Sampled-data synchronization for fuzzy inertial cellular neural networks and its application in secure communication.

This paper designs the sampled-data control (SDC) scheme to delve into the synchronization problem of fuzzy inertial cellular neural networks (FICNNs). Technically, the rate at which the information or activation of cellular neuronal transmission made can be described in a first-order differential model, but the network response concerning the received information may be dependent on time that can be modeled as a second-order (inertial) cellular neural network (ICNN) model. Generally, a fuzzy cellular neural network (FCNN) is a combination of fuzzy logic and a cellular neural network. Fuzzy logic models are composed of input and output templates which are in the form of a sum of product operations that help to evaluate the information transmission on a rule-basis. Hence, this study proposes a user-controlled FICNNs model with the same dynamic properties as FICNN model. In this regard, the synchronization approach is considerably effective in ensuring the dynamical properties of the drive (without control input) and response (with external control input). Theoretically, the synchronization between the drive-response can be ensured by analyzing the error model derived from the drive-response but due to nonlinearities, the Lyapunov stability theory can be utilized to derive sufficient stability conditions in terms of linear matrix inequalities (LMIs) that will guarantee the convergence of the error model onto the origin. Distinct from the existing stability conditions, this paper derives the stability conditions by involving the delay information in the form of a quadratic function with lower and upper bounds, which are evaluated through the negative determination lemma (NDL). Besides, numerical simulations that support the validation of proposed theoretical frameworks are discussed. As a direct application, the FICNN model is considered as a cryptosystem in image encryption and decryption algorithm, and the corresponding outcomes are illustrated along with security measures.

Distributed State Observer for Systems with Multiple Sensors under Time-Delay Information Exchange.

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Thermodynamic Stability Theories of Irreversible Processes and the Fourth Law of Thermodynamics.

Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs-Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested "fourth laws", this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation.

Dynamics, synchronization and traveling wave patterns of flux coupled network of Chay neurons.

Studies in the literature have demonstrated the significance of the synchronization of neuronal electrical activity for signal transmission and information encoding. In light of this importance, we investigate the synchronization of the Chay neuron model using both theoretical analysis and numerical simulations. The Chay model is chosen for its comprehensive understanding of neuronal behavior and computational efficiency. Additionally, we explore the impact of electromagnetic induction, leading to the magnetic flux Chay neuron model. The single neuron model exhibits rich and complex dynamics for various parameter choices. We explore the bifurcation structure of the model through bifurcation diagrams and Lyapunov exponents. Subsequently, we extend our study to two coupled magnetic flux Chay neurons, identifying mode locking and structures reminiscent of Arnold's tongue. We evaluate the stability of the synchronized manifold using Lyapunov theory and confirm our findings through simulations. Expanding our study to networks of diffusively coupled flux Chay neurons, we observe coherent, incoherent, and imperfect chimera patterns. Our investigation of three network types highlights the impact of network topology on the emergent dynamics of the Chay neuron network. Regular networks exhibit diverse patterns, small-world networks demonstrate a critical transition to coherence, and random networks showcase synchronization at specific coupling strengths. These findings significantly contribute to our understanding of the synchronization patterns exhibited by the magnetic flux Chay neuron. To assess the synchronization stability of the Chay neuron network, we employ master stability function analysis.

Feedback control strategy of networked multi-LSRMs system with semi-Markov topology switching and time delay.

This paper studies the networked control system (NCS) with semi-Markov topology switching and network delay. The time delays of the system are considered in the measurement and control channels. The control channel is between the controller and the actuator, the measurement channel is between the sensor and the controller. The topology switching and the transition process among modes are described by semi-Markov sojourn-time probability density function and Markov transition probability matrix respectively. The mean square stability conditions for the networked multi-LSRMs system are obtained by constructing a new Lyapunov function. To ensure the σ-error mean square stability of the closed loop system, a state feedback controller is designed by combining the variation technique of inequalities and Lyapunov stability theory. Finally, several experiments results verify the effectiveness and rationality of the proposed control strategy.

Stability enhancement of battery energy storage and renewable energy-based hybrid AC/DC microgrids using terminal sliding mode backstepping control approaches.

In this paper, a terminal sliding mode backstepping controller (TSMBC) has been proposed for various components of a hybrid AC/DC microgrid (HADMG) to enhance its dynamic stability. The proposed control technique is employed to generate switching control signals for converters, which serve as the primary interface between the DC bus and the AC bus in a hybrid microgrid. Additionally, this technique facilitates the interface of PMSG-based wind generators, solar photovoltaic generators, and battery energy storage systems with the DC bus. Through the implementation of the composite control technique, the global stability of the microgrid is ensured by driving all the states of the HADMG associated with various components to converge towards their intended values. Afterward, the Lyapunov control theory has been used to analyze the converter and inverter's large-signal stability while ensuring the robustness of the proposed robust composite controller. Finally, an extensive simulation study was conducted on a hybrid microgrid to verify the efficacy of the designed controller in maintaining power balance amidst variations in the system's operational regimes. Moreover, the effectiveness of the controller's practical implementation is confirmed by real-time processor-in-the-loop analysis. Simulation results clearly show that the proposed TSMBC improves the overall dynamic performance of the hybrid microgrid with less overshoot (0%) and settling time (110 ms) in DC bus voltage when compared to the existing sliding mode controller.

