Uniting observers

International audienceWe propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviours for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: one, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behaviour. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented

Robust output stabilization: improving performance via supervisory control

We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid observer that ensures ``fast'' convergence with ``low'' overshoots. As a second application of our main results we use hybrid control in the context of synchronization of chaotic oscillators with the goal of reducing control effort; an originality of the hybrid control in this context with respect to other contributions in the area is that it exploits the structure and chaotic behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA

Sequential processing and performance optimization in nonlinear state estimation

We propose a framework for designing observers for noisy nonlinear systems with global convergence properties and performing robustness and noise sensitivity. Our state observer is the result of the combination of a state norm estimator with a bank of Kalman-type lters, parametrized by the state norm estimator. The state estimate is sequentially processed through the bank of lters. In general, existing nonlinear state observers are responsible for estimation errors which are sensitive to model uncertainties and measurement noise, depending on the initial state conditions. Each Kalman-type lter of the bank contributes to improve the estimation error performances to a certain degree in terms of sensitivity with respect to noise and initial state conditions. A sequential processing algorithm for performance optimization is given and simulations show the eectiveness of these sequential lters

On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems

We investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. First, the classical formulation based on the minimization of an estimation functional is analyzed. Second, the structure of the resulting estimator is taken into account to study the global stability properties of the estimation error by relying on the notion of input-to-state stability. A condition based on the satisfaction of a Hamilton-Jacobi inequality is proposed to construct estimators with input-to-state stable dynamics of the estimation error, where the disturbances affecting such dynamics are regarded as input. Third, the so-developed general framework is applied to the special case of high-gain observers for a class of nonlinear systems

Semi-global stabilization by an output feedback law from a hybrid state controller

International audienceThis article suggests a design method of a hybrid output feedback for SISO continuous systems. We focus on continuous systems for which there exists a hybrid state feedback law. A local hybrid stabilizability and a (global) complete uniform observability are assumed to achieve the stabilization of an equilibrium with a hybrid output feedback law. This is an existence result. Moreover, assuming the existence of a robust Lyapunov function instead of a stabilizability assumption allows to design explicitely this hybrid output feedback law. This last result is illustrated for linear systems with reset saturated controls

Hysteresis-based switching observers for linear systems using quadratic boundedness

Switched-gain observers are investigated for the purpose of estimating the state of linear systems affected by bounded noises. Under mild assumptions, hybrid observers with switching gains are proposed and provided with stability analysis based on quadratic boundedness for the estimation error. Such observers are designed by solving optimization problems aimed at minimizing upper bounds on the estimation error in such a way as to get the smallest invariant set. The effectiveness of the proposed approach is evaluated with some numerical case studies

Stitching Dynamic Movement Primitives and Image-based Visual Servo Control

Utilizing perception for feedback control in combination with Dynamic Movement Primitive (DMP)-based motion generation for a robot's end-effector control is a useful solution for many robotic manufacturing tasks. For instance, while performing an insertion task when the hole or the recipient part is not visible in the eye-in-hand camera, a learning-based movement primitive method can be used to generate the end-effector path. Once the recipient part is in the field of view (FOV), Image-based Visual Servo (IBVS) can be used to control the motion of the robot. Inspired by such applications, this paper presents a generalized control scheme that switches between motion generation using DMPs and IBVS control. To facilitate the design, a common state space representation for the DMP and the IBVS systems is first established. Stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically. The developed method is validated by two real world experiments using the eye-in-hand configuration on a Baxter research robot.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A simple finite-time distributed observer design for linear time-invariant systems

International audienceA design of a distributed observer is proposed for continuous-time systems with nonlinear observer nodes such that the estimation errors converge in a finite time to zero. By taking advantage of individual observability decompositions, the designs for the locally observable and the unobservable substate are made independent from each other. For the observable substate of each node, standard centralized finite-time observer techniques are applied. To estimate distributively the unobservable substate, the observer nodes employ consensus coupling in a linear term and an additional term embedded in a fractional power. The approach is derived using homogeneity arguments and it leads to a simple design with an LMI that is guaranteed to be feasible under general conditions