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In this paper, we propose the problem of connectivity maintenance for a group of robots that are connected with wireless communication. The communication between the agents is modeled by a fading channel, and the exchange of information is possible at permissible distances. The distributed controller is designed to maintain the global connectivity of the network communication graph. On the other hand, obtaining the best communication quality between agents is the definition of good network connectivity. Therefore, the Laplacian matrix is defined as a weighted graph according to the communication parameters. Initially, the controller uses the supergradation algorithm to remake the network Laplacian matrix for having a bigger second eigenvalue. While each agent in the network only has access to the neighbor's information. The control algorithm uses a multi-agent estimator to find the eigenvector corresponding to the second small eigenvalue. The formation problem has been considered in the second step after the reference topology has been obtained. Because of the nonlinear dynamics of the agents, the sliding mode controller has been used for this purpose. This robust controller could be a suitable choice due to the modeling uncertainty and sensor measurement uncertainty. Finally, an example of multi-agent robots is provided to evaluate the algorithm.

Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order (FO) nonlinear systems under these two practical constraints. Two primary methodologies are employed: the vector Lyapunov function method, integrated with the M-matrix approach, and the second one is the Lyapunov-like function method, which incorporates diffusive realization and the Lipchitz condition. An optimization framework is proposed to design stabilizing controllers based on the derived stability conditions. The proposed methods are validated numerically through their application to the FO Lorenz and Liu systems, demonstrating their effectiveness in handling actuator saturation and time delay.

Sliding mode control is a robust controller against modeling imprecisions and external disturbances, successfully employed to the dynamic positioning of autonomous underwater robot. In order to improve the performance of the whole system, the discontinuity in the control law must be smoothed out to avoid the undesirable chattering and unwanted ripples. One of the disadvantages of conventional sliding mode is great vulnerability in the presence of noise. However, noise and some initial condition causing undesirable chattering phenomenon and unwanted ripples in the control input. This paper describes the development of a depth control system for autonomous underwater robot. In this paper we used the sliding surface term and its derivation with adaptive gains in control law instead of the sign function with fixed gain. The proposed controller has been designed to solve great vulnerability of sliding mode control at the presence of noise. For contrast one of factors causing chattering, big controller gain, the gain of controller adapted according to state condition and uncertainties. Due to in the proposed controller there is no sign function, so our controller is not vulnerability to noise. Using this controller, ripples and unexpected sharp peak of the input control signal were canceled and control signal was smoother than conventional sliding mode controller with boundary layer. The stability and convergence properties of the closed-loop system are analytically proved using Lyapunov stability theorem. Simulation results are presented in order to demonstrate the control system performance.

A higher-order sliding approach to control a bioreactor model is proposed by non-commensurate fractional equations. The model outputs by the help of a controller reached the desired values and track them. According to existing conditions and chattering reduction, a high-order sliding mode has been chosen to design the controller. The purpose of the paper is to choose proper sliding surfaces. Here, for a better conclusion, a comparison has been made between the high-order sliding mode and the standard sliding mode. High-order sliding mode controllers have been taken in accordance with the structure of integer order system. Thus, in order for the system to apply more precise calculations, it should somehow turn to integer order. The sliding surfaces have been selected so appropriately that we can benefit from the structure of integer order controllers for fractional order system. The sliding surface in both controllers has also been the same so as to provide conditions for comparison. Finally, simulation results indicate that the high-order sliding mode controller has a great impact on chattering reduction.

Abstract Cross‐backstepping control for a type of uncertain non‐strict‐feedback non‐linear systems with time‐varying partial state constraints is the main subject of this work. Non‐strict‐feedback non‐linear systems are partitioned into two strict‐feedback non‐linear subsystems: constrained subsystem and unconstrained subsystem. An integral barrier Lyapunov function (IBLF) is used in each step of the backstepping design for the constrained subsystem to guarantee the boundedness of the fictional or actual state tracking errors. The effect of uncertainty is reduced using a hybrid cross‐backstepping sliding mode control (SMC) technique. The algorithm employs a systematic approach to developing control laws for non‐linear systems with matched and unmatched uncertainties. The simulation results of the proposed controller are juxtaposed with those of the cross backstepping with the time‐varying barrier Lyapunov function (TVBLF). The results demonstrate the overall better performance of the proposed method.

The robust adaptive leader-follower formation control of uncertain unmanned surface vehicles (USVs) subject to stochastic environmental loads is investigated in this paper. The stochastic additive noises are included in the kinematics which stands for the un-modeled dynamics and uncertainty. The disturbances induced by waves, wind and ocean currents in the kinetics are also separated into deterministic and stochastic components. A comprehensive model including kinematics and kinetics of each USV agent is then derived as stochastic differential equations including standard Wiener processes. Thus, the problem formulation is much more challenging and practical since both the exogenous disturbances and kinematics states are defined by stochastic differential equations. In order to guarantee that all the tracking errors converge to a ball centered at the origin in probability, quartic Lyapunov functions synthesis, dynamic surface control (DSC) technique, the projection algorithm, and neural networks (NNs) are employed. Finally, the simulation experiments quantify the effectiveness of proposed approach.

