Browsing by Subject "Observer"
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Item Open Access Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach(Elsevier, 2018) Ahmed, Saeed; Mazenc, F.; Özbay, HitayA new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable.Item Open Access Finite time estimation for time-varying systems with delay in the measurements(Elsevier, 2019) Ahmed, Saeed; Malisoff, M.; Mazenc, F.We build finite time observers for time-varying nonlinear systems with delays in the outputs, using a dynamic extension that computes fundamental matrices. Our observers achieve finite time convergence when no disturbances are present. When disturbances are present, we provide approximate values for the solutions, which lead to an upper bound on the approximation error after a suitable finite time. We illustrate our work in a class of systems arising in the study of vibrating membranes, where time-varying coefficients can be used to represent intermittent measurements.Item Open Access Finite time estimation through a continuous-discrete observer(John Wiley and Sons, 2018) Mazenc, F.; Ahmed, S.; Malisoff, M.We study two broad classes of nonlinear time-varying continuous-time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance affects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the efficacy of our methods.Item Open Access Finite time estimation via piecewise constant measurements⁎(Elsevier B.V., 2018) Mazenc, F.; Ahmed, S.We study a broad class of linear continuous-time time-varying systems that contain piecewise continuous disturbances and piecewise constant outputs. Under an observability assumption, we construct a new type of observer to estimate the state of the system in a predetermined finite time in the presence of the disturbances. In contrast to the well-established finite time observer design techniques which estimate the system state using a continuous output, our proposed observer only requires a piecewise constant output. Our simulations illustrate the efficacy of our observer.Item Open Access Observer design and output feedback Stabilization of time varying systems(2018-07) Ahmed, SaeedWe study observer design and output feedback stabilization of switched and nonlinear time varying systems. To establish the stability of feedback switched systems with delay, we develop a new extension of a recently proposed trajectory based approach which is fundamentally different from classical Lyapunov function based methods. This new extension of trajectory based approach, which is of interest for its own sake, can be applied to a wide range of time varying systems with time varying delays and it tackles the issue of finding appropriate Lyapunov functions to establish stability results. Our stabilization methodology does not require stabilizability and detectability of all of the subsystems of the switched system and we do not impose any constraint on the derivative of the time varying delay. For nonlinear time varying systems, we build a new type of finite-time smooth observer in the case where a state dependent disturbance affects the linear approximation. We combine this finite time observer design and a switched systems approach to develop stabilizing feedbacks for nonlinear time varying systems whose outputs are only available on some finite time intervals. Again, we use an extension of the trajectory based approach to conclude the stability of the closed-loop system. Motivated by the fact that the measured components of the state do not need to be estimated, we also construct reduced order finite time observers for a broad class of nonlinear time varying systems. We show how these reduced order finite time observers can be used to solve dynamic output feedback stabilization problem for multiple input, multiple output nonlinear time varying systems. Finally, we design a finite time observer to estimate the exact state of a continuous-time linear time varying system from sampled output in the presence of a piecewise continuous disturbance.Item Open Access Output feedback stabilization by reduced order finite time observers using a trajectory based approach(IEEE, 2019) Malisoff, M.; Mazenc, F.; Ahmed, SaeedWe use finite time reduced order continuous-discrete observers to solve an output feedback stabilization problem for a class of nonlinear time-varying systems whose outputs contain uncertainty. Unlike earlier works, our feedback is discontinuous, but it does not contain distributed control terms. Our trajectory based approach is based on a contractivity condition. We illustrate our control in the context of a tracking problem for nonholonomic systems in chained form.Item Open Access Reduced order finite time observers for time-varying nonlinear systems(Institute of Electrical and Electronics Engineers Inc., 2019) Mazenc, F.; Ahmed, Saeed; Malisoff, M.; Teel, A. R.; Egerstedt, M.We build reduced order finite time observers for a large class of nonlinear time-varying continuous-time systems. We illustrate our results using a tracking problem for nonholonomic systems in chained form.Item Open Access Stabilization of higher order Schrödinger equations on a finite interval: Part I(AIMS Press, 2021-12) Batal, Ahmet; Özsarı, Türker; Yılmaz, K.C.We study the backstepping stabilization of higher order linear and nonlinear Schrödinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a prescribed rate of decay. The construction of the backstepping kernel is based on a challenging successive approximation analysis. This contrasts with the case of second order pdes. Second, we consider the case where the full state of the system cannot be measured at all times but some partial information such as measurements of a boundary trace are available. For this problem, we simultaneously construct an observer and the associated backstepping controller which is capable of stabilizing the original plant. Wellposedness and regularity results are provided for all pde models. Although the linear part of the model is similar to the KdV equation, the power type nonlinearity brings additional difficulties. We give two examples of boundary conditions and partial measurements. We also present numerical algorithms and simulations verifying our theoretical results to the fullest extent. Our numerical approach is novel in the sense that we solve the target systems first and obtain the solution to the feedback system by using the bounded invertibility of the backstepping transformation.Item Open Access Stabilization of higher order Schrödinger equations on a finite interval: part II(AIMS Press, 2021-07) Özsarı, Türker; Yılmaz, K. C.Backstepping based controller and observer models were designed for higher order linear and nonlinear Schrödinger equations on a finite interval in [3] where the controller was assumed to be acting from the left endpoint of the medium. In this companion paper, we further the analysis by considering boundary controller(s) acting at the right endpoint of the domain. It turns out that the problem is more challenging in this scenario as the associated boundary value problem for the backstepping kernel becomes overdetermined and lacks a smooth solution. The latter is essential to switch back and forth between the original plant and the so called target system. To overcome this difficulty we rely on the strategy of using an imperfect kernel, namely one of the boundary conditions in kernel PDE model is disregarded. The drawback is that one loses rapid stabilization in comparison with the left endpoint controllability. Nevertheless, the exponential decay of the L2-norm with a certain rate still holds. The observer design is associated with new challenges from the point of view of wellposedness and one has to prove smoothing properties for an associated initial boundary value problem with inhomogeneous boundary data. This problem is solved by using Laplace transform in time. However, the Bromwich integral that inverts the transformed solution is associated with certain analyticity issues which are treated through a subtle analysis. Numerical algorithms and simulations verifying the theoretical results are given.