In this paper, we propose an architecture for realizing distributed reinforcement learning of distributed controllers for a class of unknown hierarchical systems, where homogeneous subsystems are interconnected through a complete graph. All these controllers consist of two sub-controllers for average and difference dynamics of the system, respectively. First, we show that optimal sub-controllers can be trained individually by a reinforcement learning (RL) method for average/difference data. Due to the smaller-scale of the data, the learning time of the proposed method can be drastically reduced compared to existing RL methods. However, the computation for obtaining the average data requires all-to-all communication among subsystems, which is undesirable in terms of communication costs and security. Hence, by exploiting a distributed consensus observer, we propose an architecture that enables us to learn distributed optimal controllers in a distributed manner. The control performance of the trained controller is shown to be ideally optimal. Moreover, the proposed architecture is completely scalable, i.e., its computational cost is independent from the number of subsystems. The effectiveness is shown through numerical simulations.

Various data mining models and/or methods have been proposed to date. A statistical test rule induction method (STRIM) has been proposed as one of them, that induces if-then rules hidden in a dataset known as the decision table generated based on a simple hypothesis. This study improves the previous data generation model using a hypothesis similar to human rating and the rule induction method to adapt to real-world datasets. Specifically, 1) the hypothesis is expanded from a complete correspondence hypothesis to a partial correspondence hypothesis. 2) The previous rule induction method is developed into a Bayesian STRIM, that infers and/or explores the causes based on the results. The applied rule induction method’s validity and usefulness are confirmed using a verification system. The relationship and difference between Bayesian STRIM against a maximum a posteriori probability estimate and a Bayesian network method are also studied in the rule induction problem.