A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong 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 the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Robust H∞ filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation: The finite-horizon case

This article is posted with the permission of IEEE - Copyright @ 2011 IEEEThis paper addresses the robust H∞ filtering problem for a class of discrete time-varying Markovian jump systems with randomly occurring nonlinearities and sensor saturation. Two kinds of transition probability matrices for the Markovian process are considered, namely, the one with polytopic uncertainties and the one with partially unknown entries. The nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the Bernoulli distributions. The main purpose of this paper is to design a robust filter, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the time-varying Markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation. Sufficient conditions are established for the existence of the desired filter satisfying the H∞ performance constraint in terms of a set of recursive linear matrix inequalities. Simulation results demonstrate the effectiveness of the developed filter design scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60825303, and 61004067, National 973 Project under Grant 2009CB320600, the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) from the Ministry of Education of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K., under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu 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.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei 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.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

Recursive filtering for a class of nonlinear systems with missing measurements

This paper is concerned with the finite-horizon recursive filtering problem for a class of nonlinear time-varying systems with missing measurements. The missing measurements are modeled by a series of mutually independent random variables obeying Bernoulli distributions with possibly different occurrence probabilities. Attention is focused on the design of a recursive filter such that, for the missing measurements, an upper bound for the filtering error covariance is guaranteed and such an upper bound is subsequently minimized by properly designing the filter parameters at each sampling instant. The desired filter parameters are obtained by solving two Riccati-like difference equations that are of a recursive form suitable for online applications. A simulation example is exploited to demonstrate the effectiveness of the proposed filter design scheme. © 2012 IEEE.published_or_final_versio

Sequence-based Anytime Control

We present two related anytime algorithms for control of nonlinear systems when the processing resources available are time-varying. The basic idea is to calculate tentative control input sequences for as many time steps into the future as allowed by the available processing resources at every time step. This serves to compensate for the time steps when the processor is not available to perform any control calculations. Using a stochastic Lyapunov function based approach, we analyze the stability of the resulting closed loop system for the cases when the processor availability can be modeled as an independent and identically distributed sequence and via an underlying Markov chain. Numerical simulations indicate that the increase in performance due to the proposed algorithms can be significant.Comment: 14 page

Robust execution for stochastic hybrid systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 177-180).Unmanned systems, such as Autonomous Underwater Vehicles (AUVs), planetary rovers and space probes, have enormous potential in areas such as reconnaissance and space exploration. However the effectiveness and robustness of these systems is currently restricted by a lack of autonomy. Previous work introduced the concept of a model-based executive, which increases the level of autonomy, elevating the level at which systems are commanded. This simplifies the operator's task and leaves degrees of freedom in the plan that allow the executive to optimize resources and ensure robustness to uncertainty. Uncertainty arises due to uncertain state estimation, disturbances, model uncertainty and component failures. This thesis develops a model-based executive that reasons explicitly from a stochastic hybrid discrete-continuous system model to find the optimal course of action, while ensuring the required level of robustness to uncertainty is achieved. Our first contribution is a novel 'Particle Control' approach for robust execution of state plans with stochastic hybrid systems. We introduce the notion of chance-constrained state plan execution; this means that the executive ensures tasks in the state plan have at least a specified minimum probability of success. The minimum probabilities are specified by the operator, enabling conservatism to be traded against performance. In order to make optimal chance-constrained execution tractable, the Particle Control approach approximates the system's state distribution using samples or 'particles' and optimizes the evolution of these particles to achieve chance-constrained state plan execution. In this manner particle control solves a tractable deterministic approximation to the original stochastic problem; furthermore the approximation becomes exact as the number of particles approaches infinity.(cont.) For an important class of hybrid discrete-continuous system known as Jump Markov Linear Systems, the resulting deterministic optimization can be posed as a Mixed Integer Linear Program and solved to global optimality using efficient commercially-available solvers. Our second contribution is 'active' hybrid estimation subject to state plan constraints. Exact hybrid state estimation in stochastic hybrid systems is, in general, intractable. Tractable approximate hybrid estimation methods can lose track of the true hybrid state. In this thesis we develop an active hybrid estimation capability, which probes the system in order to reduce uncertainty in the hybrid state. This approach generates control sequences to minimize the probability of approximate hybrid estimation losing the true mode sequence, while ensuring that the state plan is satisfied subject to chance constraints. In order to make this problem tractable, we develop an analytic upper bound on the probability of losing the true mode sequence, and use a convex constraint tightening approach to approximate the chance constraints in the problem. Our final contribution is a novel hybrid model-learning approach. Specifying accurate hybrid system models is essential for accurate estimation and control, but is also extremely challenging. The hybrid executive must therefore determine hybrid system models from observed data. In this thesis we present an approximate Expectation-Maximization method for hybrid model learning; this method extends prior approaches to deal with mode transitions that depend on the continuous state.by Lars James Christopher Blackmore.Ph.D