The paper introduces a novel adaptive fuzzy fractional-order (FO) fast terminal sliding mode control procedure for a class of nonlinear systems in the presence of uncertainties and external disturbances. For this purpose, firstly, using fractional calculus, a new FO nonlinear sliding surface is proposed and then, the corresponding FO fast terminal sliding mode controller (FOFTSMC) is designed to satisfy the sliding condition in finite time. Next, to eliminate the chattering phenomenon, a fuzzy system is constructed to design a continuous switching control law. The finite-time stability of the proposed adaptive fuzzy FOFTSMC (AFFOFTSMC) is proved using the concept of Lyapunov stability theorem. Finally, to illustrate the effectiveness of the proposed AFFOFTSMC, three examples are given as case studies. The numerical simulation results confirm the superiority of the proposed controller, which are the better robust performance, faster convergence, finite-time stability of the closed-loop control system, and a chattering free control effort compared to other mentioned control methods.

The knee hybrid exoskeleton is a system that aids in the rehabilitation of patients with mobility disorders. It comprises a powered exoskeleton and functional electrical stimulation, which moves the knee joint by stimulating the muscles. However, electrical stimulation of muscles can lead to muscle fatigue. For the first time, this article investigates the regulation of muscle fatigue by controlling muscle activation. To control muscle activation, an innovative adaptive controller for FES is designed. The adaptation law is designed utilizing a time-varying estimation of the muscle activation time parameter. The proportional-integral controller is designed to regulate the knee joint angle utilizing an electrical motor. The proportional-integral controller gains are calculated using an optimization method. A cooperative control structure is presented to use the electrical motor and functional electrical stimulation simultaneously. The muscle activation error is uniformly ultimately bounded, and its boundedness is proven through Lyapunov analysis; the error bound is also determined. The simulation results showed knee joint angle regulation and muscle fatigue regulation. The proposed control method results were compared with those based on model predictive control and switching control, which showed significant improvement in the joint angle error and muscle fatigue. The proposed method is appropriate for practical implementation based on the obtained results.

Lyapunov's theorem is the basic criteria to establish the stability properties of the nonlinear dynamical systems. In this method, it is a necessity to find the positive definite functions with negative definite or negative semi-definite derivative. These functions that named Lyapunov functions, form the core of this criterion. The existence of the Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems. On the other hand, for the cases where the equilibrium point is stable in the sense of Lyapunov, converse Lyapunov theorems only ensure non-smooth Lyapunov functions. In this paper, it is proved that there exist some autonomous nonlinear systems with stable equilibrium points that despite stability don’t admit convex Lyapunov functions. In addition, it is also shown that there exist some nonlinear systems that despite the fact that they are stable at the origin, but do not admit smooth Lyapunov functions in the form of V(x) or V(t,x) even locally. Finally, a class of non-autonomous dynamical systems with uniform stable equilibrium points, is introduced. It is also proven that this class do not admit any continuous Lyapunov functions in the form of V(x) to establish stability.

Nowadays, sea wave energy is widely regarded as an energy source that is clean, renewable and highly available for power extraction. The subject of extracting the maximum power from sea waves in Iran is of great importance due to access to the Caspian Sea and the Persian Gulf. Moreover, there is a need for resources with no air pollution besides providing a part of the country's power demand without costly infrastructure, so this research field is highly interesting although has rarely been addressed so far. The main purpose of this paper is to use an appropriate control strategy to improve the performance of point absorbers. In this scheme, to consider high uncertainty in the parameters of the power take-off system in different atmospheric conditions and improve controller performance, a new improved black hole algorithm is introduced to tune fuzzy controller parameters. The proposed method is then implemented for tuning the fuzzy controller parameters in order to obtain the maximum power capture of wave energy converters. Compared to particle swarm optimization and conventional black hole algorithm, the results of the proposed method indicate enhancements in reference velocity tracking and absorbed power. Finally, some simulations are performed and the proposed controller is implemented for the wave spectrum of the Persian Gulf waters, so the performance of the proposed controller is evaluated.

In this paper, a novel optimal control design method by discontinuous quadratic Lyapunov function and continuous quadratic Lyapunov function for 2-dimensional piecewise affine systems via semi-definite programming and LMI constraints is proposed.In fact, for designing optimal control we use from two different criteria. At the first, an upper bound for a quadratic cost function for a stable closed-system is obtained. Then after, considering a state-feedback control approach, not only sufficient conditions for the stability of the closed-loop system but also the upper bound of the cost function are obtained. The optimization problem is formulated as a semi-definite programming with bilinear constraints (BMI). Some variables in BMIs are searched by genetic algorithm, so the bilinear constraints are converted to linear constraints and the controller coefficients are calculated. The effectiveness of the proposed method is verified by numerical examples. The simulation results show that discontinuous quadratic lyapunov functions are more efficient that continuous quadratic lyapunov functions.

