Publications

DETERMINISTIC LEARNING OF NONLINEAR DYNAMICAL SYSTEMS

In this paper, we investigate the problem of identifying or modeling nonlinear dynamical systems undergoing periodic and period-like (recurrent) motions. For accurate identification of nonlinear dynamical systems, the persistent excitation condition is normally required to be satisfied. Firstly, by using localized radial basis function networks, a relationship between the recurrent trajectories and the persistence of excitation condition is established. Secondly, for a broad class of recurrent trajectories generated from nonlinear dynamical systems, a deterministic learning approach is presented which achieves locally-accurate identification of the underlying system dynamics in a local region along the recurrent trajectory. This study reveals that even for a random-like chaotic trajectory, which is extremely sensitive to initial conditions and is long-term unpredictable, the system dynamics of a nonlinear chaotic system can still be locally-accurate identified along the chaotic trajectory in a deterministic way. Numerical experiments on the Rossler system are included to demonstrate the effectiveness of the proposed approach.

Chaotification of polynomial continuous-time systems and rational normal forms

In this paper we study the chaotification problem of polynomial continuous-time systems in a semiglobal setting. Our results are based on the computation of rational normal forms and time-delay anticontroller design. As examples, the Rössler system, some Sprott systems and the Lorenz system are considered.

Design and Analysis of Replica Piecewise M-Ary DCSK Scheme for Power Line Communications With Asynchronous Impulsive Noise

Previous studies have shown that impulsive noise can weaken the performance of power line communication (PLC). Though DCSK can improve the performance in an order of magnitude comparing to the direct sequence differential phase shift keying (DS-DPSK), it is still a challenge to further improve the BER performance with signal redesign without the need of advanced and expensive extra noise suppression technologies. The paper introduces the model of asynchronous impulsive noise of Middleton class-A noise and corresponding multipath fading channels in PLC, and analyzes the bit error rate (BER) performance of the M-ary differential chaos shift keying (MDCSK) scheme over different channels. Furthermore, a new replica piecewise frame of MDCSK (RP-MDCSK) is proposed to resist the impulse noise. In the proposed scheme, one piecewise of signals is transmitted first. Then, it replicates pw times, which serves as the reference signal transmitted in the first half symbol period. The information-bearing signal combines the reference signal with its Hilbert transform in the second half. At the receiver, one piece of reference signals is extracted and then correlated with its corresponding information-bearing part. The BER expressions of the MDCSK and the proposed scheme are derived and analyzed over different channels, and verified by simulations. Comparing with the corresponding schemes, it is found that the BER of the proposed scheme is by 2-3 orders of magnitude lower.

Design and FPGA-Based Realization of a Chaotic Secure Video Communication System

This paper initiates a systematic methodology for real-time chaos-based video encryption and decryption communications on the system design and algorithm analysis. The proposed system design and algorithm analysis have been validated on an FPGA hardware platform via Verilog Hardware Description Language (Verilog HDL). Based on the fundamental anti-control principles of dynamical systems, a 6-D real domain chaotic system is designed, and then the corresponding Verilog HDL algorithm is developed. The proposed Verilog HDL algorithm is utilized to design a real-time chaos-based secure video communication system, with a generalized design principle derived, which is implemented on an FPGA hardware platform equipped with an XUP Virtex-II chip. Following this line, the designed working mechanism is demonstrated by hardware experiments. The security performance is tested using the TESTU01 statistical test suites, the differential analysis, and the sensitivity of key parameters mismatch. Both theoretical analysis and experimental results validate the feasibility and reliability of the proposed system.

Network science research: some recent progress in China and beyond

No abstract is provided for this article.

Observer-based optimal/sub-optimal digital trackers for analog neutral systems with multiple discrete and distributed time delays

In this paper, observer-based finite/infinite time optimal hybrid tracking problems for analog neutral systems with multiple discrete and distributed time delays are formatted and studied. Two continuous-time optimal performance indices with a highgain property are used for tracking control specification. The Newton center interpolation formula and the linear interpolation formula, together with a newly modified rectangular ruler and an extended state vector, are utilized to construct the associate problems of extended discrete-time finite/infinite stage optimal regulators. Consequently, using the discrete-time optimal control theory and the new alternative digital redesign technique with a predictive feature, three effective digital trackers are designed for a given analog neutral system. When the states of the system are not available, a new optimal digital observer for the original analog neutral system is developed for achieving the desired goals of tracker design.

Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation

This paper investigates the distributed finite-time consensus tracking problem for a group of autonomous agents modeled by multiple non-identical second-order nonlinear systems. First, a class of distributed finite-time protocols are proposed based on the relative position and relative velocity measurements. By providing a topology-dependent Lyapunov function, it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded. Then, a new class of observer-based algorithms are designed to solve the finite-time consensus tracking problem without using relative velocity measurements. The main contribution of this paper is that, by computing the value of the Lyapunov function at the initial point, the finite settling time can be theoretically estimated for second-order multi-agent systems with the proposed control protocols. Finally, the effectiveness of the analytical results is illustrated by an application in low-Earth-orbit spacecraft formation flying.

