On State Aggregation in a Class of Cyber Physical Energy Systems

Various cyber physical energy systems (CPES) are discrete event dynamic systems (DEDS), in which the states are discrete and the dynamics of state transitions are triggered by events. Markov decision process (MDP) is the major mathematical framework for formulating and analyzing such systems. Look-up table algorithms are usually applied to solve optimization problems in the framework of MDP. The table stores value functions of states. When the system scale is large, it consumes huge memory space and computation budget to store and update the table. Methods like state aggregation are implemented to approximate the value functions. By aggregating several states into a “super” state, the memory space and computation budget are saved when the states are aggregated properly. In the existing researches, all the system state variables are treated equally. Actually, different state variables varies in features. In this paper, we look into the nature of different state variables in a class of cyber physical energy systems, where the state variables can be classified into two categories, action-free and action-based. These two types of state variables are mathematically defined in this paper. We also define the concept of aggregation complexity to measure the level of aggregation of different state variables. Aggregations of these two state variables are studied. Numerical experiments are conducted by a toy example of signal tracking problem and a real example of shared electric vehicles (EVs) scheduling in CPES. It is observed that aggregating the states of action-free state variables has better performance than aggregating action-based ones under the same complexity.