This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) switched system with interval uncertainty and unstable subsystems. It is proved that the system would be stable by using a common Lyapanov function whose derivative is negative and bounded by a quadratic function within activation regions of each subsystem. First, a sufficient condition for the stability of an Linear Time Invariant switched system with interval uncertainty, based on the convex analysis and interval set theoretical approach, is presented and proved. Moreover, conservatism in the stability robustness bound is obtained. Then, a switching control law is designed to shift the Linear Time Invariant switched system among subsystems to ensure the decrease of the Lyapanov function within the state space. Finally, in order to decrease the switching frequency and to avoid chattering, the switching law is modified. Two examples are included to demonstrate the effectiveness of the theoretical findings.

In this paper, a continuous globally stable tracking control algorithm is proposed for spacecraft in the presence of unknown actuator failure. The design method is based on nonlinear dynamic inversion and  in contrast to traditional fault-tolerant control methods, the proposed controller does not require knowledge of the actuator faults and is implemented without explicit fault detection and isolation processes. The stability proof is based on a Lyapunov analysis and the properties of the singularity free quaternion representation of spacecraft dynamics. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of external disturbances and actuator failures.

Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is contaminated with noise is investigated and compared with some traditional chaos-based measures. Materials and Methods: In the proposed method, the phase space of the time series is reconstructed and then partitioned using ordinal patterns. The partitions can be labeled using a set of symbols. Therefore, the state trajectory is converted to a symbol sequence. A finite state machine is then constructed to model the sequence. A new complexity measure is proposed to detect dynamical changes using the state transition matrix of the state machine. The proposed complexity measure was applied to detect epilepsy in short and noisy EEG signals and the results were compared with some chaotic measures. Results: The results indicate that this complexity measure can distinguish normal and epileptic EEG signals with an accuracy of more than 97% for clean EEG and more than 75% for highly noised EEG signals. Discussion and Conclusion: The complexity measure can be computed in a very fast and easy way and, unlike traditional chaotic measures, is robust with respect to noise corrupting the data. This measure is also capable of dynamical change detection in short time series data.

Abstract Background Although previous studies have linked emotional intelligence to nurses’ job performance, research lacks how moral intelligence and occupational stress mediate this relationship. Addressing this gap is essential for improving nursing care outcomes. This study aims to determine the mediating effect of moral intelligence and occupational stress in this relationship among Iranian nurses. Methods This descriptive cross-sectional correlational study was conducted in Urmia Teaching Hospital from February to April 2022. Six hundred and twenty-one nurses were recruited using quota sampling. Data were collected using a demographic questionnaire, Lenik and Kiel’s Moral Intelligence Questionnaire (LK-MIQ), Siberia Schering’s Emotional Intelligence Questionnaire (SS-EISQ), Patterson’s Job Performance Questionnaire (P-JPQ), and the Nursing Stress Scale (NSS). Data were analyzed using IBM SPSS ver. 23 and Smart-PLS ver. 3.0. Results The effect of emotional intelligence on job performance was positive, direct, and weak (β = 0.099, t-value = 2.285, p = 0.023). Emotional intelligence had a negative, direct, and weak effect on moral intelligence (β = − 0.257, t-value = 4.754, p = 0.000) and a negative, direct, and moderate effect on occupational stress (β = − 0.316, t-value = 6.482, p = 0.000). Moral intelligence mediates the relationship between emotional intelligence and occupational stress (β = 0.0842, 95% CI: 0.0532, 0.1194). However, the mediating role of occupational stress between emotional intelligence and job performance was not supported (β = 0.003, 95% CI: − 0.0139, 0.0184). Conclusion Moral and emotional intelligence should be key criteria for selecting nursing staff and managers to create a safe, low-stress environment that boosts nurses’ job performance. Healthcare managers should promote nurses’ emotional intelligence by offering practical courses for enhancing nurses’ self-awareness, self-management, social awareness, and relationship management skills. It is essential to support moral intelligence by organizing educational classes that improve their integrity, responsibility, compassion, and forgiveness.

Abstract Background Although previous studies have linked professional autonomy to nurses’ job performance, research lacks how job satisfaction and organizational commitment mediate this relationship. Addressing this gap is essential for improving nursing practice outcomes. This study aims to determine the mediating effect of job satisfaction and organizational commitment in this relationship among Iranian nurses. Methods This descriptive-correlational study was conducted in Urmia teaching hospitals from October 2022 to June 2023. Four hundred twenty nurses were recruited using quota sampling. Eligible participants were selected non-randomly from predetermined numbers at four hospitals, and recruitment continued until the required sample size was achieved. Data were collected using demographic questionnaires, the Varjus Professional Autonomy Scale, the Porter Organizational Commitment Questionnaire, the Minnesota Satisfaction Questionnaire, and the Paterson Job Performance Questionnaire. Data were analyzed using SPSS ver. 23 and SmartPLS ver. 3. Results Professional autonomy had a positive, direct, and strong effect on nurses’ job performance (β = 0.708, t-value = 9.867, p