Improving Tracking of Trajectories through Tracking Rate Regulation: Application to UAVs.

The tracking problem (that is, how to follow a previously memorized path) is one of the most important problems in mobile robots. Several methods can be formulated depending on the way the robot state is related to the path. "Trajectory tracking" is the most common method, with the controller aiming to move the robot toward a moving target point, like in a real-time servosystem. In the case of complex systems or systems under perturbations or unmodeled effects, such as UAVs (Unmanned Aerial Vehicles), other tracking methods can offer additional benefits. In this paper, methods that consider the dynamics of the path's descriptor parameter (which can be called "error adaptive tracking") are contrasted with trajectory tracking. A formal description of tracking methods is first presented, showing that two types of error adaptive tracking can be used with the same controller in any system. Then, it is shown that the selection of an appropriate tracking rate improves error convergence and robustness for a UAV system, which is illustrated by simulation experiments. It is concluded that error adaptive tracking methods outperform trajectory tracking ones, producing a faster and more robust convergence tracking, while preserving, if required, the same tracking rate when convergence is achieved.

A novel Lyapunov stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays.

The major target of this research article is to conduct a new Lyapunov stability analysis of a special model of Cohen-Grossberg neural networks that include multiple delay terms in state variables of systems neurons and multiple delay terms in time derivatives of state variables of systems neurons in the network structure. Employing some proper linear combinations of three different positive definite and positive semi-definite Lyapunov functionals, we obtain some novel sufficient criteria that guarantee global asymptotic stability of this type of multiple delayed Cohen-Grossberg type neural systems. These newly derived stability results are determined to be completely independent of the involved time delay terms and neutral delay terms, and they are totally characterized by the values of the interconnection parameters of Cohen-Grossberg neural system. Besides, the validation of the obtained stability criteria can be justified by applying some simple appropriate algebraic equations that form some particular relations among the constant system elements of the considered neutral neural systems. A useful and instructive numerical example is analysed to exhibit some major advantages and novelties of these newly proposed global stability results in this paper over some previously reported corresponding asymptotic stability conditions.

Adaptive control of time delay teleoperation system with uncertain dynamics.

A bilateral adaptive control method based on PEB control structure is designed for a class of time-delay force feedback teleoperation system without external interference and internal friction to study the uncertainty of dynamic parameters and time delay. The stability and tracking performances of the closed-loop constant time delay teleoperation system are analyzed by Lyapunov stability theory. Finally, the controller designed in this paper is successfully applied to the teleoperation system composed of a two-degree of freedom rotating manipulator as the master robot and the slave robot. The simulation is carried out in no operator and environment force or with operator and environment force. The adaptive bilateral control method's control performance is compared with that of the traditional time-delay teleoperation system. Finally, it is verified that the method has good control performance.

An Effective Synchronization Approach to Stability Analysis for Chaotic Generalized Lotka-Volterra Biological Models Using Active and Parameter Identification Methods.

In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka-Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapunov stability theory (LST) to construct the desired controllers, which ensures the global asymptotical convergence of a trajectory following synchronization errors. In addition, simulations were conducted in a MATLAB environment to illustrate the accuracy and efficiency of the proposed techniques. Exceptionally, both experimental and theoretical results are in excellent agreement. Comparative analysis between the considered strategy and previously published research findings is presented. Lastly, we describe an application of our considered combination difference synchronization in secure communication through numerical simulations.

Disturbance observer-based adaptive reinforcement learning for perturbed uncertain surface vessels.

This article considers a problem of tracking, convergence of disturbance observer (DO) based optimal control design for uncertain surface vessels (SVs) with external disturbance. The advantage of proposed optimal control using adaptive/approximate reinforcement learning (ARL) is that consideration for whole SVs with only one dynamic equation and without conventional separation technique. Additionally, thanks to appropriate disturbance observer, the attraction region of tracking error is remarkably reduced. On the other hand, the particular case of optimal control problem is presented by directly solving for the purpose of choosing the suitable activation functions of ARL. Furthermore, the proposed ARL based optimal control also deals with non-autonomous property of closed tracking error SV model by considering the equivalent system. Based on the Lyapunov function candidate using optimal function and quadratic form of estimated error of actor/critic weight, the stability and convergence of the closed system are proven. Some examples are given to verify and demonstrate the effectiveness of the new control strategy.

Adaptive interval type-2 fuzzy recurrent RBFNN control design using ellipsoidal membership functions with application to MEMS gyroscope.

