27,333 research outputs found

    H∞ observer design for a class of nonlinear discrete systems

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    Necessary and sufficient conditions are presented under which a discrete-time autonomous system with outputs is locally diffeomorphic to an output-scaled linear observable system or an output-scaled nonlinear system in the observer form. As a consequence of such characterizations, the nonlinear observer design problem is studied for a broader class of discrete-time nonlinear systems by using the exact linearization technique that is based on the differential geometric approac

    H ∞  sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

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    Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

    Observers Design for a Class of Lipschitz Discrete-Time Systems with Time-Delay

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    The observer design problem for nonlinear time-delay systems becomes more and more a subject of research in constant evolution Germani et al. (2002), Germani & Pepe (2004), Aggoune et al. (1999), Raff & Allgöwer (2006), Trinh et al. (2004), Xu et al. (2004), Zemouche et al. (2006), Zemouche et al. (2007). Indeed, time-delay is frequently encountered in various practical systems, such as chemical engineering systems, neural networks and population dynamic model. One of the recent application of time-delay is the synchronization and information recovery in chaotic communication systems Cherrier et al. (2005). In fact, the time-delay is added in a suitable way to the chaotic system in the goal to increase the complexity of the chaotic behavior and then to enhance the security of communication systems. On the other hand, contrary to nonlinear continuous-time systems, little attention has been paid toward discrete-time nonlinear systems with time-delay. We refer the readers to the few existing references Lu & Ho (2004a) and Lu & Ho (2004b), where the authors investigated the problem of robust H∞ observer design for a class of Lipschitz time-delay systems with uncertain parameters in the discrete-time case. Their method show the stability of the state of the system and the estimation error simultaneously. This chapter deals with observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay. The main result lies in the use of a new structure of the proposed observer inspired from Fan & Arcak (2003). Using a Lyapunov-Krasovskii functional, a new nonrestrictive synthesis condition is obtained. This condition, expressed in term of LMI, contains more degree of freedom than those proposed by the approaches available in literature. Indeed, these last use a simple Luenberger observer which can be derived from the general form of the observer proposed in this paper by neglecting some observer gains. An extension of the presented result to H∞ performance analysis is given in the goal to take into account the noise which affects the considered system. A more general LMI is established. The last section is devoted to systems with differentiable nonlinearities. In this case, based on the use of the Differential Mean Value Theorem (DMVT), less restrictive synthesis conditions are proposed

    New Approach to Observer-Based Finite-Time H∞ Control of Discrete-Time One-Sided Lipschitz Systems with Uncertainties

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    This paper investigates the finite-time H∞ control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties. Using the one-sided Lipschitz and quadratically inner-bounded conditions, the authors derive less conservative criterion for the controller design and observer design. A new criterion is proposed to ensure the closedloop system is finite-time bounded (FTB). The sufficient conditions are established to ensure the closed-loop system is H∞ finite-time bounded (H∞ FTB) in terms of matrix inequalities. The controller gains and observer gains are given. A numerical example is provided to demonstrate the effectiveness of the proposed results

    Filter And Observer Design For Polynomial Discrete-Time Systems: A Sum Of Squares Based Approach

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    The polynomial discrete-time systems are the type of systems where the dynamics of the systems are described in polynomial forms.This system is classified as an important class of nonlinear systems due to the fact that many nonlinear systems can be modelled as,transformed into,or approximated by polynomial systems.The focus of this thesis is to address the problem of filter and observer design for polynomial discrete-time systems.The main reason for focusing on this area is because the filter and observer design for such polynomial discrete-time systems is categorised as a difficult problem.This is due to the fact that the relation between the Lyapunov matrix and the filter and observer gain is not jointly convex when the parameter-dependent or state-dependent Lyapunov function is under consideration.Therefore the problem cannot possibly be solved via semidefinite programming (SDP).In light of the aforementioned problem, we establish novel methodologies of designing filters for estimating the state of the systems both with and without H∞ performance and also designing an observer for state estimation and also as a controller.We show that through our proposed methodologies,a less conservative design procedure can be rendered for the filter and observer design.In particular,a so-called integrator method is proposed in this research work where an integrator is incorporated into the filter and observer structures.In doing so, the original systems can be transformed into augmented systems.Furthermore,the state-dependent function is selected in a way that its matrix is dependent only upon the original system state.Through this selection,a convex solution to the filter and observer design can be obtained efficiently.The existence of such filter and observer are given in terms of the solvability of polynomial matrix inequalities (PMIs).The problem is then formulated as sum of squares (SOS) constraints,therefore it can be solved by any SOS solvers.In this research work,SOSTOOLS is used as a SOS solver.Finally,to demonstrate the effectiveness and advantages of the proposed design methodologies in this thesis,numerical examples are given in filter design system.The simulation results show that the proposed design methodologies can estimate and stabilise the systems and achieve the prescribed performance requirements

    Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay

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    [EN] This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.This work was partially supported by: Ministerio de Economía y Competitividad, Spain (TIN2017-86520-C3-1-R); Universitat Politècnica de València (FPI-UPV 2014 PhD Grant); and Israel Science Foundation (Grant No. 1128/14).Sanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2020). Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay. International Journal of Control. 93(2):217-225. https://doi.org/10.1080/00207179.2018.1562204S217225932Ahmed-Ali, T., Cherrier, E., & Lamnabhi-Lagarrigue, F. (2012). Cascade High Gain Predictors for a Class of Nonlinear Systems. IEEE Transactions on Automatic Control, 57(1), 221-226. doi:10.1109/tac.2011.2161795Artstein, Z. (1982). Linear systems with delayed controls: A reduction. 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Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control, 15(3), 109-125. doi:10.1002/rnc.978Karafyllis, I., & Krstic, M. (2017). Predictor Feedback for Delay Systems: Implementations and Approximations. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-42378-4Krstic, M. (2008). Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica, 44(11), 2930-2935. doi:10.1016/j.automatica.2008.04.010Léchappé, V., Moulay, E., Plestan, F., Glumineau, A., & Chriette, A. (2015). New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica, 52, 179-184. doi:10.1016/j.automatica.2014.11.003Léchappé, V., Moulay, E. & Plestan, F. (2016). 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    A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

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    We address the problem of state estimation and attack isolation for general discrete-time nonlinear systems when sensors are corrupted by (potentially unbounded) attack signals. For a large class of nonlinear plants and observers, we provide a general estimation scheme, built around the idea of sensor redundancy and multi-observer, capable of reconstructing the system state in spite of sensor attacks and noise. This scheme has been proposed by others for linear systems/observers and here we propose a unifying framework for a much larger class of nonlinear systems/observers. Using the proposed estimator, we provide an isolation algorithm to pinpoint attacks on sensors during sliding time windows. Simulation results are presented to illustrate the performance of our tools.Comment: arXiv admin note: text overlap with arXiv:1806.0648
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