arXiv subjects

Jean-Pierre Barbot

Publications and source records attributed to Jean-Pierre Barbot.

6 recordsLinked to original sources

arXiv2026

Model-Free Based Computations of Recursive Control Barrier Function: Ultra-Local Model Approach

Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.

eess.SY↗

arXiv2024

A note about high-order semi-implicit differentiation: application to a numerical integration scheme with Taylor-based compensated error

In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor expansion refinement. The proposed algorithm is dual to the interconnected approach since it offers alternative flexibility to be tuned and to be implemented in real-time processes. In particular, an application to a numerical integration scheme is presented as the Taylor refinement can be of interest to improve the global convergence. Numerical results are presented to support the rightness of the proposed method.

math.NA↗

arXiv2024

A Power Tower Control: A New Sliding Mode Control

A control based power tower function at order 2 is proposed in this paper. This leads to a new sliding mode control, which allows employing backstepping technique that combines both guaranteed and finite time convergence. The proposed control is applied to a double integrator subject to perturbation $d$. Both guaranteed and finite convergence are ensured by the controller when $d$ is considered constant and bounded, without knowing its upper bound. For the case, when $d$ is variable and bounded with its upper bound known, only a finite time convergence is obtained. Simulation results are given to show the well founded of the proposed novel control.

math.DS↗

arXiv2022

Implicit function theorem for nonlinear time-delay systems with algebraic constraints

In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems. An iterative algorithm is proposed to check the conditions and to construct the desired bicausal change of coordinates for the proposed implicit function theorem. Moreover, we show that our results can be applied to delayed differential-algebraic equations (DDAEs) to reduce their indices and to get their solutions. Some numerical examples are given to illustrate our results.

eess.SY↗

arXiv2021

Active fault tolerant control for twin wind turbine subject to asymmetric fault

This paper addresses the problem of control of a twin wind turbine which is subject to an electrical fault affecting only one stator phase of one turbine. An active fault tolerant control is proposed. The performance and robustness of the proposed control, comparing to a passive fault tolerant one developed in the literature, are shown through numerical simulations.

eess.SY↗

arXiv2019

Secure State Estimation and Attack Reconstruction in Cyber-Physical Systems: Sliding Mode Observer Approach

A cyber-physical system (CPS) is a tight coupling of computational resources, network communication, and physical processes. They are composed of a set of networked components, including sensors, actuators, control processing units, and communication agents that instrument the physical world to make smarter. However, cyber components are also the source of new, unprecedented vulnerabilities to malicious attacks. In order to protect a CPS from attacks, three security levels of protection, detection, and identification are considered. In this chapter, we will discuss the identification level, i.e., secure state estimation and attack reconstruction of CPS with corrupted states and measurements. Considering different attack plans that may assault the states, sensors, or both of them, different online attack reconstruction approaches are discussed. Fixed-gain and adaptive-gain finite-time convergent observation algorithms, specifically sliding mode observers, are applied to the online reconstruction of sensor and state attacks. Next, the corrupted measurements and states are to be cleaned up online in order to stop the attack propagation to the CPS via the control signal. The proposed methodologies are applied to an electric power network, whose states and sensors are under attack. Simulation results illustrate the efficacy of the proposed observers.

eess.SY↗