The Behavioral Approach to Trajectory-based Control

This paper considers the receding horizon control design of dynamical systems using their trajectories, which would contribute towards the emerging big data-centric control paradigm to utilize the ever-increasingly rich process data available in modern industries. The development is in the behavioral framework, in which dynamical systems are defined by their behaviors, i.e., the set of all admissible trajectories of the systems, and interconnections are interpreted as constraints on the choice of trajectories. This work takes a set-theoretic viewpoint, and the results are completely representation-free. The interconnection, control performance specification, and controller constraints are treated as systems. Such a viewpoint leads to the development of necessary and sufficient conditions for the existence of implementable controlled behavior along with the corresponding controller behavior. These results provide a generic framework for trajectory-based receding horizon control design of general systems.