Framework Of Differential Inclusions Research Articles

A Recurrent Neural Network Approach for Constrained Distributed Fuzzy Convex Optimization.

This article investigates a class of constrained distributed fuzzy convex optimization problems, where the objective function is the sum of a set of local fuzzy convex objective functions, and the constraints include partial order relation and closed convex set constraints. In undirected connected node communication network, each node only knows its own objective function and constraints, and the local objective function and partial order relation functions may be nonsmooth. To solve this problem, a recurrent neural network approach based on differential inclusion framework is proposed. The network model is constructed with the help of the idea of penalty function, and the estimation of penalty parameters in advance is eliminated. Through theoretical analysis, it is proven that the state solution of the network enters the feasible region in finite time and does not escape again, and finally reaches consensus at an optimal solution of the distributed fuzzy optimization problem. Furthermore, the stability and global convergence of the network do not depend on the selection of the initial state. A numerical example and an intelligent ship output power optimization problem are given to illustrate the feasibility and effectiveness of the proposed approach.

Observer‐based bipartite Mittag‐Leffler time‐varying formation for fractional multi‐agent systems with discontinuous inherent dynamics

SummaryIn this article, the bipartite Mittag‐Leffler time‐varying formation issue of fractional multi‐agent systems is discussed, where the dynamical nodes of followers are modeled to be discontinuous and nondecreasing. A observer‐based adaptive distributed control scheme, which is dependent on output information, is designed to realized the bipartite formation control goal. Meanwhile, the efficient algorithm with respect to the control protocol also is presented. Under fractional Filippov differential inclusion framework, by constructing Lur'e Postnikov‐type Lyapunov functional and applying Clarke's non‐smooth analysis technique, the bipartite Mittag‐Leffler time‐varying formation conditions are derived in terms of linear matrix inequalities. At last, a simulation example is carried out to verify the effectiveness of the proposed scheme.

Fixed-time projective synchronization of delayed memristive neural networks via aperiodically semi-intermittent switching control

This paper studies the fixed-time projective synchronization problem for a class of delayed memristive neural networks via aperiodically semi-intermittent switching control. Instead of using the common traditional controller containing two power exponent terms, a novel aperiodically semi-intermittent switching controller is designed, containing only one power exponent term which serves as a function of the state of the error system. With the aid of the extended differential inclusion framework, the analysis method, and the inequality technique, some new sufficient conditions are derived to guarantee fixed-time projective synchronization for the considered systems. Compared with periodically semi-intermittent control methods, the control time width of each section in aperiodically semi-intermittent control can be adjusted. Especially, the settling time is directly reckoned, which is closely related to the number of neurons and the maximum ratio of the second subinterval span in each non-periodic span to all non-periodic time spans rather than the initial value. Additionally, the projection synchronization has a strong practicality, as the projection coefficient can be adjusted for different needs instead of being fixed. Meanwhile, the study improves some previous related works. Ultimately, a numerical example is given to substantiate the correctness of the obtained results.

Global Mittag-Leffler consensus for fractional singularly perturbed multi-agent systems with discontinuous inherent dynamics via event-triggered control strategy

In this paper, the global Mittag-Leffler consensus tracking issue is considered for fractional singularly perturbed multi-agent systems (FSPMASs) based on event-triggered control strategy, where the inherent dynamic is modeled to be a discontinuous function with nondecreasing property. Firstly, a differential inequality with respect to fractional-order derivative of convex function is developed. As the special cases, the inequalities about fractional-order derivative of three known functions are also addressed. Secondly, a distributed event-triggered control scheme is designed to guarantee that the considered FSPMASs can achieve the global Mittag-Leffler consensus. Moreover, the Mittag-Leffer convergence speed of tracking the leader for followers can be adjusted to any desired values in advance. In addition, under fractional Filippov differential inclusion framework, by applying Lur’e Postnikov-type Lyapunov functional with variable upper limit integral item and Clarke’s non-smooth analysis technique, the global Mittag-Leffler consensus conditions are addressed in terms of matrix inequalities (MIs). Finally, two numerical simulations are provided to illustrate the validity of the proposed design method and theoretical results.

