In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws...In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.展开更多
The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within...The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.展开更多
In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions....In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions.At first,the integer order model is converted to fractional order model in Caputo sense.Then,the new operator Katugampola fractional derivative is used to present the model.The new such kind of operator is illustrated in Caputo sense.HPTM is described to get the solution of the proposed model using the new kind of operator.Also,there are some analyses about the new kind of operator to prove the efficiency of the operator.展开更多
基金supported by National Natural Science Foundation of China (No. 60934007, No. 61074060)China Postdoctoral Science Foundation (No. 20090460627)+1 种基金Shanghai Postdoctoral Scientific Program (No. 10R21414600)China Postdoctoral Science Foundation Special Support (No. 201003272)
文摘In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.
基金Partially supported by a research grant from Department of Science and Technology(DST),India(No.SB/FTP/MS-003/2013)
文摘The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.
文摘In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions.At first,the integer order model is converted to fractional order model in Caputo sense.Then,the new operator Katugampola fractional derivative is used to present the model.The new such kind of operator is illustrated in Caputo sense.HPTM is described to get the solution of the proposed model using the new kind of operator.Also,there are some analyses about the new kind of operator to prove the efficiency of the operator.
