Generic observability of dynamical systems.
Genericity of observability and the existence of asymptotic observers
In this paper, we deal with the genericity of the observability property and the existence of asymptotic observers for nonlinear systems. In the case where the number of outputs is larger than the number of inputs and the state space is compact, we prove that observability in a very strong sense (more or less, observability for each sufficiently differentiable input) is generic. This is obtained by using standard (but not easy) transversality arguments. For the inputs that are bounded with their...
Genericity of observability of control-affine systems
Genericity of observability of control-affine systems
For smooth or real-analytic single-input, control-affine, non-linear systems, with at least two ouputs, observability for any input of a given class is generic. This class can be either the class of inputs bounded with their derivatives up to a certain order, or the class of polynomial inputs with bounded degree.
Geometrical characterization of observability in Interpreted Petri Nets
This work is concerned with observability in Discrete Event Systems (DES) modeled by Interpreted Petri Nets (IPN). Three major contributions are presented. First, a novel geometric characterization of observability based on input-output equivalence relations on the marking sequences sets is presented. Later, to show that this characterization is well posed, it is applied to linear continuous systems, leading to classical characterizations of observability for continuous systems. Finally, this paper...
Global Carleman estimate for stochastic parabolic equations, and its application
This paper is addressed to proving a new Carleman estimate for stochastic parabolic equations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X. Zhang, SIAM J. Control Optim. 48 (2009) 2191–2216.], Thm. 5.2), one extra gradient term involving in that estimate is eliminated. Also, our improved Carleman estimate is established by virtue of the known Carleman estimate for deterministic parabolic equations. As its application, we prove the existence of insensitizing controls...
Global finite-time observers for a class of nonlinear systems
Global finite-time observers are designed for a class of nonlinear systems with bounded varying rational powers imposed on the increments of the nonlinearities whose solutions exist and are unique for all positive time. The global finite-time observers designed in this paper are with two homogeneous terms. The global finite-time convergence of the observation error system is achieved by combining global asymptotic stability and local finite-time stability.
Global stability of linearizing control with a new robust nonlinear observer of the induction motor
This paper mainly deals with the design of an advanced control law with an observer for a special class of nonlinear systems. We design an observer with a gain as a function of speed. We study the solution to the output feedback torque and rotor flux-tracking problem for an induction motor model given in the natural frame. We propose a new robust nonlinear observer and prove the global stability of the interlaced controller-observer system. The control algorithm is studied through simulations and...
Gradient observability for diffusion systems
The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm...