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Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Intelligent Control and Automation 2012年第1期3卷 20-25页

作者： fateme ghomanjani Department of Applied Mathematics Ferdowsi University of Mashhad Iran

Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedule these injections effectively and/or how to apply drugs in a way to decrease toxic side effects of drugs such that the tumor growth to be stopped or at least to be limited. Here, the theory of optimal control has been applied to find the optimal schedule of injections of an immunotherapeutic agent against cancer. The numerical method employed works for any dynamic linear system and has almost precise solution. In this work, it was tested for a well known model of the tumor immune system interaction.

关键词： Immunotherapy Bezier Control Points Constrained Optimal Control

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Variational Iterative Method Applied to Variational Problems with Moving Boundaries

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Applied Mathematics 2012年第5期3卷 395-402页

作者： fateme ghomanjani Sara Ghaderi Department of Applied Mathematics Ferdowsi University of Mashhad Mashhad Iran

In this paper, He’s variational iterative method has been applied to give exact solution of the Euler Lagrange equation which arises from the variational problems with moving boundaries and isoperimetric problems. In this method, general Lagrange multipliers are introduced to construct correction functional for the variational problems. The initial approximations can be freely chosen with possible unknown constant, which can be determined by imposing the boundary conditions. Illustrative examples have been presented to demonstrate the efficiency and applicability of the variational iterative method.

关键词： Variational Iterative Method Variational Problems Moving Boundaries Isoperimetric Problems

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The Bezier Control Points Method for Solving Delay Differential Equation

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Intelligent Control and Automation 2012年第2期3卷 188-196页

作者： fateme ghomanjani Mohammad Hadi Farahi Department of Applied Mathematics Ferdowsi University of Mashhad Mashhad Iran

In this paper, Bezier surface form is used to find the approximate solution of delay differential equations (DDE’s). By using a recurrence relation and the traditional least square minimization method, the best control points of residual function can be found where those control points determine the approximate solution of DDE. Some examples are given to show efficiency of the proposed method.

关键词： Bezier Control Points Delay Differential Equation Residual Function Boundary Value Problem Proportional Delays

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Solving the Optimal Control of Linear Systems via Homotopy Perturbation Method

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Intelligent Control and Automation 2012年第1期3卷 26-33页

作者： fateme ghomanjani Sara Ghaderi Mohammad Hadi Farahi Department of Applied Mathematics Ferdowsi University of Mashhad Mashhad Iran

In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter , which is considered as a “small parameter”. Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method.

关键词： Homotopy Perturbation Method Optimal Control Problem Hamilton System

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