Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

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

Robust filtering for bilinear uncertain stochastic discrete-time systems

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic system is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prespecified value. It is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities. In particular, we establish both the existence conditions and the explicit expression of desired robust filters. A numerical example is included to show the applicability of the present method

Nonparametric Uncertainty Quantification for Stochastic Gradient Flows

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce a stochastic matrix whose generator is a discrete approximation to the backward Kolmogorov operator of the underlying dynamics. The eigenvectors of this stochastic matrix, which we will refer to as the diffusion coordinates, are discrete approximations to the eigenfunctions of the Kolmogorov operator and form an orthonormal basis for functions defined on the data set. Using this basis, we consider the projection of three uncertainty quantification (UQ) problems (prediction, filtering, and response) into the diffusion coordinates. In these coordinates, the nonlinear prediction and response problems reduce to solving systems of infinite-dimensional linear ordinary differential equations. Similarly, the continuous-time nonlinear filtering problem reduces to solving a system of infinite-dimensional linear stochastic differential equations. Solving the UQ problems then reduces to solving the corresponding truncated linear systems in finitely many diffusion coordinates. By solving these systems we give a model-free algorithm for UQ on gradient flow systems with isotropic diffusion. We numerically verify these algorithms on a 1-dimensional linear gradient flow system where the analytic solutions of the UQ problems are known. We also apply the algorithm to a chaotically forced nonlinear gradient flow system which is known to be well approximated as a stochastically forced gradient flow.Comment: Find the associated videos at: http://personal.psu.edu/thb11

Robust Filtering and Smoothing with Gaussian Processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding point estimates of a parametric function representation. In this article, we present a principled algorithm for robust analytic smoothing in GP dynamic systems, which are increasingly used in robotics and control. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail.Comment: 7 pages, 1 figure, draft version of paper accepted at IEEE Transactions on Automatic Contro

Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including on-line and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods