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The purpose of this paper is to find new non-traveling wave solutions and study its localized structure of Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation.

The authors apply the Lie group method twice and combine with the Exp-function method and Riccati equation mapping method to the (2+1)-dimensional CDGKS equation.

The authors have obtained some new non-traveling wave solutions with two arbitrary functions of time variable.

As non-linear evolution equations is characterized by rich dynamical behavior, the authors just found some of them and others still to be found.

These results may help the authors to investigate some new localized structure and the interaction of waves in high-dimensional models. The new non-traveling wave solutions with two arbitrary functions of time variable are obtained for CDGKS equation using Lie group approach twice and combining with the Exp-function method and Riccati equation mapping method by the aid of Maple.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to analyze the frame of a missile formation cooperative control system, and present an optimal keeping controller of a missile formation in the cooperative engagement.

A missile relative motion model is established directly based on the kinematics relationships in the relative coordinated frame, following that is the detailed process of designing an optimal formation controller, which is analyzed through the small disturbance linearized method and transforming control variables method, respectively, these two methods both have themselves properties. The equations and control variables are intuitive during the linearized analysis, but errors brought by the linearized method are unavoidable, which will reduce the control precision. As for the transforming method, the control accuracy is greatly increased although the control form is a little complex, so in this paper the transforming control variable method is mainly researched to design an optimal formation controller. Considering the states of a leader as input perturbation variables, we design an optimal formation controller based on the linear quadric theory, which has quadric optimal performances of the missile flight states and control quantity. In order to obtain a higher accurate solution, the precise integration algorithm is introduced to solve the Riccati Equation that significantly affects the accuracy of an optimal control problem.

The relative motion model established directly in the relative coordinate frame has intuitive physical significance, and the optimal controller based on this relative motion model is capable of restraining the invariable or slowly varying perturbation brought by the velocity of a leader and the input perturbations caused by the maneuver of the leader, at the same time this optimal controller can implement formation reconfiguration and keeping to an expected states rapidly, steadily and exactly; the steady errors can be greatly decreased by analyzing the relative motion model through transforming control variables method compared to the small disturbance linearized operation.

The main frame of a missile formation cooperative engagement system can be found in this paper, which shows a clear structure and relations of each part of this complex system. The relations between each subsystem including the specific input and output variables can also be used to guide and restrict how to design each subsystem. The emphasis of this paper is on designing an optimal formation keeping controller which can overcome slowly varying or invariable perturbations and implement quadric optimal keeping control rapidly, stably and accurately.

This paper provides a new method to analyze the missile relative motion model. The proposed proportional and integral (PI) optimal controller based on this model, and utilizing the Precise Integration Algorithm to solve this optimal controller are also new thoughts for formation control problems.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

The purpose of this paper is to improve the behaviors coordination mechanism, to maintain the system's long time‐scale and stable competitive capability, when the agents in the system focus on cooperating with each other.

Effort level for every agent, whose dynamics can be described as a stochastic partial differential equation, and the incentive of effort as the control of the corresponding agent, are introduced to describe agents' behavior abstracted. The cooperative stochastic differential game model is constructed: first, the optimal resolve trajectory mapping with profit maximization of the system are obtained, then the transitory imputation coupled with effort initial state of the system by introducing dynamic Shapley value imputation method. Based on the results obtained, the profit distribution strategies and the equilibration incentive compensation mechanism are given, due to the evolution law of the payoff and the state variable.

It is concluded that: the transitory compensation to agent for efforts and incentive, which can be changed with the system state at current and in history and in future changed, would guarantee the realization of the Shapley value imputation throughout the game horizon.

In this paper, the interactivity between agents in the system is considered first. The dynamical Shapley imputation mechanism and the transitory compensatory mechanism are provided to make the imputation more stable and feasible.

In this paper, improvements in reducing transmitted accelerations in a full vehicle are obtained by optimizing the gain parameters of an active control in a roughness road profile.

