Distributed Model Predictive Control and Estimation of Large-Scale Multi-Rate Systems

In this paper, we propose a new method for control of large-scale multi-rate systems with linear dynamics that are coupled via inputs. These systems are multi-rate systems in the sense that either output measurements or input updates are not available at certain sampling times. Such systems can arise, e.g., when the number of sensors is less than the number of variables to be controlled, or when measurements of outputs cannot be completed simultaneously because of applicational limitations. The multi-rate nature gives rise to lack of information, which will cause uncertainty in the system's performance. A distributed model predictive control (MPC) approach based on Nash game theory is proposed to control multi-agent multi-rate systems in which multiple control agents each determine actions for their own parts of the system. Via communication, the agents can in a cooperative way take one another's actions into account. To compensate for the information loss due to the multi-rate nature of the systems under study, a distributed Kalman Filter is proposed to provide the optimal estimation of the missing information. Using simulation studies on a distillation column the added value of the proposed distributed MPC and Kalman Filter method is illustrated in comparison with a centralized MPC with centralized Kalman Filter, and a distributed MPC method with a fully decentralized (i.e., no communication) Kalman Filter.