arXiv subjects

Yasmine Marani

Publications and source records attributed to Yasmine Marani.

4 recordsLinked to original sources

arXiv2026

Integrating Deep Learning and Contraction Theory for Robust Nonlinear State Estimation via Unsupervised Scientific Machine Learning

A common way to design observers is to add a correction term to a copy of the system; however, designing the correction term for nonlinear systems remains a significant long-standing challenge. Contraction theory offers a unified approach to designing this correction term by solving a matrix partial differential inequality (MPDI) and identifying a contraction metric. However, solving the MPDI for both the correction term and the contraction metric is highly challenging, both analytically and numerically. Therefore, the aim of this paper is to propose a learning-based approach to determine both the observer's correction term and the contraction metric by incorporating the contraction requirements into the learning process. The proposed approach relies on a scientific machine learning formulation that embeds the contraction conditions into the training loss function. The proposed approach is then extended to non-autonomous systems while keeping the correction term and contraction metric static to avoid generalization issues arising from time-dependent training. Computable bounds on the learning errors of the proposed observer are established as a function of the training residual and the sampling resolution. Furthermore, the robustness of the proposed observer to measurement noise and learning errors are established in an exponential input-to-state stability sense. Based on the robustness analysis, the present paper takes a further step by proposing a robust learning-based contraction nonlinear observer. The proposed observers are evaluated in numerical simulations for different contraction rates and measurement noise levels.

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arXiv2026

Control and State Estimation of Vehicle-Mounted Aerial Systems in GPS-Denied, Non-Inertial Environments

We present a robust control and estimation framework for quadrotors operating in Global Navigation Satellite System(GNSS)-denied, non-inertial environments where inertial sensors such as Inertial Measurement Units (IMUs) become unreliable due to platform-induced accelerations. In such settings, conventional estimators fail to distinguish whether the measured accelerations arise from the quadrotor itself or from the non-inertial platform, leading to drift and control degradation. Unlike conventional approaches that depend heavily on IMU and GNSS, our method relies exclusively on external position measurements combined with a Extended Kalman Filter with Unknown Inputs (EKF-UI) to account for platform motion. The estimator is paired with a cascaded PID controller for full 3D tracking. To isolate estimator performance from localization errors, all tests are conducted using high-precision motion capture systems. Experimental results in a moving-cart testbed validate our approach under both translational in X-axis and Y-axis dissonance. Compared to standard EKF, the proposed method significantly improves stability and trajectory tracking without requiring inertial feedback, enabling practical deployment on moving platforms such as trucks or elevators.

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arXiv2024

Unsupervised Physics-Informed Neural Network-based Nonlinear Observer design for autonomous systems using contraction analysis

Contraction analysis offers, through elegant mathematical developments, a unified way of designing observers for a general class of nonlinear systems, where the observer correction term is obtained by solving an infinite dimensional inequality that guarantees global exponential convergence. However, solving the matrix partial differential inequality involved in contraction analysis design is both analytically and numerically challenging and represents a long-lasting challenge that prevented its wide use. Therefore, the present paper proposes a novel approach that relies on an unsupervised Physics Informed Neural Network (PINN) to design the observer's correction term by enforcing the partial differential inequality in the loss function. The performance of the proposed PINN-based nonlinear observer is assessed in numerical simulation as well as its robustness to measurement noise and neural network approximation error.

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arXiv2023

Non-Asymptotic State and Disturbance Estimation for a Class of Triangular Nonlinear Systems using Modulating Functions

Dynamical models are often corrupted by model uncertainties, external disturbances, and measurement noise. These factors affect the performance of model-based observers and as a result, affect the closed-loop performance. Therefore, it is critical to develop robust model-based estimators that reconstruct both the states and the model disturbances while mitigating the effect of measurement noise in order to ensure good system monitoring and closed-loop performance when designing controllers. In this article, a robust step by step non-asymptotic observer for triangular nonlinear systems for the joint estimation of the state and the disturbance is developed. The proposed approach provides a sequential estimation of the states and the disturbance in finite time using smooth modulating functions. The robustness of the proposed observer is both in the sense of model disturbances and measurement noise. In fact, the structure of triangular systems combined with the modulating function-based method allows the estimation of the states independently of model disturbances and the integral operator involved in the modulating function-based method mitigates the noise. Additionally, the modulating function method shifts the derivative from the noisy output to the smooth modulating function which strengthens its robustness properties. The applicability of the proposed modulating function-based estimator is illustrated in numerical simulations and compared to a second-order sliding mode super twisting observer under different measurement noise levels.

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