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

Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

This paper addresses the challenge of synchronizing the dynamics of two distinct 3D chaotic systems, specifically the Rabinovich and Rabinovich-Fabrikant systems, employing a finite-time synchronization approach. These chaotic systems exhibit diverse characteristics and evolving chaotic attractors, influenced by specific parameters and initial conditions. Our proposed low-cost finite-time synchronization method leverages the signum function's tracking properties to facilitate controlled coupling within a finite time frame. The design of finite-time control laws is rooted in Lyapunov stability criteria and lemmas. Numerical experiments conducted within the MATLAB simulation environment demonstrate the successful asymptotic synchronization of the master and slave systems within finite time. To assess the global robustness of our control scheme, we applied it across various system parameters and initial conditions. Remarkably, our results reveal consistent synchronization times and dynamics across these different scenarios. In summary, this study presents a finite-time synchronization solution for non-identical 3D chaotic systems, showcasing the potential for robust and reliable synchronization under varying conditions

A new fractional-order chaotic system with its analysis, synchronization, and circuit realization for secure communication applications

YesThis article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the sug-gested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications

Network analysis of complex biological systems : boundedness of weakly reversible chemical reaction networks and conditions for synchronisation of coupled oscillators

Imperial Users onl

Advanced methods for analysing and modelling multivariate palaeoclimatic time series

The separation of natural and anthropogenically caused climatic changes is an important task of contemporary climate research. For this purpose, a detailed knowledge of the natural variability of the climate during warm stages is a necessary prerequisite. Beside model simulations and historical documents, this knowledge is mostly derived from analyses of so-called climatic proxy data like tree rings or sediment as well as ice cores. In order to be able to appropriately interpret such sources of palaeoclimatic information, suitable approaches of statistical modelling as well as methods of time series analysis are necessary, which are applicable to short, noisy, and non-stationary uni- and multivariate data sets. Correlations between different climatic proxy data within one or more climatological archives contain significant information about the climatic change on longer time scales. Based on an appropriate statistical decomposition of such multivariate time series, one may estimate dimensions in terms of the number of significant, linear independent components of the considered data set. In the presented work, a corresponding approach is introduced, critically discussed, and extended with respect to the analysis of palaeoclimatic time series. Temporal variations of the resulting measures allow to derive information about climatic changes ...thesi

Stochastic neural network dynamics: synchronisation and control

Biological brains exhibit many interesting and complex behaviours. Understanding of the mechanisms behind brain behaviours is critical for continuing advancement in fields of research such as artificial intelligence and medicine. In particular, synchronisation of neuronal firing is associated with both improvements to and degeneration of the brain’s performance; increased synchronisation can lead to enhanced information-processing or neurological disorders such as epilepsy and Parkinson’s disease. As a result, it is desirable to research under which conditions synchronisation arises in neural networks and the possibility of controlling its prevalence. Stochastic ensembles of FitzHugh-Nagumo elements are used to model neural networks for numerical simulations and bifurcation analysis. The FitzHugh-Nagumo model is employed because of its realistic representation of the flow of sodium and potassium ions in addition to its advantageous property of allowing phase plane dynamics to be observed. Network characteristics such as connectivity, configuration and size are explored to determine their influences on global synchronisation generation in their respective systems. Oscillations in the mean-field are used to detect the presence of synchronisation over a range of coupling strength values. To ensure simulation efficiency, coupling strengths between neurons that are identical and fixed with time are investigated initially. Such networks where the interaction strengths are fixed are referred to as homogeneously coupled. The capacity of controlling and altering behaviours produced by homogeneously coupled networks is assessed through the application of weak and strong delayed feedback independently with various time delays. To imitate learning, the coupling strengths later deviate from one another and evolve with time in networks that are referred to as heterogeneously coupled. The intensity of coupling strength fluctuations and the rate at which coupling strengths converge to a desired mean value are studied to determine their impact upon synchronisation performance. The stochastic delay differential equations governing the numerically simulated networks are then converted into a finite set of deterministic cumulant equations by virtue of the Gaussian approximation method. Cumulant equations for maximal and sub-maximal connectivity are used to generate two-parameter bifurcation diagrams on the noise intensity and coupling strength plane, which provides qualitative agreement with numerical simulations. Analysis of artificial brain networks, in respect to biological brain networks, are discussed in light of recent research in sleep theor

Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems

This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first. Then, based on the relationship between Caputo fractional derivative and Riemann-Liouville fractional derivative, fractional order Barbalat’s lemma with Riemann-Liouville derivative is derived. Furthermore, according to these results, a set of new formulations of Lyapunov-like lemmas for fractional order nonlinear systems are established. Finally, an example is presented to verify the theoretical results in this paper

New results on finite-/fixed-time synchronization of delayed memristive neural networks with diffusion effects

In this paper, we further investigate the finite-/fixed-time synchronization (FFTS) problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs). By utilizing the state-feedback control techniques, and constructing a general Lyapunov functional, with the help of inequality techniques and the finite-time stability theory, novel criteria are established to realize the FFTS of the considered delayed MRDNNs, which generalize and complement previously known results. Finally, a numerical example is provided to support the obtained theoretical results

An investigation of techniques for nonlinear state observation

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2016An investigation and analysis of a collection of different techniques, for estimating the states of nonlinear systems, was undertaken. It was found that most of the existing literature on the topic could be organized into several groups of nonlinear observer design techniques, of which each group follows a specific concept and slight variations thereof. From out of this investigation it was discovered that a variation of the adaptive observer could be successfully applied to numerous nonlinear systems, given only limited output information. This particular technique formed the foundation on which a design procedure was developed in order to asymptotically estimate the states of nonlinear systems of a certain form, using only partial state information available. Lyapunov stability theory was used to prove the validity of this technique, given that certain conditions and assumptions are satisfied. A heuristic procedure was then developed to get a linearized model of the error transient behaviour that could form the upper bounds of the transient times of the observer. The technique above, characterized by a design algorithm, was then applied to three well-known nonlinear systems; namely the Lorenz attractor, the Rössler attractor, and the Van Der Pol oscillator. The results, illustrated through numerical simulation, clearly indicate that the technique developed is successful, provided all assumptions and conditions are satisfied.MT201