Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator

This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.

Feedback control of nonlinear differential algebraic systems using Hamiltonian function method

The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR） structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.

Robust excitation control of multi-machine multi-load power systems using Hamiltonian function method

Using an energy-based Hamiltonian function method,this paper investigates the robust excitation control of multi-machine multi-load power systems described by a set of uncertain differential algebraic equations.First,we complete the dissipative Hamiltonian realization of the power system and adjust its operating point by the means of pre-feedback control.Then,based on the obtained Hamiltonian realization,we discuss the robust excitation control of the power system and put forward an H1 excitation control strategy.Simulation results demonstrate the effectiveness of the control scheme.

A numerical method for the solutions of the HIV infection model of CD4＋ T-cells

In this paper, the human immunodeficiency virus （HIV） infection model of CD4＋ T-cells is considered. In order to numerically solve the model problem, an operational method is proposed. For that purpose, we construct the operational matrix of integration for bases of Taylor polynomials. Then, by using this matrix operation and approximation by polynomials, the HIV infection problem is transformed into a system of algebraic equations, whose roots are used to determine the approximate solutions. An important feature of the method is that it does not require collocation points. In addition, an error estimation technique is presented. We apply the present method to two numerical examples and compare our results with other methods.

Decentralized robust control of multiple static var compensators via Hamiltonian function method

Using the energy-based Hamiltonian function method, this paper investigates the decentralized robust nonlinear control of multiple static var compensators （SVCs） in multimachine multiload power systems. First, the uncertain nonlinear differential algebraic equation model is constructed for the power system. Then, the dissipative Hamiltonian realization of the system is completed by means of variable transformation and prefeedback control. Finally, based on the obtained dissipative Hamiltonian realization, a decentralized robust nonlinear controller is put forward. The proposed controller can effectively utilize the internal structure and the energy balance property of the power system. Simulation results verify the effectiveness of the control scheme.