In this work, we present new results for a two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium at the origin. The bifurcation and multi-stability analysis for the new hyperchaotic system are discussed in detail. As a control application, we develop a feedback control based on integral sliding mode control (ISMC) for the complete synchronization of a pair of two-scroll hyperchaotic systems developed in this work. Numerical simulations using Matlab are provided to illustrate the hyperchaotic phase portraits, bifurcation diagrams and synchronization results. Finally, as an electronic application, we simulate the new hyperchaotic system using Multisim for real-world implementations.
The paper is dedicated to the robustness analysis of scalar multi-agent dynamical systems. The open problem we aim to address is the one related to the impact of additive disturbances. Set-theoretic methods are used to achieve the main results in terms of positive invariance and admissible bounds on the disturbances.
The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.
In this paper an application of the Serret–Frenet parametrization of a curve to the path following task is presented. This curvilinear parametrization method is used to obtain a control object description relative to the desired curve defined in the three-dimensional space. In order to derive proper equations, the innovative approach of the non-orthogonal projection of a control object on the given path is investigated. The non-orthogonal projection allows to design a global control algorithm. The proposed solution results in a cascade structure of the control system. Thus, the backstepping integrator algorithm was applied to create a control law. Due to the partial knowledge of control object dynamic parameters, an adaptive algorithm is taken into account. Theoretical considerations are confirmed with simulation study. Conducted simulations illustrated following paths at different levels of complexity by a holonomic non-redundant manipulator with a fixed base.
Department of Cybernetics and Robotics, Faculty of Electronics, Photonics and Microsystems, Wrocław University of Science and Technology, Janiszewskiego Street 11/17, Wrocław 50-372, Poland
This article validates the application of RT-Lab for the AGC studies of three-area systems. All the areas are employed with thermal-DSTS systems. A new controller named cascade FOPDN-FOPPIDN is employed. Its parameters are optimized using a CSA, subjecting to a new PI named HPA-ISE. The responses of the FOPDN-FOPIDN controller are related and are superior over PIDN and TIDN controllers. Moreover, the dominance of HPA-ISE is verified with ISE, and it performs better in terms of system dynamics. Further, the system performance reliability is analyzed with the AC-HVDC and is better than the AC system. Besides, sensitivity analysis recommends that the proposed FOPDN-FOPIDN at diverse conditions is robust and more reliability.
Department of Electrical and Electronics Engineering, Aditya Engineering College, Surampalem, Andhra Pradesh, India
Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U.P., India
Department of Electrical/Electronics and Instrumentation Engineering, Institute of Chemical Technology, Indianoil Odisha Campus, Bhubaneswar751013, India
Faculty of Control, Robotics and Electrical Engineering, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland
Ingenium Research Group, University of Castilla-La Mancha, Spain
The paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned ‘integrating filters’ of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization and can be identified, for example, by the classical least squares procedure. Since in the presence of correlated noise, the estimated parameter values are burdened with an unavoidable systematic error (manifested by asymptotic bias of the estimates), in order to significantly improve the identification consistency, the method of instrumental variables is used here. In our research we use an estimation algorithm based on the least absolute values (LA) criterion of the least sum of absolute values, which is optimal in identifying linear and non-linear systems in the case of sporadic measurement errors. In the paper, we propose a procedure for determining the instrumental variable for a continuous model with non-linearity (related to the Wienerian system) in order to remove the evaluation bias, and a recursive sub-optimal version of the LA estmator. This algorithm is given in a simple (LA) version and in an instrumental variable version (IV-LA), which is robust to outliers, removes evaluation bias, and is suited to the task of identifying processes with non-linear dynamics (semi-Wienerian/NLID). In conclusion, the effectiveness of the proposed algorithmic solutions has been demonstrated by numerical simulations of the mechanical system, which is an essential part of the suspension system of a wheeled vehicle.
In this note, a formula for the lower Bohl exponent of a discrete system with variable coefficients and weak variation was proved. This formula expresses the Bohl exponent through the eigenvalues of the coefficient matrix. Based on these formulas a necessary and sufficient condition for an uniform exponential instability of such systems is also presented.
The fractional order proportional, integral, derivative and acceleration (PI λD µA) controller is an extension of the classical PIDA controller with real rather than integer integration action order λ and differentiation action order µ. Because the orders λ and µ are real numbers, they will provide more flexibility in the feedback control design for a large range of control systems. The Bode’s ideal transfer function is largely adopted function in fractional control systems because of its iso-damping property which is an essential robustness factor. In this paper an analytical design technique of a fractional order PI λD µA controller is presented to achieve a desired closed loop system whose transfer function is the Bode’s ideal function. In this design method, the values of the six parameters of the fractional order PI λD µA controllers are calculated using only the measured step response of the process to be controlled. Some simulation examples for different third order motor models are presented to illustrate the benefits, the effectiveness and the usefulness of the proposed fractional order PI λD µA controller tuning technique. The simulation results of the closed loop system obtained by the fractional order PI λD µA controller are compared to those obtained by the classical PIDA controller with different design methods found in the literature. The simulation results also show a significant improvement in the closed loop system performances and robustness using the proposed fractional order PI λD µA controller design.