Group Consensus in Finite Time for Fractional Multiagent Systems With Discontinuous Inherent Dynamics Subject to Hölder Growth.

This article is concerned with the global Mittag-Leffler group consensus and group consensus in finite time for fractional multiagent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to the local Hölder nonlinear growth in a neighborhood of continuous points. First, a fractional differential inequality on convex functions and a global convergence principle in finite time for absolutely continuous functions are developed, respectively. Second, two new distributed control protocols are designed to realize the consensus between the follower agents in each subgroup and respective leaders. In addition, under the fractional Filippov differential inclusion framework, by applying the Lur'e Postnikov-type convex Lyapunov functional approach and Clarke's nonsmooth analysis technique, some sufficient conditions with respect to the global Mittag-Leffler group consensus and group consensus in finite time are addressed in terms of linear matrix inequalities (LMIs), respectively. Moreover, the settling time for the group consensus in finite time is estimated accurately. Finally, two simulation examples are provided to illustrate the validity of the proposed scheme and theoretical results.

Event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity

This paper is concerned with on the event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity. Firstly, the principle of the global convergence in fixed time with respect to nonlinear systems with semi-Markov switching is developed. Secondly, in order to realize the global stochastic synchronization goal in fixed time, a novel hybrid controller, which is composed of the event-triggered controller and the switching state-feedback controller, is designed. Under Filippov differential inclusion framework, by applying Lyapunov functional method and inequality analysis technique, the global stochastic synchronization conditions in fixed time are achieved in the form of linear matrix inequalities (LMIs). In addition, the upper bound of the stochastic settling time, which is adjusted in advance by choosing the controller parameters, is estimated accurately. Finally, the correctness of the theoretical results and the feasibility of the designed controller are verified by an example.

Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results.

Event-triggered stochastic synchronization in finite time for delayed semi-Markovian jump neural networks with discontinuous activations

In this paper, the global stochastic synchronization in finite time is discussed for discontinuous semi-Markovian switching neural networks with mixed time-varying delays under stochastic disturbance based on event-triggered non-fragile control scheme. By applying the novel hybrid controller, which is composed of the event-triggered controller, the non-fragile controller and the switching state-feedback controller, the global stochastic synchronization goals in finite time are achieved. Under Filippov differential inclusion framework, based on non-smooth analysis theory, general free-weighting matrix method, Lyapunov–Krasovskii functional approach and inequality analysis technique, the global stochastic synchronization conditions in finite time are addressed in terms of linear matrix inequalities. Moreover, the expressions about the upper bound of stochastic settling time are explicitly developed. Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth

This paper considers the global leader-following consensus of fractional-order multi-agent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to nonlinear growth. Firstly, based on convex functions, three formulas on fractional derivative are established respectively. By applying the proposed formulas, a principle of convergence in finite-time for absolutely continuous functions is developed. Secondly, a new nonlinear control protocol, which includes discontinuous factors, is designed. Under fractional differential inclusion framework, by means of Lyapunov functional approach and Clarke’s non-smooth analysis technique, the sufficient conditions with respect to the global consensus are achieved. In addition, the setting time is explicitly evaluated for the global leader-following consensus in finite time. Finally, two illustrative examples are provided to check the correction of the obtained results in this paper.

Fixed-Time Synchronization of Fuzzy Cellular Neural Networks With Time-Varying Delays and Discontinuous Activations

The present paper investigates the fixed-time synchronization for fuzzy cellular neural networks with time-varying delays and discontinuous activations. In the framework of differential inclusions, new and useful fixed-time synchronization criteria for the networks considered are established by utilizing the discontinuous state feedback control and constructing Lyapunov functionals, which significantly generalize and improve recent works in the literature. Numerical simulations are given to show the effectiveness of the fixed-time synchronization schemes.

