Semistability, Finite-Time Stability, Differential Inclusions, and Discontinuous Dynamical Systems Having a Continuum of Equilibria

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we extend the theory of semistability to discontinuous autonomous dynamical systems. In particular, Lyapunov-based tests for semistability and finite-time semistability for autonomous differential inclusions are established.     

Finite-Time Distributed Identification for Nonlinear Interconnected Systems

In this paper, a novel finite-time distributed identification method is introduced for nonlinear interconnected systems. A distributed concurrent learning-based discontinuous gradient descent update law is presented to learn uncertain interconnected subsystems’ dynamics. The concurrent learning approach continually minimizes the identification error for a batch of previously recorded data collected from each subsystem as well as its neighboring subsystems. The state information of neighboring in...     

On Finite-Time Stability for Fractional-Order Neural Networks with Proportional Delays

Neural Processing Letters - This paper is concerned with fractional-order neural networks with proportional delays. Applying inequality technique, some sufficient criteria which ensure the...     

Biomorphic Dynamical Networks for Cognition and Control

Advances in understanding the neuronal code employed by cortical networks indicate that networks of parametrically coupled nonlinear iterative maps, each acting as a bifurcation processing element, furnish a potentially powerful tool for the modeling, simulation, and study of cortical networks and the host of higher-level processing and control functions they perform. Such functions are central to understanding and elucidating general principles on which the design of biomorphic learning and intelligent systems can be based. The networks concerned are dynamical in nature, in the sense that they compute not only with static (fixed-point) attractors but also with dynamic (periodic and chaotic) attractors. As such, they compute with diverse attractors, and utilize transitions (bifurcation) between attractors and transient chaos to carry out the functions they perform. An example of a dynamical network, a parametrically coupled net of logistic processing elements, is described and discussed together some of its behavioural attributes that are relevant to elucidating the possible role for coherence, bifurcation, and chaos in higher-level brain functions carried out by cortical networks.     

Adaptive Synchronization-Based Approach for Finite-Time Parameters Identification of Genetic Regulatory Networks

Neural Processing Letters - This paper presents an approach to identify the unknown parameters of genetic regulatory network (GRN) in finite-time. The adaptive synchronization-based method is used...     

Finite-Time Stabilization for Static Neural Networks with Leakage Delay and Time-Varying Delay

Neural Processing Letters - The problem of finite-time stabilization (FTS) for static neural networks (SNNs) with leakage delay and time-varying delay is investigated in this paper. By introducing...     

New Results on Robust Finite-Time Passivity for Fractional-Order Neural Networks with Uncertainties

Neural Processing Letters - In this paper, the robust finite-time passivity for a class of fractional-order neural networks with uncertainties is considered. Firstly, the definition of finite-time...     

Identification of Nonlinear Dynamical System Based on Raised-Cosine Radial Basis Function Neural Networks

Neural Processing Letters - In this paper, we present and investigate a new type of radial basis function (RBF) neural networks mechanism using raised-cosine (RC) function to identify nonlinear...     

Finite-Time Stabilization of Memristive Neural Networks with Time Delays

Neural Processing Letters - This paper investigates the finite-time stabilization (FTS) problem of memristive neural networks (MNNs) with time-varying delays. First, a novel memristive connection...     

Linear and Nonlinear Dynamical Chaos

Interrelations between dynamical and statistical laws in physics on the one hand, and between the classical and quantum mechanics on the other hand, are discussed with the emphasis on the new phenomenon of dynamical chaos.The principal results of the studies into chaos in classical mechanics are presented in some detail within the general picture of chaos as a specific case of dynamical behavior. These results include the strong local instability and robustness of motion, continuity of both the phase space as well as the motion spectrum, and time reversibility but nonrecurrency of statistical evolution.The analysis of apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of the quantum chaos as a new generic dynamical phenomenon is outlined together with a few other examples of such a chaos, including linear (classical) waves and a digital computer.I conclude with the discussion of two fundamental physical problems: the quantum measurement (-collapse) and the causality principle, which both appear to be related to the phenomenon of dynamical chaos.     

Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties

In this note, non-smooth finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated. To solve this problem, the input-to-state stability property is used to characterize unmeasured dynamic uncertainties. A constructive partial-state control design is proposed on the basis of involved combined use of Lyapunov, backstepping and input-to-state stability techniques. Under small-gain type local conditions, a solution for the finite-time regulation of a class of uncertain nonlinear systems is obtained     

Finite-Time Synchronization of Memristive Neural Networks with Proportional Delay

The problem of finite-time synchronization for memristive neural networks (MNNs) with proportional delay is considered. Since proportional delay is unbounded and different from infinite-time distributed delay, the classical finite-time analytical techniques are not applicable anymore. First, a discontinuous state feedback controller is designed such that the delayed MNNs achieve drive-response synchronization in a finite settling time. By using Filippov solution and Lyapunov functional method, sufficient conditions are derived. It is shown that, though the proportional delay is unbounded, complete synchronization can still be realized and the settling time can be explicitly estimated. Second, a special adaptive controller is designed for the finite-time problem in order to reduce the control gains. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.     

Finite-Time Parameter Estimation in Adaptive Control of Nonlinear Systems

This note presents a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied. The robustness of the routine to an unknown bounded disturbance or modeling error is also shown. The result is independent of the control and identifier structures employed. The true parameter value is obtained without requiring the measurement or computation of the velocity state vector. Moreover, the technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved.     

Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers

There exist semi-global and finite-time converging observers for nonlinear systems that are uniformly observable and globally Lipschitzian. This was achieved with local finite-time stability theory, together with application of the technique of high-gain observers (the gain is constant). Under the same conditions, it is shown that these systems admit global finite-time observers. The proposed finite-time observers are based on a modified version of high-gain observer (now the gain is an exponential function with arbitrary growth rate). Design procedures are worked out for such observers, and a numerical example is presented to show the effectiveness of the proposed method.      

Finite-Time Stability of Neural Networks with Impulse Effects and Time-Varying Delay

This paper introduces the design of the hyperconic multilayer perceptron (HC-MLP). Complex non-linear decision regions for classification purposes are generated by quadratic hyper-surfaces spawned by the hyperconic neurons in the hidden layer (for instance, spheres, ellipsoids, paraboloids, hyperboloids and degenerate conics). In order to generate quadratic hyper-surfaces, the hyperconic neurons’ transfer function includes the estimation of a quadratic polynomial. The proper assignment of decision regions to classes is achieved in the output layer by using spheres to determine whether a point is inside or outside the spherical region. The particle swarm optimization algorithm is used for training the HC-MLP. The learning of the HC-MLP selects the best conic surface that separates the data set vectors. For illustration purposes, two experiments are conducted using two distributions of synthetic data in order to show the advantages of HC-MLP when the patterns between classes are contiguous. Furthermore a comparison to the traditional multilayer perceptron is carried out to evaluate the complexity (in terms of the number of estimated patterns) and classification accuracy. HC-MLP is the principal component to implement a diagnosis system to detect faults in an induction motor and to implement an image segmentation system. The performance of HC-MLP is compared to other leading algorithms by using 4 databases commonly used in related literature.     

一类不确定非线性系统的停息时间可调的有限时间镇定

研究了一类带有零动态不确定非线性系统有限时间镇定问题, 给出了具有更强实用性的停息时间可调的有限时间稳定控制设计方法. 基于有限时间稳定的Lyapunov理论和反推技术, 给出了停息时间可调有限时间稳定控制器的设计步骤. 所设计的状态反馈控制器使得闭环系统全局有限时间稳定, 且停息时间可调整, 特别是当系统初始值已知时, 停息时间可以任意调节. 仿真例子验证了本文的主要结论.     

Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay

Neural Processing Letters - Based on the framework of Filippov solutions, this paper considers synchronization of inertial neural networks (INNs) with discontinuous activation functions and...