Exact solution of the one-dimensional Klein-Gordon equation with scalar and vector linear potentials in the presence of a minimal length

Using the momentum space representation, we solve the Klein--Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterized by a finite minimal uncertainty in position. The expressions of bound state energies and the associated wave functions are exactly obtained.

Global robust optimal sliding mode control for uncertain affine nonlinear systems

The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.

A sliding-mode variable-structure controller based on exact feedback linearization for automatic navigation system

In order to improve the path tracking accuracy and robustness of the agricultural machinery navigation system,a sliding-mode variable-structure controller based on exact feedback linearization was presented.Firstly,based on the differential geometry theory and the affine nonlinear kinematics model,the corresponding nonlinear coordinate change matrix and nonlinear state variable feedback equations were deduced,and an exact feedback linearization model was then established.Secondly,based on the exact feedback linearization model,a sliding-mode variable-structure controller was designed by selecting suitable linear switching function and exponential reaching law.Finally,the comparative experiments were carried out.And the experimental results indicated that the proposed method had a high tracking accuracy and robustness.The maximum lateral error of the straight line tracking was less than 0.06 m,and maximum lateral error of the curve path tracking was less than 0.09 m.Experimental results show that the transplanter based on this automatic navigation system can effectively track the predefined path.

Finite-time State Feedback Stabilization Method for a Class of Flexible Manipulators

Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.

Data-driven Power Flow Method Based on Exact Linear Regression Equations

Power flow(PF)is one of the most important calculations in power systems.The widely-used PF methods are the Newton-Raphson PF(NRPF)method and the fast-decoupled PF(FDPF)method.In smart grids,power generations and loads become intermittent and much more uncertain,and the topology also changes more frequently,which may result in significant state shifts and further make NRPF or FDPF difficult to converge.To address this problem,we propose a data-driven PF(DDPF)method based on historical/simulated data that includes an offline learning stage and an online computing stage.In the offline learning stage,a learning model is constructed based on the proposed exact linear regression equations,and then the proposed learning model is solved by the ridge regression(RR)method to suppress the effect of data collinearity.In online computing stage,the nonlinear iterative calculation is not needed.Simulation results demonstrate that the proposed DDPF method has no convergence problem and has much higher calculation efficiency than NRPF or FDPF while ensuring similar calculation accuracy.

Exact investigation of the electronic structure and the linear and nonlinear optical properties of conical quantum dots

Intersubband linear and third-order nonlinear optical properties of conical quantum dots with infinite barrier potential are studied. The electronic structure of conical quantum dots through effective mass approximation is determined analytically. Linear, nonlinear, and total absorption coefficients, as well as the refractive indices of GaAs conical dots, are calculated. The effects of the size of the dots and of the incident electromagnetic field are investigated. Results show that the total absorption coefficient and the refractive index of the dots largely depend on the size of the dots and on the intensity and polarization of the incident electromaenetic field.

The Dynamics Characteristics of Flexible Spacecraft and Its Closed-Loop Stability with Passive Control

Passive control is the most popular methodology for flexible spacecraft while it remains an open problem whether the closed-loop performance can be achieved only with passive control subject to the coupling modes of rigid and flexibility.Also,the closed-loop performance of passive PD control based on the dynamics of the Euler angle parameterization of spacecraft,which has been widely used in practice,is yet to be addressed.Towards these challenges,by introducing the input-output exact linearization theory and Lyapunov theory,the authors show that the closed-loop performance for flexible spacecraft with rigid and flexible modes can be achieved by adjusting the parameters of the passive controllers sufficiently large.This is done by firstly transforming the flexible spacecraft dynamics into an exact feedback linearization standard form,and then analyzing the closed-loop performance of flexible spacecraft.

H_∞ Control of a 5th- order Model of Synchronous Generators

：This paper deals with H∞ control of a 5th-order model of synchronous generators. First,byusing the method of exact linearization, we transform the 5th-order model into a linear one. Then we assignthe pole of the linearized model in the open left half plane. Finally, we apply the design method of linear H∞control to get a state feedback controller.