely to introduce additional conservatism

A distributed iterative algorithm for multi-agent MILPs: finite-time feasibility and performance characterization

We deal with decision making in a large-scale multiagent system, where each agent aims at minimizing a local cost function subject to local constraints, and the local decision variables of all agents are coupled through a global constraint. We consider a cooperative framework where the multi-agent decision problem is formulated as a constrained optimization program with the sum of the local costs as global cost to be minimized with respect to the local decision variables of all agents, subject to both local and global constraints. We focus on a non-convex linear set-up where all costs and constraints are linear but local decision variables are discrete or include a discrete component, and propose a distributed iterative scheme based on dual decomposition and consensus to solve the resulting Mixed Integer Linear Program (MILP). Our approach extends recent results in the literature to a distributed set-up with a time-varying communication network and allows to: reduce the computational and communication effort, achieve resilience to communication failures, and also preserve privacy of local information. The approach is demonstrated on a numerical example of optimal charging of plug-in electric vehicles

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

Distributed optimization for energy management in building networks

We formulate and solve an energy management problem for a cooperative network of buildings sharing some resource and communicating over a time varying network, each of which desires to maintain its privacy. As the network is time-varying, we are able to accommodate communication constraints or failure between agents. We begin by introducing validated bilinear modelling techniques for individual buildings, and continue by showing how the energy management problem involving a network of buildings can be addressed using a distributed optimization algorithm recently proposed in the literature, with individual buildings treated as agents. To facilitate these assumptions, we linearize the bilinear models generated, and introduce linear local and coupling constraints to model a shared thermal energy storage device. We formulate a linear objective function to minimize based on the cost of energy used by the agent not taken from the storage. Finally, we demonstrate the efficacy of the distributed algorithm as applied to the energy management problem using an extensive simulation based study

Etude et realisation d'un systeme de commande adapte a la robotique spatiale

SIGLECNRS T 57992 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Linear programs for resource sharing among heterogeneous agents: a probabilistic analysis of the maximum capacity in terms of number of agents

We consider a multi-agent resource sharing problem that can be represented by a linear program. The amount of resource to be shared is fixed, and each agent adds to the linear cost and constraint a term that depends on some randomly extracted parameters, thus modelling heterogeneity among agents. We study the probability that the arrival of a new agent does not affect the optimal value and the resource share of the other agents, which means that the system cannot accommodate the request of a further agent and has reached its saturation limit. In particular, we determine the maximum number of requests for the shared resource that the system can accommodate in a probabilistic sense. This result is proven by first formulating the dual of the resource sharing linear program, and then showing that this is a random linear program. Using results from the scenario theory for randomized optimization, we bound the probability of constraint violation for the dual optimal solution, and prove that this is equivalent with the primal optimal value remaining unchanged upon arrival of a new agent. We discuss how this can be thought of as probabilistic sensitivity analysis and offer an interpretation of this setting in an electric vehicle charging control problem