Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian

Summary

This paper proposes a data-driven feedback linearization framework in which multilayer perceptrons approximate the drift, input, and output maps of an unknown control-affine SISO system, and the classical feedback-linearizing control law is rebuilt entirely from differentiable 'neural Lie derivatives'. Its distinctive element is training-time structure enforcement: the relative-degree conditions θ'_p(x)g_φ(x)=0 (p=0,…,n−2) are imposed as equality constraints at all m data samples and handled with an augmented Lagrangian (multiplier and penalty updates, Algorithm 1). Theorem 2 gives a practical stability claim: under universal approximation on a compact domain and Hurwitz gains, bounded identification errors yield a bounded residual d(t,x), hence ultimately bounded tracking error. Validation is a single simulated armature-controlled DC motor (n=2, cubic friction), trained on 2,000 samples with Gaussian noise σ=0.2 added to states and derivatives; reported results include close model fits (Figs. 3-4), small constraint residuals (Fig. 5), stable tracking of r(t)=1−e^(−t) with poles at −3/−5, and an empirical residual bound d̄≈1.04 (Fig. 8). Main limitations: no comparison against unconstrained identification plus classical FBL, the authors' own sparse-regression method [17], or Koopman/GP alternatives; constraints and the nonvanishing decoupling condition are verified only at training samples, not on the continuous domain; the stability proof assumes derivative-level error bounds that C⁰ function approximation does not provide; and there are no held-out metrics, seed repetitions, or released code.