Separation of learning and control for cyber–physical systems

Abstract

Most cyber–physical systems (CPS) encounter a large volume of data which is added to the system gradually in real time and not altogether in advance. In this paper, we provide a theoretical framework that yields optimal control strategies for such CPS at the intersection of control theory and learning. In the proposed framework, we use the actual CPS, i.e., the “true” system that we seek to optimally control online, in parallel with a model of the CPS that is available. We then institute an information state for the system which does not depend on the control strategy. An important consequence of this independence is that for any given choice of a control strategy and a realization of the system’s variables until time t, the information states at future times do not depend on the choice of the control strategy at time t but only on the realization of the decision at time t, and thus they are related to the concept of separation between estimation of the state and control. Namely, the future information states are separated from the choice of the current control strategy. Such control strategies are called separated control strategies. Hence, we can derive offline the optimal control strategy of the system with respect to the information state, which might not be precisely known due to model uncertainties or complexity of the system, and then use standard learning approaches to learn the information state online while data are added gradually to the system in real time. We show that after the information state becomes known, the separated control strategy of the CPS model derived offline is optimal for the actual system. We illustrate the proposed framework in a dynamic system consisting of two subsystems with a delayed sharing information structure.