Interval matrix method based synchronization criteria for fractional-order memristive neural networks with multiple time-varying delays

This paper addresses the issue of globally asymptotical synchronization of fractional-order memristive neural networks (FMNNs) with multiple time-varying delays. First, a more practical model for FMNNs with multiple time-varying delays is proposed because of considering the characteristics of a real memristor. Under the framework of differential inclusions, the FMNN is transformed into a fractional-order neural network (FNN) with interval uncertainties. Thus, the synchronization of two FMNNs is converted into the synchronization of two FNNs with interval parameters. The main problems to overcome are: (1) establishing an effective differential inequality for fractional-order systems with multiple time-varying delays; (2) finding a better upper bound for the norm of interval matrices. In this paper, a new upper bound for the norm of interval matrices is derived and meanwhile the fractional Halanay inequality is generalized to the case of multiple time-varying delays. Then, synchronization control strategies are elaborately designed to achieve globally asymptotical synchronization. By exploiting the newly-built fractional Halanay inequality and constructing appropriate Lyapunov functions, some new sufficient conditions for globally asymptotical synchronization of FMNNs with time-varying delays are derived. The synchronization criteria, expressed by LMIs, are easy to check and extend some previously published results. An illustrative numerical example is given to demonstrate the effectiveness of the theoretical results.

Non-fragile robust finite-time synchronization for fractional-order discontinuous complex networks with multi-weights and uncertain couplings under asynchronous switching

This paper focus on the global robust non-fragile finite-time synchronization issue for fractional-order complex networks with multi-weights and uncertain couplings under asynchronous switching topology, where nonlinear dynamic nodes are discontinuous and non-decreasing. Firstly, the non-fragile controller with switching gains is designed. Secondly, under the fractional Filippov differential inclusion framework and the network topologies with no-delayed and delayed couplings, by adopting multiple Lur’e Postnikov-type Lyapunov functional, nonsmooth analysis method and the average dwell time technique, the global robust non-fragile finite-time synchronization conditions are achieved in terms of linear matrix inequalities (LMIs), respectively. Finally, the validity of the theoretical results developed in this paper is verified by two numerical simulations.

Adaptive synchronization of memristor-based neural networks with discontinuous activations

This paper investigates the adaptive synchronization of memristor-based neural networks (MNNs) with discontinuous activations. First, by using a decoupling strategy, the extensively used models of MNNs are improved, which can describe the real dynamics more accurately. Moreover, we extend the asymptotic synchronization criteria for MNNs with the consideration of discontinuous activation functions. Additionally, a general adaptive controller is devised to synchronize the drive and response systems, and the sufficient stability conditions are established via Lyapunov functional method within the framework of differential inclusions. Finally, numerical simulations are conducted to show the effectiveness of the developed methods.

Global Exponential Synchronization of Delayed Complex-Valued Recurrent Neural Networks with Discontinuous Activations

In this paper, we are concerned with the exponential synchronization for a class of two delayed complex-valued recurrent neural networks (CVRNNs) with discontinuous neuron activations. By separating CVRNNs into real and imaginary parts, forming an equivalent real-valued subsystems, under the framework of differential inclusions, novel state feedback controllers are designed and novel criteria are established to ensure the exponential stability of error system, and thus the drive system exponentially synchronize with the response system. The obtained results are essentially new and complement previously known ones. The practicability of theoretical results is also supported via a numerical example.

Global Nonfragile Synchronization in Finite Time for Fractional-Order Discontinuous Neural Networks With Nonlinear Growth Activations.

This paper is concerned with the global nonfragile Mittag-Leffler synchronization and the global synchronization in finite time for fractional-order discontinuous neural networks, where activation functions are discontinuous at 0, or modeled as a local Hölder functions with the nonlinear growth property in a neighborhood of 0. First, two lemmas concerned with the convergence with respect to an absolutely continuous function are developed. Second, a new property, which introduces an inequality of the fractional derivative for the variable upper limit integral with respect to the nonsmooth integrable function, is presented and applied in the synchronization results' analysis. In addition, under the fractional Filippov differential inclusion framework, by utilizing the Lur'e Postnikov-type Lyapunov functional, nonsmooth analysis method, and the convergence properties developed in this paper, the synchronization conditions are derived in the form of linear matrix inequalities. Moreover, the upper bound of the setting time for the global nonfragile synchronization in finite time is calculated accurately. Finally, two illustrations are presented to verify the correctness of the theoretical results.

