arXiv subjects

Syed Pouladi

Publications and source records attributed to Syed Pouladi.

5 recordsLinked to original sources

arXiv2026

Adaptive Stability-Constrained Neural Differential Equations for Controlled Dynamical Systems with Unknown Inputs

Continuous-time neural models are attractive for identifying nonlinear systems, but a small one-step error can grow rapidly when a learned vector field is rolled out under inputs that differ from those used for training. This paper develops an adaptive stability-constrained neural differential equation (AS-NDE) for systems with measured controls and unmatched, unknown perturbations. The nominal vector field and a state--input-dependent Riemannian metric are learned jointly. Positive definiteness is enforced by construction, while a sampled differential inequality penalizes violations of a prescribed contraction rate. An incremental input-to-state bound is derived: the distance between two trajectories decays exponentially up to gains determined by differences in their controls and disturbances. The statement explicitly accounts for the time derivative of an input-dependent metric, a term that is easily omitted in heuristic stability regularizers. We give a reproducible evaluation protocol for a forced Duffing oscillator and a permanent-magnet synchronous motor (PMSM) model. Because no measured data or executed training runs accompany this draft, all numerical curves and tables are clearly identified as illustrative synthetic placeholders; their PGFPlots coordinates are embedded in the source for direct replacement. The resulting manuscript is intended as a technically consistent starting point, not as evidence of empirical superiority before the prescribed experiments are run.

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arXiv2026

Learning Stable Controlled Dynamical Systems via Input-Contraction Neural Differential Models

Learning continuous-time representations of dynamical systems from observation data has emerged as a cornerstone of data-driven control and scientific machine learning. However, existing neural differential equations either treat external control inputs heuristically without providing strict structural guarantees, or enforce stability properties under the restrictive assumption of constant or vanishing inputs. This paper proposes the Input-Contraction Neural Differential Model (ICNDM), a novel deep learning framework that seamlessly incorporates time-varying control inputs while ensuring incremental exponential convergence via input-dependent contraction regularization. By leveraging an embedded input encoder and a parameterized metric network, the proposed architecture learns both the non-autonomous neural vector fields and a generalized Riemannian contraction metric simultaneously. We derive sufficient conditions for input-dependent contraction and formally establish an input-to-state contraction property under bounded external excitations. Extensive numerical evaluations on highly nonlinear chaotic oscillators and experimental data from a Permanent Magnet Synchronous Motor (PMSM) drive system demonstrate that ICNDM yields substantial reductions in long-horizon rollout errors and exhibits superior structural robustness against input perturbations compared with state-of-the-art neural differential benchmarks.

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arXiv2026

Stable Fiber-Koopman Residual Dynamics for Environment-Constrained Robust Control

Learning-based dynamical models face a persistent tension between expressiveness and formal guarantees: richer model classes improve predictive accuracy, but their stability properties are typically verified only empirically, if at all. This paper proposes \emph{Stable Fiber-Koopman Residual Dynamics} (SFKD), a unified framework that simultaneously addresses environment-aware geometric consistency, latent-space stability certification, and bounded residual perturbation propagation. Concretely, SFKD constructs a fiber bundle latent manifold whose fibers encode environment-specific dynamics; an environment-conditioned Koopman operator governs the dominant linear evolution on each fiber; and a contraction-constrained residual neural network captures unmodeled nonlinear effects while admitting an explicit input-to-state stability (ISS) certificate. The resulting model is embedded in a sampling-based MPPI controller for autonomous vehicle path tracking under variable surface conditions and wind disturbances. Theoretical analysis establishes ISS of the latent dynamics and a finite ultimate bound on tracking error. Numerical experiments against five baselines -- Koopman MPC, Neural ODE, ICODE, ControlSynth, and ICODE-MPPI -- demonstrate a 31\% reduction in tracking RMSE, a 44\% improvement in control smoothness, and near-zero latent stability violation rate across environment-switching scenarios.

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arXiv2026

Stability-Certified Koopman Observer Design for Nonlinear Systems via Generalized Persidskii Dynamics

This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation capability for nonlinear dynamics, certifying observer convergence under model mismatch and measurement noise has remained a largely open problem. To resolve this, we establish a structural correspondence between the error dynamics of a Koopman latent-space observer and the class of generalized Persidskii systems, which admits diagonal Lyapunov functions and incremental sector characterizations. Exploiting this connection, we design a nonlinear correction term whose gain is computed via a linear matrix inequality (LMI) that simultaneously certifies input-to-state stability (ISS) of the estimation error with respect to both lifting residuals and external disturbances. Exponential convergence in the nominal case and ultimate boundedness under bounded perturbations are established analytically. Numerical validation on the Van~der~Pol oscillator and a nonlinear robotic arm with friction uncertainty demonstrates that the proposed observer substantially outperforms both the Extended Kalman Filter and a linear Koopman observer in terms of estimation accuracy and robustness, achieving up to a 42\% reduction in steady-state RMSE under lifting mismatch.

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arXiv2026

Stability Analysis and Data-Driven State Estimation for Generalized Persidskii Systems with Time Delays: Theory and Experimental Validation on PMSM Drives

This paper addresses the stability analysis and state estimation of generalized Persidskii systems subject to time-varying delays and external disturbances. The generalized Persidskii class, which couples linear dynamics with sector-bounded nonlinear feedback loops, offers a tractable yet expressive framework for modeling electromechanical and neural network systems. We develop delay-dependent conditions for input-to-state stability (ISS) via Lyapunov--Krasovskii functionals incorporating Persidskii-type integral terms, and cast these conditions as linear matrix inequalities (LMIs). A structured robust observer is proposed for systems with partial state measurement, and its convergence is guaranteed through an $H_\infty$ synchronization criterion. To handle plant uncertainty, the system matrices are identified from trajectory data using a stability-preserving Koopman lifting procedure, in which the ISS-LMI constraint is embedded as a convex side condition during parameter regression. The identified model populates the prediction horizon of an ICODE-MPPI (Input-dependent Control-oriented Dynamical Estimation -- Model Predictive Path Integral) controller. The complete framework is validated on a 1.5 kW Permanent Magnet Synchronous Motor (PMSM) drive equipped with a programmable load brake. Experimental results confirm a 35\% reduction in velocity estimation RMSE relative to an Extended Kalman Filter and a 67\% improvement in speed-tracking accuracy relative to standard Field-Oriented Control, corroborating the theoretical ISS bounds established herein.

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