A learning-enabled disturbance-rejection framework based on a Neural Extended State Observer (Neural-ESO) is presented in this letter. Unlike existing learning-based control methods that largely rely on the learned model once deployed, Neural-ESO adopts a dual-pathway architecture: a predictive pathway uses a neural network to provide a feedforward disturbance estimate that accelerates convergence, while a corrective pathway employs a conventional ESO to compensate prediction errors and prevent over-reliance on the neural component. Using Lyapunov theory and a small-gain analysis, we show that enforcing a Lipschitz bound on the learning component guarantees uniform ultimate boundedness of the closed-loop error dynamics. The proposed framework is validated on a quadrotor landing task subject to strong ground-effect disturbances across normal and out-of-distribution scenarios, demonstrating accuracy-robustness trade-off and greater operational reliability during training, deployment, and transfer compared with state-of-the-art baselines.
We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over 50 states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.
We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function Vψ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint V˙ψ+αVψ≤0, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.
The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives, thereby facilitating a fully data-driven feedback linearization framework. Furthermore, practical closed-loop stability is established by deriving sufficient conditions under which bounded identification errors lead to bounded tracking errors. The derived theoretical results are validated through their application to an armature controlled DC motor.