Control of complex systems with generalized embedding and empirical dynamic modeling

Feedback control is ubiquitous in complex systems. Effective control requires knowledge of the dynamics informing feedback compensation to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows obtaining a satisfactory mathematical representation is increasingly difficult. Further, many data-driven approaches consist of abstract internal representations that may have no obvious connection to the underlying dynamics and control, or, require extensive model design and training. Here, we remove these constraints. We demonstrate that generalized state space embedding and prediction of model dynamics within the state space provide a data-driven process model for control of complex systems and a new paradigm of model predictive control. Generalized embedding naturally encompasses multivariate dynamics and representation of multivariate interactions. Specifically, state space kernel regression of the dynamics allows inspection of intervariable dependencies. We demonstrate this with state space variable cross mapping directly quantifying multivariate contributions to the dynamics. Since generalized embedding provides a data-driven model of dynamics entirely in state space, no model design or training are required. Generalized embedding and model predictive control is demonstrated on nonlinear dynamics generated by an agent based model of 1200 interacting agents. The proposed method provides an alternative model of the process dynamics with no constraints on the the controller and is therefore generally applicable to any type of controller. The method should be applicable to any dynamic system representable in a state space.