Stochastic linear Model Predictive Control with chance constraints – A review

We address the problem to control a population of noncooperative heterogeneous agents, each with convex cost function depending on the average population state, and all sharing a convex constraint, toward an aggregative equilibrium. We assume an information structure through which a central coordinator has access to the average population state and can broadcast control signals for steering the decentralized optimal responses of the agents. We design a dynamic control law that, based on operator theoretic arguments, ensures global convergence to an equilibrium independently on the problem data, that are the cost functions and the constraints, local and global, of the agents. We illustrate the proposed method in two application domains: Network congestion control and demand side management.

Dynamic Control of Agents Playing Aggregative Games With Coupling Constraints

The advances in distributed renewable generation technologies in recent years have started to cause load balancing issues in power networks. Distributed energy storage (ES) systems, although seen as a tool to mitigate the stress on local networks, tend to be operated only to minimize the energy cost of their direct owner. In this paper, cooperative game theory is used to construct an energy grand coalition, in which ES system operations are optimized to minimize the coalitional energy cost. Case studies then show that forming energy coalitions is effective in reducing the variability of a local network load profile. The resulting cooperative game is mathematically proven to be balanced, which means the energy cost savings from the cooperative ES operation can be allocated to the players within the energy grand coalition in a manner that disincentivizes them from exiting from the grand coalition to form smaller coalitions.

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Incentivizing Prosumer Coalitions With Energy Management Using Cooperative Game Theory

Randomized Algorithms for Analysis and Control of Uncertain Systems with Applications, Second Edition, Roberto Tempo, Giuseppe Calafiore, Fabrizio Dabbene (Eds.). Springer-Verlag, London (2013), 357, ISBN: 978-1-4471-4609-4

This paper introduces a decentralized market design, which allows a distribution system operator to manage local demand constraints by obtaining flexibility from competing aggregators, which must in-turn incentivize prosumers to provide this flexibility. The novel networked market structure accounts for distribution system operator-to-aggregator and aggregator-to-prosumer ICT infrastructure and contractual arrangements, which may limit which participants can negotiate transactions with one another. The proposed flexibility market is opt-in for prosumers, which continue to obtain energy within the existing retail electricity market. At the same time, it is underpinned by bilateral energy transactions, and could be integrated into future peer-to-peer electricity markets. Through the market, the distribution system operator, aggregators, and prosumers reach agreement on a stable outcome–a set of individually beneficial transactions no group wishes to mutually deviate from. Market outcomes also satisfy Pareto efficiency, meaning that it is not possible to make a participant better off, without making another worse off.

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Designing Decentralized Markets for Distribution System Flexibility

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

In this paper, we address finite-horizon control for a stochastic linear system subject to constraints on the control and state variables. A control design methodology is proposed where the appropriate trade-off between the minimization of the control cost (performance) and the satisfaction of the state constraints (safety) can be decided by introducing appropriate chance-constrained problems depending on some parameter to be tuned. From an algorithmic viewpoint, a computationally tractable randomized approach to find approximate solutions which are guaranteed to be feasible for the original chance-constrained problem is proposed. A numerical example concludes the paper.

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Stochastic constrained control: Trading performance for state constraint feasibility

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On the connection between Nash equilibria and social optima in electric vehicle charging control games

We consider the problem of designing a controller that is able to steer an aircraft to some target position, while satisfying a set of constraints originating from physical limitations and comfort requirements. The key idea is to use feedback linearization, and then approximate the constraints in the new state and control variables so as to make them convex. This enables the on-line usage of the model predictive control strategy to aircraft motion control.

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A model predictive control approach to aircraft motion control

We develop a decentralized algorithm for 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 construct a variant of the so called Jacobi algorithm and show that, when the objective function is quadratic, convergence to some minimizer of the centralized problem counterpart is achieved. Our algorithm serves then as an effective alternative to gradient based methodologies. We illustrate its efficacy 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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Luca Deori

Papers

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

Stochastic constrained control: Trading performance for state constraint feasibility

On the connection between Nash equilibria and social optima in electric vehicle charging control games

A model predictive control approach to aircraft motion control

On decentralized convex optimization in a multi-agent setting with separable constraints and its application to optimal charging of electric vehicles