Optimal distributed finite-time consensus control of multi-agent systems with Markovian switching topologies and applications to micro-grids

This paper studies the optimal distributed finite-time consensus control problem of multi-agent systems with Markovian switching topologies. Firstly, a new distributed finite-time consensus controller (DFCC) is developed based on a mode classification method and as the basis of the studied optimization problems. Its most innovation is the quantity of DFCC can be fewer than the number of Markovian switching topologies and make the estimated settling time varying with the mode classifications. Compared with the existing methods, the advantages of DFCC are not only the synchronization assumption of switching signals between topologies and controllers is removed, but also the provided settling time is shorter. Secondly, in order to find the optimal mode classification of DFCC corresponding to the minimal settling time, the deep deterministic policy gradient (DDPG) algorithm is employed to provide a locally optimal estimated settling time and overcomes the difficulties of Karush-Kuhn-Tucker conditions ensuring the objectives and constraints convex. Thirdly, due to the count of mode classifications equal the second kind of Stirling number and resulting in DDPG having a high computational complexity, an improved hill-climbing algorithm (HCA) enhanced by Q-learning is developed for the first time and solves the challenge of giving a suboptimal or even optimal classification by only using a part of mode classifications. Finally, a practical application about micro-grids is offered so as to verify the effectiveness and superiority of the methods given in this study.