Distributed Stochastic Optimisation with Uncertain Coupling Constraints

Large-scale multi-agent systems are increasingly relevant in various aspects of society; their operation requires advances in multi-agent distributed optimisation algorithms that can handle uncertain environments. This paper presents a distributed algorithm suitable for solving convex constraint-coupled multi-agent problems with uncertainty directly affecting the coupling constraints. The algorithm exploits the problem structure to solve the large-scale uncertain problem efficiently, leveraging the scenario approach to approximate the coupling chance-constraint. We prove that the number of scenarios required to guarantee a given violation probability level is independent of the agent number, making the solution scalable. We apply the algorithm to a multi-microgrid aggregation problem to provide ancillary services to the Grid, a relevant decarbonisation and energy security topic.