Blind control synthesis for large dynamical systems with application in smart grids: A non-equilibrium statistical mechanics approach

The design of control laws for a large dynamical system is challenging, particularly when it is difficult to obtain a system model. In this paper, the extreme case of no detailed knowledge about the system dynamics is studied. To find a control law, which can restore the equilibrium as quickly as possible upon small but significant perturbations, the stochastic approximation approach is used to learn the control law according to the history of system dynamics, in a blind manner. However, since significant perturbations to the system are usually rare, there lacks sufficient training samples of perturbation for the stochastic approximations. To alleviate the insufficiency of training samples, the Onsager's Regression is applied, which is an important principle in non-equilibrium statistical mechanics and asserts that the restoration to equilibrium upon perturbations in a large system can be approximated by the correlation function around the equilibrium state. Instead of learning from the perturbations, the control law is learned from the correlation functions in the equilibrium state, which provides much more samples. Numerical simulations on large power networks demonstrated the validity of the proposed scheme.