This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive...This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.展开更多
In this paper, we study the notion of the enlarged observability for distributed parabolic systems, where the aim is to reconstruct the initial state between two prescribed profiles P1 and P2 in an internal subregion ...In this paper, we study the notion of the enlarged observability for distributed parabolic systems, where the aim is to reconstruct the initial state between two prescribed profiles P1 and P2 in an internal subregion c0 of the evolution domain f2. We give some definitions and properties of this concept, and then we solve the problem of the reconstruction of initial state using the Hilbert Uniqueness Method （HUM）. This leads to several interesting results which are performed through numerical example and simulations.展开更多
In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality ...In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.展开更多
The approach of available transfer capability （denoted as ATC） incorporating wind generation has been paid very high attention since the development of wind generation. Based on the maximum function, this paper pres...The approach of available transfer capability （denoted as ATC） incorporating wind generation has been paid very high attention since the development of wind generation. Based on the maximum function, this paper presents an ATC model. The characteristic of the new model is twofold. First, it considers wind turbines connected to power system and static security of power system simultaneously. Second, it is a system of semismooth equations and can be solved easily. By using the smoothing strategy, a smoothing Newton method is adopted for solving the proposed new ATC model. Numerical simulation results of the IEEE 30-bus and 118-bus system show that the new model and algorithm are feasible and effective. The impact of wind turbines connected to power system on ATC is also analyzed.展开更多
文摘This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.
文摘In this paper, we study the notion of the enlarged observability for distributed parabolic systems, where the aim is to reconstruct the initial state between two prescribed profiles P1 and P2 in an internal subregion c0 of the evolution domain f2. We give some definitions and properties of this concept, and then we solve the problem of the reconstruction of initial state using the Hilbert Uniqueness Method （HUM）. This leads to several interesting results which are performed through numerical example and simulations.
文摘In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871031, 10926189, the Natural Science United Foundation of Hunan-Hengyang under Grant No. 10JJS008, and the Educational Department of Hunan under Grant No. 10A015
文摘The approach of available transfer capability （denoted as ATC） incorporating wind generation has been paid very high attention since the development of wind generation. Based on the maximum function, this paper presents an ATC model. The characteristic of the new model is twofold. First, it considers wind turbines connected to power system and static security of power system simultaneously. Second, it is a system of semismooth equations and can be solved easily. By using the smoothing strategy, a smoothing Newton method is adopted for solving the proposed new ATC model. Numerical simulation results of the IEEE 30-bus and 118-bus system show that the new model and algorithm are feasible and effective. The impact of wind turbines connected to power system on ATC is also analyzed.
