Section: New Results

Finite time observers

Participants : Frédéric Mazenc, Michael Malisoff [LSU] , Saeed Ahmed [University of Kaiserslautern, Germany] , Thach Dinh [CNAM] , Tarek Raissi [CNAM] .

Finite time observers are remarkably efficient when the value of the state is needed in a short time. By contrast with them, the solutions asymptotic observers may take a long time to be close to the solutions of the studied systems and may exhibit large transient errors. Motivated by this general fact, we produced three works.

In the work [12], we proposed finite time observers for time-varying nonlinear systems with delays in the outputs. When disturbances are present, we provide approximate values for the solutions which are expressed as upper bounds on the approximation errors after a suitable finite time. We illustrated our work via systems arising in the study of vibrating membranes, where time-varying coefficients can be used to represent intermittent measurements.

In paper [36], we use finite time reduced order continuous-discrete observers to solve an output feedback stabilization problem for a broad class of nonlinear systems whose output contains uncertainty. Unlike earlier works, our feedback control is discontinuous, but it does not contain any distributed terms, which is an advantage because the implementation of these terms may cause instability. We illustrated our main result by applying it to design a dynamic output feedback to solve a tracking problem for nonholonomic systems in chained form.

The paper [35] is devoted to the construction of finite time observers for discrete-time systems. We developped a new technique, which uses past values of the output. We considered the case where the systems are affected by additive disturbances and disturbances in the output. Exact estimation or approximate estimation have been achieved, depending on the absence or the presence of unknown but bounded uncertainties, respectively.