Control-Oriented State-Space Reconstruction of Clinical EEG Signals for Dynamical Brain Modeling

Electroencephalography (EEG) signals contain a population of neurons in their aggregate electrical activity, and are commonly classified and diagnosed in statistical and deep learning approaches. Nonetheless, the majority of current methods treat EEG as a data-oriented pattern recognition problem rather than as the measurable behavior of a nonlinear dynamical system. This view restricts the construction of control-based schemes for analyzing neural modulation and stability. The paper provides a control-based state-space rebuilding model of clinical EEG signals based on nonlinear dynamical systems theory. The development of a mathematical representation of delay-coordinate embedding and nonlinear state-evolution modeling of EEG recordings as scalar observations of the unobservable neural state variables allows us to formulate a mathematical representation of the neural state. The formulation offered enables reconstruction of phase space, definition of attractors, and interpretation of brain dynamics in terms of stability. In contrast to traditional black-box methods, the framework provides a theoretical basis for observer design and closed-loop neural control strategies. The paper describes a systematic approach to integrating dynamical EEG modeling with future control and intervention strategies.