Coalitional Control: Cooperative game theory and control

TL;DR

Coalitional control advances distributed control by integrating cooperative game theory with model predictive control to form dynamic coalitions of controllers that adapt to time-varying coupling in large-scale systems. It formalizes the partitioning of subsystems into coalitions, introduces network- and coalition-cost terms, and frames the global control problem as a mixed-integer optimization over control actions and topology. The approach leverages coalition formation concepts (e.g., Shapley value) to allocate benefits and guide coalition decisions, with illustrative case studies in energy systems showing improved local trading and reduced transmission losses under appropriate penalties. The framework addresses challenges in information exchange, privacy, and computational complexity, aiming for scalable, plug-and-play control suitable for smart grids and other heterogeneous infrastructures. Overall, coalitional control provides a principled, adaptable path to balance performance and coordination effort in complex, networked control environments.

Abstract

The evolution of information and communication technologies has yielded the means of sharing measurements and other information in an efficient and flexible way, which has enabled the size and complexity of control applications to increase. At the same time, the improvements in the computational and communicational capabilities of control devices have fostered the development of noncentralized control architectures, already motivated by the inherent structural constraints of large-scale systems. Computer-based control approaches such as model predictive control (MPC) are visible beneficiaries of these advances and have registered a significant growth regarding both theoretical and applied fields. Coalitional control focuses on the local interests that motivate the controllers to assemble, an aspect so far rarely contemplated in the distributed control literature. This article presents the main concepts and challenges in coalitional control, and the links with cooperative network game theory.

Figures (7)

• Figure 1: We consider a set of nodes connected to the main grid, equipped as well with local generation and storage devices. These prosumers can establish a local energy market by aggregating into coalitions, so as to minimize the cost of buying energy from the main grid. Power losses over the distribution lines are added to the incurred costs. As a result of the application of the coalitional control algorithm, the associations of nodes are reorganized according to variations in the local demand and supply, as well as to changes in the energy prices. The figure shows the energy balance at each node.
• Figure 2: Reciprocal location of the 8 prosumers considered in the example: the distance between rows of houses is 0.5 km. This distance is taken into account for the losses in the distribution lines resulting from the local energy transfer.
• Figure 3: Evolution of the coalitions among the nodes, under different penalties $\rho_{\mathrm{coal}}$ for energy losses. Agents are allowed to reevaluate their affiliation at each time step, by updating the preference mapping $\Phi(i,\cdot,k)$. When costs for local energy transfers are significant, coalitions typically involve a restricted number of neighboring agents. Conversely, big cooperating clusters form when penalties for power losses are low.
• Figure 4: Daily demand patterns considered in the simulations for the 8 nodes.
• Figure 5: Generation profiles considered in the simulations for the 8 nodes.