Global Exponential Sampled-Data Observers for Nonlinear Systems with Delayed Measurements

This paper presents new results concerning the observer design for wide classes of nonlinear systems with both sampled and delayed measurements. By using a small gain approach we provide sufficient conditions, which involve both the delay and the sampling period, ensuring exponential convergence of the observer system error. The proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule. Moreover, new results on the robust global exponential state predictor design problem are provided, for wide classes of nonlinear systems.Comment: 17 pages, submitted for possible publication to Systems and Control Letter

Adjoint and Hamiltonian input-output differential equations

Based on developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft (1987), this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics

Contrôle non linéaire pour les DC MicroGrids isolées

International audienceThe access to electricity for isolated communities is capital for improving life in those societies. The use of renewable energy sources (renewables) and energy storage systems is the key for clean energy supply in remote areas without the main grid. The standalone operation of renew-ables represents a challenge for operation and reliability, therefore the DC MicroGrid concept is seen as a powerful solution allowing renewables integration and reliable operation of the system is simple way. This paper proposes a distributed nonlinear control strategy for an isolated MicroGrid composed of renewables and different timescale storage systems to supply a DC load. The simulations results show the behavior of the proposed MicroGrid and a comparison with classical linear control is done to highlight the control performance.L'accès à l'électricité pour les communautés isolées est un capital pour améliorer la vie dans ces sociétés. L'utilisation de sources d'énergie renouvelables et de systèmes de stockage d'énergie est la clé pour l'approvisionnement en énergie propre dans les zones reculées sans réseau principal. Le fonctionnement autonome des énergies renouvelables représente un défi pour l'exploitation et la fiabilité, par conséquent, le concept DC MicroGrid est considéré comme une solution puis-sante permettant l'intégration des énergies renouvelables et un fonctionnement fiable du système de manière simple. Cet article propose une stratégie de contrôle non linéaire distribuée pour un Micro-Grid isolé composé d'énergies renouvelables et de différents systèmes de stockage à l'échelle du temps pour fournir une charge continue. Les résultats des simulations montrent le comportement du MicroGrid proposé et une comparaison avec le contrôle linéaire classique est effectuée pour mettre en évidence les performances du contrôle

Adjoint and Hamiltonian Input-Output Differential Equations

Based on recent developments in the theory of variational and Hamiltonian control systems, this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics.

Using exponential time-varying gains for sampled-data stabilization and estimation

International audienceThis paper provides exponential stability results for two system classes. The first class includes a family of nonlinear ODE systems while the second consists of semi-linear parabolic PDEs. A common feature of both classes is that the systems they include involve sampled-data states and a time-varying gain. Sufficient conditions ensuring global exponential stability are established in terms of Linear Matrix Inequalities (LMIs) derived on the basis of Lyapunov–Krasovskii functionals. The established stability results prove to be useful in designing exponentially convergent observers based on sampled-data measurements. It is shown throughout simulated examples from the literature that the introduction of time-varying gains is beneficial to the enlargement of sampling intervals while preserving the stability of the system