Abstract:
This work addresses the problem of estimating unmeasured states and identifying
parameters of a nonlinear system using only one measurable signal. To achieve this,
we employ a KKL observer (Kazantzis–Kravaris–Luenberger), which transforms
the original system x˙ = f(x, u) into a latent linear system, where the states can
be reconstructed via an invertible transformation learned by a neural network. In
parallel, the Modulating Functions (MF) method enables parameter estimation
from differential models without requiring numerical differentiation. By multiplying
the system’s equation with a test function and integrating over a time interval, the
problem becomes a robust algebraic system, well-suited for noisy measurements.
The proposed approach is validated on a Hill-type isometric muscle model
driven by real EMG signals, including both healthy and pathological cases.
