A homogeneity property of a class of discrete-time systems

International audienceIn this paper we study a dynamic property of a class of discrete-time systems. Such a property, that we call discrete-homogeneity, is verifiable algebraically in the transition map of the system. Discrete-homogeneity allows to establish stability features of the system by considering only the discrete-homogeneity degree. Such stability properties are studied by means of Lyapunov and Lyapunov-like functions

On finite-time stability of sub-homogeneous differential inclusions

International audienceSub-homogeneity property is introduced and is related to a differential inclusion (DI). It is shown that a nonlinear ordinary differential equation (ODE), which may not admit a homogeneous approximation, can be transformed into a sub-homogeneous DI (which is a homogeneous extension of the original ODE). Using this homogeneous extension, one can directly recover finite-time stability property for some particular classes of nonlinear systems. In the last section, such a sub homogeneity property is used to design a nonlinear finite-time observer

Differential Neural Network Identification for Homogeneous Dynamical Systems ⋆

International audienceIn this paper, a non parametric identifier for homogeneous nonlinear systems affine in the input is proposed. The identification algorithm is based on the neural networks using sigmoidal activation functions. The learning algorithm is derived by means of Lyapunov function method and homogeneity theory. A numerical example demonstrates the performance of the proposed identifier

Adaptive Discontinuous Control for Homogeneous Systems Approximated by Neural Networks

International audienceThis study is devoted to the design of an adaptive discontinuous control based on differential neural networks (DNNs) for a class of uncertain homogeneous systems. The control is based on the universal approximation properties of artificial neural networks (ANNs) applied on a certain class of homogeneous nonlinear functions. The adaptation laws for the DNNs parameters are obtained with the application of the Lyapunov stability theory and the homogeneity properties of the approximated nonlinear system. The stability analysis of the closed loop system with the proposed controller is presented. The estimation error in the approximation of the uncertain homogeneous functions is considered in the stability analysis. The performance of the controller is illustrated by means of a numerical simulation of a homogeneous model

A distributed finite-time observer for linear systems

International audienceIn this paper, the problem of distributed estimation for a linear large-scale system is studied. A nonlinear distributed observer is proposed, whose estimation error converges to zero in a finite time. A fixed-time converging version of the observer is also presented. The efficiency of estimators is demonstrated by computer simulations

On Generalized Homogenization of Linear Quadrotor Controller

International audienceA novel scheme for an "upgrade" of a linear control algorithm to a non-linear one is developed based on the concepts of a generalized homogeneity and an implicit homogeneous feedback design. Some tuning rules for a guaranteed improvement of a regulation quality are proposed. Theoretical results are confirmed by real experiments with the quadrotor QDrone of Quanser T M

Robust Finite-time stability of homogeneous systems with respect tomultiplicative disturbances

International audienceLyapunov characterizations of output finite-time stability are presented for the system $x' = f (x), y = h(x)$ which is locally Lipschitz continuous out of the set $Y = {x ∈ R n : h(x) = 0}$ and continuous on $R^n$. The definitions are given in the form of $K$ and $KL$ functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples

Differentiator application in altitude control for an indoor blimp robot

International audienceThis paper presents design of altitude controller with disturbance compensation for an indoor blimp robot and its realisation. Due to hardware restrictions, the altitude control behaviour of blimp is modelled as a switched system with a constant time-delay complemented with uncertain bounded disturbances. In order to achieve state estimation, four differentiators are applied and compared, then HOMD (homo-geneous finite-time) differentiator is chosen as an observer for vertical velocity and switching signal estimation. Next, a predictor-based controller is conceived, and in order to compensate the perturbation, the method for disturbance evaluation is designed still with the help of HOMD differentiator. Control scheme is implemented by Matlab Simulink, and finally, the performance of blimp altitude controller is verified in experiments