Ensemble Control of a Large Population of Stochastic Oscillators: Periodic-Feedback Control Approach

Kaito Ito, Haruhiro Kume, Hideaki Ishii

Abstract: In this paper, we address the problem of steering the distribution of oscillators all receiving the same control input to a given desired distribution. In a large population limit, the distribution of oscillators can be described by a probability density. Then, our problem can be seen as an ensemble control problem with a constraint on the steady-state density. In particular, we consider the case where oscillators are subjected to stochastic noise. One of the difficulties of this problem is that due to the stochasticity, it is generally impossible to design a control law under which oscillators converge to a target density exactly. To avoid this issue, we first give an alternative target density that is close enough to the original target. The modified target is carefully designed via a periodic input so that the distribution of oscillators can converge to it by an appropriate control strategy. Next, we construct a controller that decreases the Kullback-Leibler divergence between the distribution of oscillators and the modified target combining a periodic input and feedback control. We exhibit some convergence results for our proposed method. The effectiveness of the proposed method is demonstrated by a numerical example.