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Solving infinite horizon nonlinear optimal control problems using an extended modal series method

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Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第8期12卷 667-677页

作者： Amin JAJARMI Naser PARIZ sohrab effati Ali VAHIDIAN KAMYAD Advanced Control and Nonlinear Laboratory Department of Electrical EngineeringFerdowsi University of Mashhad Department of Applied Mathematics Faculty of Mathematical SciencesFerdowsi University of Mashhad

This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant *** the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent ***,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are *** efficient algorithm is also presented,which has low computational complexity and a fast convergence *** a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear *** results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.

关键词： Infinite horizon nonlinear optimal control problem Pontryagin’s maximum principle Two-point boundary value problem Extended modal series method

Solving the Interval-Valued Linear Fractional Programming Problem

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American Journal of Computational Mathematics 2012年第1期2卷 51-55页

作者： sohrab effati Morteza Pakdaman Department of Applied Mathematics Ferdowsi University of Mashhad Mashhad Iran

This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.

关键词： Interval-Valued Function Linear Fractional Programming Interval-Valued Linear Fractional Programming

Artificial Neural Networks Approach for Solving Stokes Problem

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Applied Mathematics 2010年第4期1卷 288-292页

作者： Modjtaba Baymani Asghar Kerayechian sohrab effati 不详

In this paper a new method based on neural network has been developed for obtaining the solution of the Stokes problem. We transform the mixed Stokes problem into three independent Poisson problems which by solving them the solution of the Stokes problem is obtained. The results obtained by this method, has been compared with the existing numerical method and with the exact solution of the problem. It can be observed that the current new approximation has higher accuracy. The number of model parameters required is less than conventional methods. The proposed new method is illustrated by an example.

关键词： Artificial Neural Networks Stokes Problem Poisson Equation Partial Differential Equations

Maximizing of Asymptomatic Stage of Fast Progressive HIV Infected Patient Using Embedding Method

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Intelligent Control and Automation 2010年第1期1卷 48-58页

作者： Hassan Zarei Ali Vahidian Kamyad sohrab effati Department of Applied Mathematics Ferdowsi University of Mashhad

A system of ordinary differential equations, which describe various aspects of the interaction of HIV with healthy cells in fast progressive patient, is utilized, and an optimal control problem is constructed to prolong survival and delay the progression to AIDS as far as possible, subject to drug costs. Optimal control problem is approximated by linear programming model using measure theoretical approach and suboptimal combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies are proposed. The Comparison of healthy CD4+ Tcells counts, virus particles and immune response, before and after the treatment is introduced.

关键词： HIV Model Optimal Control Measure Theory Linear Programming

Embedding-Based Sliding Mode Control for Linear Time Varying Systems

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Applied Mathematics 2011年第4期2卷 487-495页

作者： Mohammad Reza Zarrabi Mohammad Hadi Farahi Ali Jafar Koshkouei sohrab effati Keith Burnham 不详

In this paper, a novel strategy using embedding process and sliding surface is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a sliding surface in the minimum time, and then tends to the origin along the sliding surface (SS). In the first, a SS is designed, then using an appropriate measure, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, after that a control is designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of sliding mode controls (SMCs) is a phenomenon, the so-called chattering. The proposed SMC here is piecewise continuous and chattering free. Some numerical examples is presented to illustrate the effectiveness and reliability of the proposed method.

关键词： Time Optimal Control Problem Measure Theory Sliding Mode Control Sliding Surface Design Equivalent Control