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

Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result

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

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

Fault tolerant control for fixed set-point control nonlinear networked control systems

U radu se predlaže pristup za dobivanje algoritma regulatora koji tolerira grešku za vrstu umreženog upravljačkog sustava koji ima regulator s čvrstom zadanom točkom i nelinearno postrojenje. Najprije opisujemo nelinearni umreženi upravljački sustav te lineariziramo model postrojenja u radnoj točki, zatim konstruiramo spojeni model cijelog sustava koji uključuje sve faktore relevantne za naše istraživanje kao što su kašnjenje inducirano mrežom, gubitak podataka, greške senzora i aktuatora itd. Na temelju ovog modela postignuto je stanje stabilnosti u sustavu konstruiranjem Lyapunove funkcije. Zatim je iz stanja stabilnosti dobiven upravljački algoritam tolerancije greške. Konačno je na numeričkom primjeru dokazana validnost teorije.This paper proposes an approach for achieving fault tolerant control algorithm for a kind of networked control system which is fixed set-point control and with nonlinear plant. We firstly describe the nonlinear networked control system and linearize the model of the plant at the operating point, then construct a synthesis model of the whole system, which includes all relevant factors in our research such as network induced time delay, data packet loss, the faults of sensors and actuators etc. Based on this model, the stability condition in meaning square sense of the system is gained by constructing a Lyapunov function. Then the fault tolerant control algorithm is obtained from the stability condition. Lastly, a numerical example is used to prove the validity of the theory

State Estimation for Time-Delay Systems with Markov Jump Parameters and Missing Measurements

This paper is concerned with the state estimation problem for a class of time-delay systems with Markovian jump parameters and missing measurements, considering the fact that data missing may occur in the process of transmission and its failure rates are governed by random variables satisfying certain probabilistic distribution. By employing a new Lyapunov function and using the convexity property of the matrix inequality, a sufficient condition for the existence of the desired state estimator for Markovian jump systems with missing measurements can be achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Furthermore, the gain of state estimator can also be derived based on the known conditions. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed method

Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization

Copyright @ 2014 Elsevier Ltd. All rights reserved.This paper deals with the finite-horizon reliable H∞ output feedback control problem for a class of discrete time-varying systems with randomly occurring uncertainties (ROUs), randomly occurring nonlinearities (RONs) as well as measurement quantizations. Both the deterministic actuator failures and probabilistic sensor failures are considered in order to reflect the reality. The actuator failure is quantified by a deterministic variable varying in a given interval and the sensor failure is governed by an individual random variable taking value on [0,1]. Both the nonlinearities and the uncertainties enter into the system in random ways according to Bernoulli distributed white sequences with known conditional probabilities. The main purpose of the problem addressed is to design a time-varying output feedback controller over a given finite horizon such that, in the simultaneous presence of ROUs, RONs, actuator and sensor failures as well as measurement quantizations, the closed-loop system achieves a prescribed performance level in terms of the H∞-norm. Sufficient conditions are first established for the robust H∞ performance through intensive stochastic analysis, and then a recursive linear matrix inequality approach is employed to design the desired output feedback controller achieving the prescribed H∞ disturbance rejection level. A numerical example is given to demonstrate the effectiveness of the proposed design scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61134009, 61273156, 61333012, 61422301 and 61374127, the Scientific and Technology Research Foundation of Heilongjiang Education Department of China under Grant 12541061, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K., the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany