  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 a-priori specification of functions to represent the
dynamics. To remove these constraints we demonstrate that generalized state
space embedding and prediction can provide data-driven process model
representation for control of complex systems. Generalized embedding naturally
encompasses multivariate dynamics enabling state space variable cross mapping
for direct assessment of multivariate contributions to the dynamics. Further,
state space kernel regression allows inspection of intervariable dependencies.
To illustrate this an agent based model is used to generate nonlinear dynamics
which are then modeled by generalized state space embedding providing state
predictions to a controller regulating the system dynamics. The method is
generally applicable to any dynamic system representable in a state space.

Systems and Control;Systems and Control