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

Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems

The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the process by using an optimal quantization technique. The main advantage of this approach is that it makes pre-computations possible. We derive a Lipschitz property for the solution of the Riccati equation and a general result on the convergence of perturbed solutions of semi-Markov switching Riccati equations when the perturbation comes from the driving semi-Markov chain. Based on these results, we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step. We employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the Kalman-Bucy filter and the Markovian linear minimum mean squares estimator

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 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

On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method

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

Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)