In this article, a hybrid control approach is provided to control the micro-electro-mechanical system (MEMS) triaxial gyroscope as a multi-input multi-output (MIMO) system. Control design includes a fast non-singular terminal sliding mode control (FNTSMC) as a main part of the proposed hybrid control method and since the MEMS gyroscope performance is affected by parameter variations, quadrature errors, and external disturbances in the core of the main controller, adaptive interval type-2 recurrent fuzzy radial basis function neural network (IT2-RFRBF-NN) is employed to estimate the lumped uncertainties. The proposed hybrid approach has four main attributes: (1) it lies in the category of model-free control structures; (2) There is no negative power involved. Hence, the suggested method does not have the singularity problem; (3) to enhance the capability of the proposed method in the present of noise the ellipsoidal membership functions are employed to design adaptive IT2-RFRBF-NN; (4) the Fourier series expansion as a function approximation technique is efficiently used to online estimate the discontinuous component by establishing a soft switching in the proposed controller. With the help of the Lyapunov stability theory, guaranteeing the closed-loop control system stability by the suggested control design is confirmed. The findings of the simulations and comparison with other approaches confirm the superiority of the suggested hybrid approach.

An active disturbance rejection control for hysteresis compensation based on Neural Networks adaptive control.

In the present paper, an active disturbance rejection control(ADRC) scheme via radial basis function(RBF) neural networks is designed for adaptive control of non-affine nonlinear systems facing hysteresis disturbance in which RBF neural network approximation is utilized to tackle the system uncertainties and ADRC is designed to real-time estimate and compensate disturbance with unknown backlash-like hysteresis. Combining the adaptive neural networks design with ADRC design techniques, a new dual-channel composite controller scheme is developed herein whereby adaptive neural networks are used as feed-forward inverse control and ADRC as closed-loop feedback control. Furthermore, as compared to adaptive neural networks control algorithm, the proposed RBF-ADRC dual-channel composite controller can guarantee that the desired signal can be tracked with a small domain of the origin and it is confirmed to be effective under Lyapunov stability theory and MATLAB simulations.

High Performance Both in Low-Speed Tracking and Large-Angle Swing Scanning Based on Adaptive Nonsingular Fast Terminal Sliding Mode Control for a Three-Axis Universal Inertially Stabilized Platform.

In order to improve the performance in the practical engineering applications including so called low-speed video tracking and large-angle swing scanning imaging at the same time for a three-axis universal inertially stabilized platform (UISP), we propose an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) strategy subjected to the uncertain disturbances and input saturation constraints. First of all, a second-order dynamic model is established with uncertain disturbances and input saturation constraints. Secondly, a nonsingular fast terminal sliding mode controller (NTSMC) is constructed to ensure the system error converges to zero fast in a finite time; meanwhile, a novel reaching law based on a modified normal distribution function is designed to adjust the control gain. Thirdly, an adaptive control law is designed to online estimate the parameters of the lumped uncertain disturbances. Additionally, the stability of the control system is proved by Lyapunov theory. Finally, extensive comparative simulations and experiments are carried out, the results comprehensively show the effectiveness and superiority of the proposed control method, which can accelerate convergence, weaken the chattering, and has the better control accuracy and robust performance both in the low-speed tracking and large-angle swing scanning applications. Moreover, the exact dynamic model and the prior knowledge of the upper bounds of the disturbances are not required during the procedure of the controller design, which make it have more extensive application value in practical engineering.

A New Model for Complex Dynamical Networks Considering Random Data Loss.

Model construction is a very fundamental and important issue in the field of complex dynamical networks. With the state-coupling complex dynamical network model proposed, many kinds of complex dynamical network models were introduced by considering various practical situations. In this paper, aiming at the data loss which may take place in the communication between any pair of directly connected nodes in a complex dynamical network, we propose a new discrete-time complex dynamical network model by constructing an auxiliary observer and choosing the observer states to compensate for the lost states in the coupling term. By employing Lyapunov stability theory and stochastic analysis, a sufficient condition is derived to guarantee the compensation values finally equal to the lost values, namely, the influence of data loss is finally eliminated in the proposed model. Moreover, we generalize the modeling method to output-coupling complex dynamical networks. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed model.

Adaptive backstepping-based tracking control design for nonlinear active suspension system with parameter uncertainties and safety constraints.

This paper proposes a novel constraint adaptive backstepping based tracking controller for nonlinear active suspension system with parameter uncertainties and safety constraints. By introducing the virtual control input and reference trajectories, the adaptive control law is developed to stabilize both of the vertical and pitch motions of vehicle body using backstepping technique and Lyapunov stability theory, and further to track the predefined reference trajectories within a finite time, which not only ensure the safety performance requirements, but also achieve improvements in riding comfort and handling stability of vehicle active suspension system. Next, the stability analysis on zero dynamics error system is conducted to ensure that all the safety performance indicators are all bounded and the corresponding upper bounds are estimable. Finally, a numerical simulation is provided to verify the effectiveness of the proposed controller and to address the comparability between the classical Barrier-Lyapunov Function based adaptive tracking controller and the proposed controller.

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.