A new fixed-time stability theorem and its application to the synchronization control of memristive neural networks

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0 Collapse

Key Words

• Cellular neural networks
• Complex-valued neural networks
• Fixed-time synchronization
• Fuzzy neural networks
• Non-separation approach

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MESH Headings

• Neural Networks, Computer
• Fuzzy Logic
• Computer Simulation
• Algorithms
• Time Factors

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Grants Collapse

Affiliation(s)

Jingsha Zhang Hebei Provincial Innovation Center for Wireless Sensor Network Data Application Technology, Hebei Provincial Key Laboratory of Information Fusion and Intelligent Control, Hebei Normal University, Shijiazhuang 050024, China.
Jing Yang Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050003, China.
Qintao Gan Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050003, China.
Huaiqin Wu School of Science, Yanshan University, Qinhuangdao 066001, China.
Jinde Cao School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea.

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Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication

This paper investigates the finite/fixed-time synchronization problem of delayed inertial memristive neural networks (DIMNNs) using interval matrix-based methods within a unified control framework. By employing set-valued mapping and differential inclusion theory, two distinct methods are applied to handle the switching behavior of memristor parameters: the maximum absolute value method and the interval matrix method. Based on these different approaches, two control strategies are proposed to select appropriate control parameters, enabling the system to achieve finite and fixed-time synchronization, respectively. Additionally, the resulting theoretical criteria differ based on the chosen control strategy, with one expressed in algebraic form and the other in the form of linear matrix inequalities (LMIs). Numerical simulations demonstrate that the interval matrix method outperforms the maximum absolute value method in terms of handling memristor parameter switching, achieving faster finite/fixed-time synchronization. Furthermore, the theoretical results are extended to the field of image encryption, where the response system is utilized for decryption and expanding the keyspace.

Fixed-time synchronization of delayed memristive neural networks with impulsive effects via novel fixed-time stability theorem

In this study, the fixed-time synchronization (FXTS) of delayed memristive neural networks (MNNs) with hybrid impulsive effects is explored. To investigate the FXTS mechanism, we first propose a novel theorem about the fixed-time stability (FTS) of impulsive dynamical systems, where the coefficients are extended to functions and the derivatives of Lyapunov function (LF) are allowed to be indefinite. After that, we obtain some new sufficient conditions for achieving FXTS of the system within a settling-time using three different controllers. At last, to verify the correctness and effectiveness of our results, a numerical simulation was conducted. Significantly, the impulse strength studied in this paper can take different values at different points, so it can be regarded as a time-varying function, unlike those in previous studies (the impulse strength takes the same value at different points). Hence, the mechanisms in this article are of more practical applicability.

New Fixed-Time Stability Criteria of Time-Varying Delayed Discontinuous Systems and Application to Discontinuous Neutral-Type Neural Networks

This article mainly focuses on putting forward new fixed-time (FIXT) stability lemmas of delayed Filippov discontinuous systems (FDSs). By providing the new inequality conditions imposed on the Lyapunov-Krasovskii functions (LKF), novel FIXT stability lemmas are investigated with the help of inequality techniques. The new settling time is also given and its accuracy is improved in comparison with pioneer ones. For the purpose of illustrating the applicability, a class of discontinuous fuzzy neutral-type neural networks (DFNTNNs) is considered, which includes the previous NTNNs. New criteria are derived and detailed FIXT synchronization results have been obtained. Finally, typical examples are carried out to demonstrate the validity of the main results.

New Fixed-Time Stability Analysis of Delayed Discontinuous Systems via an Augmented Indefinite Lyapunov-Krasovskii Functional

This article discusses the fixed-time stability (FTS) of a kind of delayed discontinuous system (DS) in Filippov sense. Based on the set-valued map, the FTS analysis of the general solution is first transformed into the zero solution of the differential inclusion. Second, the new criteria of the Lyapunov-Krasovskii functional (LKF) are given and LKF is proved to possess the indefinite derivatives by using the simple integral inequalities. In addition, the FTS of the considered delayed DS is achieved and the new settling time is estimated. Third, to demonstrate the applicability of the new FTS theorems, the FTS control of a class of discontinuous inertial neural networks (DINNs) with time-varying delays is solved. Finally, two numerical examples are given to examine the theoretical results and simulations are also provided to make some illustrations.

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

Analysis of random synchronization under bilayer derivative and nonlinear delay networks of neuron nodes via fixed time policies

In order to solve a challenging problem, i.e., fixed time synchronization of bilayer networks with derivative coupling and nonlinear delay coupling, fixed time polices are brought to achieve random synchronization for bilayer multiple weight hybrid coupled networks of neuron nodes. Being different from the synthesis method, which is often used to get theoretical conclusions from known conditions for synchronization of networks in general articles, analysis method is applied to seek parameters in fixed time controllers and sufficient conditions for synchronization from conclusions. After analysis, we obtain a relationship between coefficients of controllers and coefficients of a formula which is related to Lyapunov function. Moreover, we find that fixed settling time for synchronization is affected by the maximum eigenvalue of a matrix associated with network topology, parameters in the designed controllers and the size of networks. Finally, synchronous tests of bilayer networks of Hindmarsh-Rose (HR) neuron nodes are carried out to show the effectiveness of theoretical results.

Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks

This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.

Fixed-time ESO based fixed-time integral terminal sliding mode controller design for a missile

This paper studies a novel fixed-time extended state observer based fixed-time integral terminal sliding mode controller for partial integrated guidance and control design. Firstly, a class of arbitrary-order systems with fixed-time stability is proposed by utilizing homogeneous approach, whose upper bound of convergence time is given. Then, an arbitrary-order fixed-time integral terminal sliding mode control is designed based on the proposed arbitrary-order fixed-time stable system, which avoids the singular problem. Subsequently, this paper constructs a new fixed-time extended state observer to further actively compensate for the disturbance caused by unknown target acceleration. Finally, numerical simulations show the effectiveness of the proposed controller.

Predefined-time synchronization of competitive neural networks

In this paper, the predefined-time synchronization of competitive neural networks (CNNs) is researched based on two different predefined-time stability theorems. In view of the bilayer structure of CNNs, we design two bilayer predefined-time controllers. The first controller utilizes sign function, while the second controller utilizes exponential function and Lyapunov function. In these two controllers, the predefined time is set as a controller parameter, and it can be an arbitrary positive constant. Under these two controllers, the considered CNNs can achieve synchronization within the predefined time regardless of the initial values. A specific example is presented to validate the theoretical results.

Enhancing the settling time estimation of fixed-time stability and applying it to the predefined-time synchronization of delayed memristive neural networks with external unknown disturbance

This paper concentrates on the global predefined-time synchronization of delayed memristive neural networks with external unknown disturbance via an observer-based active control. First, a global predefined-time stability theorem based on a non-negative piecewise Lyapunov function is proposed, which can obtain more accurate upper bound of the settling time estimation. Subsequently, considering the delayed memristive neural networks with disturbance, a disturbance-observer is designed to approximate the external unknown disturbance in the response system with a Hurwitz theorem and then to eliminate the influence of the unknown disturbance. With the help of global predefined-time stability theorem, the predefined-time synchronization is achieved between two delayed memristive neural networks via an active control Lyapunov function design. Finally, two numerical simulations are performed, and the results are given to show the correctness and feasibility of the predefined-time stability theorem.