For a classically designed linear quadratic regulator (LQR) control, the vibration attenuation performance will depend on weighting matrices Q and R. A methodology is proposed in this work to determine the optimal elements of these matrices by using a genetic algorithm method to get enhanced controller performance. The active control is implemented in an eight degrees of freedom (8-DOF) vehicle suspension model, subjected to a standard ISO road profile. The control performance is compared against a controlled system with few Q and R parameters, an active system without optimized gain matrices, and an optimized passive system.

The control with 12 optimized parameters for Q and R provided the best vibration attenuation, reducing significantly the Root Mean Square (RMS) accelerations at the driver’s seat and car body.

The research has positive implications in a wide class of active control systems, especially those based on a LQR, which was verified by the multibody dynamic systems tested in the paper.

Better active control gains can be devised to improve performance in vibration attenuation.

The main contribution proposed in this work is the improvement of the Q and R parameters simultaneously, in a full 8-DOF vehicle model, which minimizes the driver’s seat acceleration and, at the same time, guarantees vehicle safety.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

The purpose of this paper is to propose a new algorithm for pendulum‐like oscillation control of an unmanned rotorcraft (UR) in a reconnaissance mission and improve the stabilizing performance of the UR's hover and stare.

The algorithm is based on linear‐quadratic regulator (LQR), of which the determinable parameters are optimized by the artificial bee colony (ABC) algorithm, a newly developed algorithm inspired by swarm intelligence and motivated by the intelligent behaviour of honey bees.

The proposed algorithm is tested in a UR simulation environment and achieves stabilization of the pendulum oscillation in less than 4s.

The presented algorithm and design strategy can be extended for other types of complex control missions where relative parameters must be optimized to get a better control performance.

The ABC optimized control system developed can be easily applied to practice and can safely stabilize the UR during hover and stare, which will considerably improve the stability of the UR and lead to better reconnaissance performance.

This research presents a new algorithm to control the pendulum‐like oscillation of URs, whose performance of hover and stare is a key issue when carrying out new challenging reconnaissance missions in urban warfare. Simulation results show that the presented algorithm performs better than traditional methods and the design process is simpler and easier.

The main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical physics and astrophysics.

This method is based on a combination of Chebyshev interpolation and standard variational iteration method (VIM) and matching it to a sequence of subintervals. Unlike the spectral method and the VIM, the proposed PSVIM does not require the solution of any linear or nonlinear system of equations and analytical integration.

Some well-known classes of Lane-Emden type equations are solved as examples to demonstrate the accuracy and easy implementation of this technique.

In this paper, a new and efficient technique is proposed to solve the nonlinear Lane-Emden equations. The proposed method overcomes the difficulties arising in calculating complicated and time-consuming integrals and terms that are not needed in the standard VIM.

The purpose of this paper was to present the process of building hardware and software for a collision avoidance system of a quadrotor capable of an indoor autonomous flight.

The system development was carried out in two steps. First, the quadrotor system was designed to mount mission equipments for an indoor flight. The prediction error minimization (PEM) method was used for system identification of the quadrotor, and the linear quadratic regulator (LQR) control method was used for the attitude control. Second, a collision detection system was realized by using a Kinect sensor, an embedded board and a ground control system (GCS). A Kinect sensor with embedded board can send the 3D depth information to GCS and then the GCS displays the 3D depth information with a warning message.

As the controller design requires a linear model, the PEM method was used in system identification. The LQR was used in controller design. It was found that the use of the PEM method for system identification was effective for developing a linear model required for a practical control system using LQR. As 3D depth information from a Kinect sensor is quite accurate in an indoor environment, a collision detection system with Kinect was successfully developed.

The step-by-step approach presented in this paper can be used to develop an autonomous aerial vehicle capable of navigating in an indoor environment with obstacles.

The primary contribution of the paper is the presentation of a practical method for developing a low-cost collision avoidance system for a quadrotor vehicle.