Jul 2026· International Conference on Control, Decision and Information Technologies· pp. 2430-2435· 0 citations· 20 references
Abstract
This paper evaluates Liquid Neural Networks (LNNs) on an energy-optimal quadrotor control benchmark formulated as a behavioral cloning problem. Several LNN variants, including ordinary differential equation (ODE)-based formulations and closed-form continuous-time (CfC) models, are compared against classical recurrent architectures and a reference multilayer perceptron (MLP). Results show that ODE-based LNNs achieve the strongest closed-loop performance among recurrent models, demonstrating robustness to discretization effects and partial observability while maintaining stable behavior across network sizes. In contrast, CfC variants provide competitive performance under nominal conditions but degrade more significantly under scaling, revealing limitations of its closed-form approximation. While the MLP baseline achieves superior steady-state accuracy and lowest inference latency, it is less reliable under degraded observability and numerical perturbations. Overall, the results emphasize complementary trade-offs between continuous-time recurrent models and feedforward architectures, suggesting that LNNs are particularly well-suited for control tasks involving temporal uncertainty or limited state information.
Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks. We evaluate this prior under a controlled protocol in which an HNN and a parameter-matched feedforward baseline are trained on the same RK4-generated trajectories, use the same central-difference derivative targets and optimization settings, and are integrated at inference with the same RK4 scheme. Results are reported over five independent training seeds. On the nonlinear pendulum, the HNN reduces mean energy drift by 42-fold and mean trajectory MSE by 15.8-fold at T = 100, approximately 16 pendulum periods. Its energy drift also remains bounded and exhibits substantially lower seed-to-seed variability than the standard-network baseline. An energy-stratified analysis shows that the difference becomes more pronounced as trajectories explore more nonlinear regions of phase space. As an additional diagnostic, we examine an explicit St\"ormer--Verlet-style rollout of the learned HNN. Because the learned Hamiltonian is not constrained to the separable form H(q,p) = T(p) + V(q), the standard symplecticity guarantee of velocity Verlet does not directly apply. We further apply the same matched-integrator protocol to the three-dimensional Kepler two-body problem. The HNN again exhibits lower trajectory, energy, and angular-momentum drift than the parameter-matched baseline. These experiments provide a controlled study of how Hamiltonian parameterization affects long-horizon prediction and physical consistency across two conservative dynamical systems.
This work uses SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings, alleviating the curse of dimensionality.
Matteo Tomasetto, Francesco Braghin, J. Kutz et al.· 0 citations
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.
Fan Zhang, Richie R. Suganda, Jinfeng Chen et al.· IEEE Robotics and Automation...· 1 citation
This paper derives sufficient conditions for input-dependent contraction and formally establish an input-to-state contraction property under bounded external excitations, and develops a novel deep learning framework that seamlessly incorporates time-varying control inputs while ensuring incremental exponential convergence via input-dependent contraction regularization.
Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.
An adaptive stability-constrained neural differential equation (AS-NDE) for systems with measured controls and unmatched, unknown perturbations and a reproducible evaluation protocol for a forced Duffing oscillator and a permanent-magnet synchronous motor model is given.