arXiv subjects

Mustapha Oudani

Publications and source records attributed to Mustapha Oudani.

6 recordsLinked to original sources

arXiv2026

A Feasible-Velocity Framework for Local Controllability of Nonlinear Systems with Zero-Excluding Input Constraints

This paper studies local controllability of nonlinear control-affine systems subject to state-dependent box constraints that strictly exclude the zero input. Such constraints arise naturally in cable-driven robots and other systems with strictly positive actuation, but fall outside classical small-time local controllability theory and existing frameworks for positive or cone-constrained controls. We introduce the admissible balancing set, an input-space object that classifies reference states without requiring the control distribution to have full rank. When an admissible balancing input lies in the interior of the input set, a locally uniform input shift recovers a symmetric-control system, allowing classical accessibility and small-time local controllability criteria to be applied. When no admissible balancing input exists, the feasible-velocity set is strictly separated from the origin. We show that the resulting separating covector defines a local barrier functional that increases at a uniform positive rate along every admissible trajectory, thereby providing a quantitative obstruction to small-time local controllability. This obstruction does not exclude finite-time reachability through trajectories leaving the barrier neighborhood, which motivates the notion of admissible excursions. The framework is illustrated on an underactuated planar cable-driven parallel robot, for which the barrier is certified numerically over a prescribed state neighborhood.

math.OC↗

arXiv2025

Designing Robust Software Sensors for Nonlinear Systems via Neural Networks and Adaptive Sliding Mode Control

Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to designing software sensors for nonlinear dynamical systems expressed in their most general form. Unlike traditional model-based observers that rely on explicit transformations or linearization, the proposed framework integrates neural networks with adaptive Sliding Mode Control (SMC) to design a robust state observer under a less restrictive set of conditions. The learning process is driven by available sensor measurements, which are used to correct the observer's state estimate. The training methodology leverages the system's governing equations as a physics-based constraint, enabling observer synthesis without access to ground-truth state trajectories. By employing a time-varying gain matrix dynamically adjusted by the neural network, the observer adapts in real-time to system changes, ensuring robustness against noise, external disturbances, and variations in system dynamics. Furthermore, we provide sufficient conditions to guarantee estimation error convergence, establishing a theoretical foundation for the observer's reliability. The methodology's effectiveness is validated through simulations on challenging examples, including systems with non-differentiable dynamics and varying observability conditions. These examples, which are often problematic for conventional techniques, serve to demonstrate the robustness and broad applicability of our approach. The results show rapid convergence and high accuracy, underscoring the method's potential for addressing complex state estimation challenges in real-world applications.

math.DS↗

arXiv2025

PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems

State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems. Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process. The observer adaptively learns an optimal gain matrix, ensuring convergence of the estimated states to the true system states. A rigorous theoretical analysis establishes formal convergence guarantees, demonstrating that the proposed approach achieves uniform error minimization under mild observability conditions. The effectiveness of PINN-Obs is validated through extensive numerical simulations on diverse nonlinear systems, including an induction motor model, a satellite motion system, and benchmark academic examples. Comparative experimental studies against existing observer designs highlight its superior accuracy, robustness, and adaptability.

cs.LG↗

arXiv2023

EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equations

Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult to solve, and classical numerical methods can be computationally expensive. In this paper, we present an innovative approach for solving the NSE using Physics Informed Neural Networks (PINN) and several novel techniques that improve their performance. The first model is based on an assumption that involves approximating the velocity component by employing the derivative of a stream function. This assumption serves to simplify the system and guarantees that the velocity adheres to the divergence-free equation. We also developed a second more flexible model that approximates the solution without any assumptions. The proposed models can effectively solve two-dimensional NSE. Moreover, we successfully applied the second model to solve the three-dimensional NSE. The results show that the models can efficiently and accurately solve the NSE in three dimensions. These approaches offer several advantages, including high trainability, flexibility, and efficiency.

physics.comp-ph↗

arXiv2019

Modelling the Incomplete Intermodal Terminal Location Problem

In this paper, we introduce and study the incomplete version of the intermodal terminal location problem. It's a generalization of the classical version by relaxing the assumption that the induced graph by located terminals is complete. We propose a mixed integer program to model the problem and we provide several extensions. All models are tested through validation in CPLEX solver. Numerical results are reported using well-known data set from the literature.

math.OC↗

arXiv2017

Solving the Uncapacitated Single Allocation p-Hub Median Problem on GPU

A parallel genetic algorithm (GA) implemented on GPU clusters is proposed to solve the Uncapacitated Single Allocation p-Hub Median problem. The GA uses binary and integer encoding and genetic operators adapted to this problem. Our GA is improved by generated initial solution with hubs located at middle nodes. The obtained experimental results are compared with the best known solutions on all benchmarks on instances up to 1000 nodes. Furthermore, we solve our own randomly generated instances up to 6000 nodes. Our approach outperforms most well-known heuristics in terms of solution quality and time execution and it allows hitherto unsolved problems to be solved.

cs.DM↗