Modulating function based algebraic observer coupled with stable output predictor for LTV and sampled-data systems

This paper proposes an algebraic observer-based modulating function approach for linear time-variant systems and a class of nonlinear systems with discrete measurements. The underlying idea lies in constructing an observability transformation that infers some properties of the modulating function approach for designing such algebraic observers. First, we investigate the algebraic observer design for linear time-variant systems under an observable canonical form for continuous-time measurements. Then, we provide the convergence of the observation error in an L2-gain stability sense. Next, we develop an exponentially stable sampled-data observer which relies on the design of the algebraic observer and an output predictor to achieve state estimation from available measurements and under small inter-sampling periods. Using a trajectory-based approach, we prove the convergence of the observation error within a convergence rate that can be adjusted through the fixed time-horizon length of the modulating function and the upper bound of the sampling period. Furthermore, robustness of the sampled-data algebraic observer, which yields input-to-state stability, is inherited by the modulating kernel and the closed-loop output predictor design. Finally, we discuss the implementation procedure of the MF-based observer realization, demonstrate the applicability of the algebraic observer, and illustrate its performance through two examples given by linear time-invariant and linear time-variant systems with nonlinear input-output injection terms.Comment: 15 pages, 9 figures, submitted to Automatic

Continuous-discrete time observer design for Lipschitz systems with sampled measurements

International audienceThis technical note concerns observer design for Lipschitz nonlinear systems with sampled output. Using reachability analysis, an upper approximation of the attainable set is given. When this approximation is formulated in terms of a convex combination of linear mappings, a sufficient condition is given in terms of linear matrix inequalities (LMIs) which can be solved employing an LMIs solver. This novel approach seems to be an efficient tool to solve the problem of observer synthesis for a class of Lipschitz systems of small dimensions

Continuous output feedback stabilization for nonlinear systems based on sampled and delayed output measurements

This paper addresses the problem of output feedback stabilization for nonlinear systems with sampled and delayed output measurements. Firstly, sufficient conditions are proposed to ensure that a class of hybrid systems are globally exponentially stable. Then, based on the sufficient conditions and a dedicated construction continuous observer, an output feedback control law is presented to globally exponentially stabilize the nonlinear systems. The output feedback stabilizer is continuous and hybrid, and can be derived without discretization. The maximum allowable sampling period and the maximum delay are also given. At last, a numerical example is provided to illustrate the design methods.The National Science Foundation of China (61174216, 61374028, 51177088, 61273183]), the Grant National Science Foundation of Hubei Provincial (2013CFA050), the Scientific Innovation Team Project of Hubei Provincial Department of Education (T201504).http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-12392017-09-30hb2016Electrical, Electronic and Computer Engineerin

Continuous observer design for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements

In this paper, continuous observer is designed for a class of multi-output nonlinear systems with multirate sampled and delayed output measurements. The time delay may be larger or less than the sampling intervals. The sampled and delayed measurements are used to update the observer whenever they are available. Sufficient conditions are presented to ensure global exponential stability of the observation errors by constructing a Lyapunov–Krasovskii function. A numerical example is given to illustrate the effectiveness of the proposed methods.http://www.elsevier.com/locate/automatica2018-01-31hb2017Electrical, Electronic and Computer Engineerin

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Fuzzy H-infinity output feedback control of nonlinear systems under sampled measurements

This paper studies the problem of designing an H∞ fuzzy feedback control for a class of nonlinear systems described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are allowed to be unavailable. We develop a technique for designing an H∞ fuzzy feedback control that guarantees the L2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value. A design algorithm for constructing the H∞ fuzzy feedback controller is given

Contracting Nonlinear Observers: Convex Optimization and Learning from Data

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.Comment: conference submissio