Pinning Control of Complex Dynamical Networks

This article introduces the notion of pinning control for complex dynamical networks regarding their stabilization, synchronization and control. Specifically, it will first review the concept of network pinning control and then address the fundamental issues of network stabilizability, synchronizability and controllability. Basic ideas will be explained, technical derivations will be outlined, and important theoretical problems will be briefly discussed. It will show that the self-contained theoretical framework of pinning control technology is promising for practical applications in network science and engineering.

Evolutionary Algorithms and Chaotic Systems

No abstract is provided for this article.

A New Method for Topology Identification of Complex Dynamical Networks

Topology identification of complex dynamical networks received extensive attention in the past decade. Most existing studies rely heavily on the linear independence condition (LIC). We find that a critical step in using this condition is not rigorous. Besides, it is difficult to verify this condition. Without regulating the original network, possible identification failure caused by network synchronization cannot be avoided. In this paper, we propose a new method to overcome these shortcomings. We add a regulation mechanism to the original network and construct an auxiliary network consisting of isolated nodes. Along with the outer synchronization between the regulated network and the auxiliary network, we show that the original network can be identified. Our method can avoid identification failure caused by network synchronization. Moreover, we show that there is no need to check the LIC. We finally provide some examples to demonstrate that our method is reliable and has good performances.

Cryptanalysis of a secure communication scheme combining chaos and noise

一般不等速度と位置結合を有するコンセンサスまたは二重積分器の群れエージェントの指定された収束率問題【Powered by NICT】

No abstract is provided for this article.

Non-revisiting stochastic search revisited: Results, perspectives, and future directions

The non-revisiting genetic algorithm (NrGA) uses the entire search history with parameter-less adaptive mutation to significantly enhance search performance. In the past decade, a family of non-revisiting stochastic search (NrSS) methods has been developed. Using the entire (or partial) search history to assist evolutionary computation can achieve not only the goal of duplicated solution prevention, but also other utilizations such as adaptive parameter-less local search and fitness landscape estimation. In this survey, the focus is on the memory-assisted stochastic search techniques that store the search history in a binary space partitioning (BSP) tree. First, the basic NrGA is reviewed. Then, the development of the family of NrSS is reviewed from three aspects: 1) the basic NrSS algorithms, 2) conceptual extension of non-revisit and usage of the search history as novel operators and estimators, and 3) application of NrSS to different problem types, such as multi-objective problems, dynamic problems, and multi-modal problems. A comprehensive classification of search history-assisted algorithms suggests that the cumulative historical search information can be developed in a more functional manner; for example, a BSP tree can be simultaneously used for revisit prevention, fitness landscape estimation, and adaptive operation. Both the application on real-world problems and the theoretical analysis of NrSS are reviewed. Possible future work suggestions include a deeper understanding of the non-revisiting scheme in theory, a more comprehensive functional usage of search history, and a closer cooperation with data-driven techniques.

A model for quantum game on networks

Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.

Stability and bifurcation of disease spreading in complex networks

A general nonlinear model of disease spreading is proposed, describing the effect of the new link-adding probability p in the topological transition of the N-W small-world network model. The new nonlinear model covers both limiting cases of regular lattices and random networks, and presents a more flexible internal nonlinear interaction than a previous model. Hopf bifurcation is proved to exist during disease spreading in all typical cases of regular lattices, small-world networks, and random networks described by this model. It is shown that probability p not only determines the topological transition of the N-W small-world network model, but also dominates the stability of the local equilibria and bifurcating periodic solutions, and moreover can be further applied to stabilize a periodic spreading behaviour onto a stable equilibrium over the network.

Stability analysis of nonlinear fuzzy PI control systems

In this paper, we analyze the stability of nonlinear fuzzy PI (proportional-integral) control systems. The fuzzy PI controller involved is actually a nonlinear adaptive PI controller whose gains change continuously with output of the processes under control. We have employed the "small gain theorem" to obtain a simple sufficient condition for the global asymptotic stability of the nonlinear fuzzy PI control systems. In addition, we have proven that in a conventional PI control system, if the linear PI controller is replaced by the nonlinear fuzzy PI controller, then the stability of the resulting control system remains unchanged. This result is true no matter the given process is linear or not. We have also derived explicit formulas for the computation of the fuzzy PI controller parameters, using only the proportional and integral gains of the corresponding linear PI controller.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Special Attractors and Dynamic Transport of the Hybrid-Order Complex Lorenz System

Combining the advantages of both integer-order and fractional-order complex chaotic systems, we propose a hybrid-order complex Lorenz system. We demonstrate its abundant chaotic characteristics, including symmetry and dissipation, fixed points and their stability and Lyapunov exponents, with 0-1 test. Then we show that, as the initial value, parameters and the order are varying, the system exhibits diverse dynamical behaviors, with fixed points, limit cycles and chaotic attractors. We further show that the system has coexisting attractors and parametric attractors. In addition, we find that the system generates different chaotic attractors as the system hybrid order varies, referred to as order attractors. Finally, we examine the dynamic transport of the hybrid-order complex Lorenz system and design a piecewise continuous controller to realize offset boosting control. By varying the initial value, parameters or orders, we realize the dynamic transport of the system. Our simulation results confirm the dynamic transport of the hybrid-order complex Lorenz system.