Stochastic Control Approach for Distributed Generation Units Interacting on Graphs

This chapter introduces a novel online adaptive learning distributed control approach for a system of distributed generation units with disturbances in their dynamical environments. The interactions between the generation units are restricted by a graph topology, which means that the dynamics of the generation units are coupled. The coordination ideas or distributed synchronization protocols are utilized to maintain synchronization among the generation units. The cost function is designed to take into account the neighborhood interactions and the graph topology. Coupled Bellman optimality equations are developed for the distributed generation network. A distributed online reinforcement learning approach that employs a Kalman filter is employed to solve the optimal control problem of the multiagent system. This control approach is implemented in real time using neural network approximations and it does not need to know the full dynamics of the generation systems. The validity of the distributed control approach is tested using a system of distributed generation units working under disturbances.