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Mathematical models of neuronal networks play a crucial role in understanding sleep dynamics and associated disorders. However, validating these models through parameter estimation remains a significant challenge. In this work, we introduce an automated parameter estimation framework for sleep models that satisfy two key assumptions: (i) they consist of competing neuronal populations, each driving a distinct sleep stage (stage-promoting), and (ii) their dynamics evolve independently of weakly observed variables or external inputs (self-contained). We apply our method to a system of coupled nonlinear ordinary differential equations (ODEs) representing three interacting neuronal populations. Direct firing rates of these populations are typically unobservable, and hypnograms provide only the dominant sleep stage at each time point. Despite the limited information available in hypnograms, we successfully estimate ODE parameters for the underlying neuronal population model directly from hypnogram data. We use a smoothed winner-takes-all strategy within a constrained minimization framework, reformulate the problem in an unconstrained setting through the Lagrangian, and derive the corresponding optimality conditions from state and adjoint equations. A projected nonlinear conjugate gradient scheme is then used to estimate the parameters numerically. We validate our approach by accurately reconstructing 111 out of 139 hypnograms from the Sleep-EDF database. The inferred population-level parameters provide insights into sleep regulation by capturing interaction strengths, timescale constants and non-rapid eye movement-related variability.