Section: New Results
Observers
Participants : Frederic Mazenc, Michael Malisoff [LSU] , Saeed Ahmed [Inria] , Ali Zemouche [CRAN] , Rajesh Rajamani [University of Minneapolis, USA] , Maruthi Akella [University of Texas, USA] .
We produced several works which pertain to the case where only a part of the state variables can be measured.
In the paper [58], we adopted a technique based on the indroduction of several observers in cascade (such a cascade is called 'sequential observer') for a class of time-varying linear systems in which the inputs and outputs containing sampling and arbitrarily long delays. The observers are of a continuous-discrete type. We used the observers to design controllers that ensure a strong robustness property with respect to uncertainties in the system and the output, under delays and sampling. A fundamental aspect of the approach is that it produces the observers and controllers without distributed terms. We have assessed the performance of the control laws through two examples, which inlcude a DC motor model that illustrates the utility of the work in engineering applications.
In two papers, we developped the theory of the finite time observers. In [53], we study a class of linear continuous-time time-varying systems with piecewise continuous disturbances and piecewise constant outputs. Under a classical assumption of observability, we designed a new type of observers to estimate the solutions of the system in a predetermined finite time. In contrast to the well-established finite time observer design techniques which estimate the system state using a continuous output, our proposed observer applies when only piecewise constant measurements are available. In [54], we construct finite-time reduced order observers for a broad family of nonlinear time-varying continuous-time systems. The motivation for this is the fact that in practice the time-varying aspect of a system may be an obstacle to the design of full-order finite-time observers, but not for the design of reduced order ones. We illustrated our results using a tracking problem for nonholonomic systems in chained form.
Two of our works present construction of asymptotic observers without delay.
The paper [61] solves an
The work [16] is dedicated to the design of a smooth six-degree-of-freedom observer to estimate the incorporating linear and angular velocity, called dual angular velocity, for a rigid body. The approach is based on the dual-quaternion description and we proved that the estimation errors exhibit asymptotic convergence. Furthermore, to achieve tracking control objective, we combined the proposed observer with an independently designed proportional-derivative-like feedback control law (using full-state feedback), and a special Lyapunov "strictification" process is employed to ensure a separation property between the observer and the controller. We performed numerical simulations for a prototypical spacecraft hovering mission application.