Non-fragile robust finite-time stabilization and $$H_{\infty }$$H∞ performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching

In this paper, the global non-fragile robust finite-time stabilization and $$H_{\infty }$$ performance analysis are investigated for uncertain switched fractional-order neural networks with discontinuous activations, time delay and external disturbance under the asynchronous switching. Firstly, a new inequality, which is concerned with the fractional derivative of the variable upper limit integral for the nonsmooth integrable functional, is developed. Secondly, the non-fragile switched controller with two types of gain perturbations is designed. Under the Filippov fractional differential inclusion framework, the global non-fragile robust finite-time stabilization conditions are addressed in terms of linear matrix inequalities (LMIs) by applying nonsmooth analysis theory, inequality analysis technique, average dwell-time method and Lyapunov functional approach. In addition, the global non-fragile robust finite-time $$H_{\infty }$$ performance analysis is performed, and the global non-fragile robust finite-time stabilization conditions with $$H_{\infty }$$ disturbance attenuation level are also derived in the form of LMIs. Finally, two numerical examples are given to illustrate the feasibility of the proposed non-fragile switched controller and the validity of the theoretical results.

Stochastic finite-time synchronization for discontinuous semi-Markovian switching neural networks with time delays and noise disturbance

Abstract This paper deals with the global stochastic finite-time synchronization in probability for discontinuous semi-Markovian switching neural networks with time delays and noise disturbance. Firstly, the formula for calculating the global stochastic settling time of semi-Markovian switching nonlinear system with Brown motion is developed. Secondly, the novel state-feedback controllers, which include discontinuous factors and integral terms, are designed to realize the global stochastic finite-time synchronization goal. Under Filippov stochastic differential inclusion framework, by applying Lyapunov–Krasovskii functional approach, stochastic analysis theory, inequality analysis technique and the developed stochastic finite-time stability theorem, the global stochastic finite-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Moreover, the expressions about the upper bound of stochastic settling time are explicitly proposed. In addition, the relativity among the obtained results is analytically interpreted. Finally, two numerical examples are provided to demonstrate the validity of the proposed design methods and theoretical results.

Finite-time synchronization of delayed fuzzy cellular neural networks with discontinuous activations

In this paper, we study the finite-time synchronization issue for delayed fuzzy cellular neural networks with discontinuous activations. Under the framework of differential inclusions, by utilizing the discontinuous state feedback control method and constructing Lyapunov functionals, new and useful finite-time synchronization criteria for the considered networks are established, which significantly generalize and improve recent works in literature. Finally, two examples with simulations are presented to show the effectiveness of the synchronization schemes.

Non-fragile chaotic synchronization for discontinuous neural networks with time-varying delays and random feedback gain uncertainties

This paper is concerned with the non-fragile synchronization issue for neural networks with discontinuous activation functions, time-varying delays and random feedback gain uncertainties, where the randomly occurring phenomena are modeled by stochastic variables satisfying the Bernoulli distribution. The appropriate non-fragile controllers are designed to ensure that the global synchronization can be achieved easily. Under the extended Filippov differential inclusion framework, by applying non-smooth analysis theory with a generalized Lyapunov–Krasovskii functional with multiple integral terms and Wirtinger-based multiple integral inequality analysis technique, the global asymptotical stochastic stability of the synchronization error dynamical system is analytically proved, and the non-fragile synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the feasibility of the proposed non-fragile controller and the validity of the theoretical results.

Set-valued discrete-time sliding-mode control of uncertain linear systems

This paper focuses on the discrete-time sliding-mode control problem, that is, given an uncertain linear system under the effect of external matched perturbations, to design a set-valued control law that achieves the robust regulation of the plant and at the same time reduces substantially the chattering effect in both the input and the sliding variables. The cornerstone is the implicit Euler discretization technique together with a differential inclusion framework which allow us to make a suitable selection of the control values that will compensate for the disturbances. Numerical examples confirm the effectiveness of the proposed methodology.