Differential geometry is a strong and highly effective mathematical subject for robot gripper design when grasping within the predetermined trajectories of path planning. This study in grasping focuses on differential geometry analysis utilizing the Lie algebra, geodesic, and Riemann Curvature Tensors (RCT). The novelty of this article for 2RR robot mechanisms lies in the approach of the body coordinate with the geodesic and RCT. The importance of this research is significant especially in grasping and regrasping objects with varied shapes. In this article, the types of workspaces are clarified and classified for grasping and regrasping kinematics. The regrasp has not been sufficiently investigated of body coordinate systems in Lie algebra. The reason for this is the difficulty in understanding relative coordinates in Lie algebra via the body coordinate system. The complexity of the equations has not allowed many researchers to overcome this challenge. The symbolic mathematics toolbox in the Maxima, on the other hand, aided in the systematic formulation of the workspaces in Lie algebra with geodesic and RCT. The Lie algebra se(3) equations presented here have already been developed for robot kinematics from many references. These equations will be used to derive the followingworkspace types for grasping and regrasping. Body coordinate workspace, spatial coordinate workspace with constraints, body coordinate workspace with constraints, spatial coordinate workspace with constraints are the workspace types. The RCT and geodesic solutions exploit these four fundamental workspace equations derived using Lie algebra.
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
Mathematics Section, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences, Ibri, Sultanate of Oman
Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R& D Institute of Science and Technology, Avadi, Chennai-62, India
Faculty of Computer Science and Mathematics, University of Kufa, Iraq
Generalized observers are proposed to relax the existing conditions required to design Luenberger observers for rectangular linear descriptor systems with unknown inputs. The current work is focused on designing index one generalized observers, which can be naturally extended to higher indexes. Sufficient conditions in terms of system operators for the existence of generalized observers are given and proved. Orthogonal transformations are used to derive the results. A physical model is presented to show the usefulness of the proposed theory.
Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in theNeumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
In this work, we report a new chaotic population biology system with one prey and two predators. Our new chaotic population model is derived by introducing two nonlinear interaction terms between the prey and predator-2 to the Samardzija-Greller population biology system (1988).We show that the new chaotic population biology system has a greater value of Maximal Lyapunov Exponent (MLE) than the Maximal Lyapunov Exponent (MLE) of the Samardzija- Greller population biology system (1988).We carry out a detailed bifurcation analysis of the new chaotic population biology system with one prey and two predators. We also show that the new chaotic population biology model exhibits multistability with coexisting chaotic attractors. Next, we use the integral sliding mode control (ISMC) for the complete synchronization of the new chaotic population biology system with itself, taken as the master and slave chaotic population biology systems. Finally, for practical use of the new chaotic population biology system, we design an electronic circuit design using Multisim (Version 14.0).
Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information from four aspects: approval, objection, abstention and refusal. The partitioned Maclaurin symmetric mean (PMSM) operator is an effective information fusion tool, which can fully capture the interrelationships among any multiple attributes in the same block whereas attributes in different block are unrelated. Therefore, in this paper,we first extendPMSM operator to spherical fuzzy environment and develop spherical fuzzy PMSM (SFPMSM) operator as well as spherical fuzzy weighted PMSM (SFWPMSM) operator. Meanwhile, we discuss some properties and special cases of these two operators. To diminish the impact of extreme evaluation values on decision-making results, then we integrate power average (PA) operator and PMSM operator to further develop spherical fuzzy power PMSM (SFPPMSM) operator and spherical fuzzy weighted power PMSM (SFWPPMSM) operator and also investigate their desirable properties. Subsequently, a new multiple attribute group decision making (MAGDM) method is established based on SFWPPMSM operator under spherical fuzzy environment. Finally, two numerical examples are used to illustrate the proposed method, and comparative analysis with the existing methods to further testy the validity and superiority of the proposed method.
This study investigates Thomas’ cyclically symmetric attractor dynamics with mathematical and electronic simulations using a proportional fractional derivative to comprehend the dynamics of a given chaotic system. The three-dimensional chaotic flow was examined in detail with Riemann-Liouville derivative for different values of the fractional index to highlight the sensitivity of chaotic systems with initial conditions. Thus, the dynamics of the fractional index system were investigated with Eigenvalues, Kaplan–Yorke dimension, Lyapunov exponent, and NIST testing, and their corresponding trajectories were visualized with phase portraits, 2D density plot, and Poincaré maps. After obtaining the results, we found that the integer index dynamics are more complex than the fractional index dynamics. Furthermore, the chaotic system circuit is simulated with operational amplifiers for different fractional indices to generate analog signals of the symmetric attractor, making it an important aspect of engineering. The qualitative application of our nonlinear chaotic system is then applied to encrypt different data types such as voice, image, and video, to ensure that the developed nonlinear chaotic system can widely applied in the field of cyber security.
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