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A NEW APPROACH FOR ASYMPTOTIC STABILITY A SYSTEM OF THE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
Effati, Sohrab,Nazemi, Ali Reza 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.
Solving a Class of Nonlinear Optimal Control Problems via He’s Variational Iteration Method
Mohammad Shirazian,Sohrab Effati 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.2
This paper presents an analytical approximate solution for a class of nonlinear quadratic optimal control problems. The proposed method consists of a Variational Iteration Method (VIM) together with a shooting method like procedure, for solving the extreme conditions obtained from the Pontryagin’s Maximum Principle (PMP). This method is applicable for a large class of nonlinear quad-ratic optimal control problems. In order to use the proposed method, a control design algorithm with low computational complexity is presented. Through the finite iterations of algorithm, a suboptimal control law is obtained for the nonlinear optimal control problem. Two illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.
Mostafa Zarefard,Sohrab Effati 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4
In this paper, the synchronization of two non-identical bidirectional associative memory (BAM) neural networks with unknown parameters and time-varying delays is investigated. Two adaptive controllers are designed to guarantee the global asymptotic synchronization of state trajectories for two non-identical BAM neural networks. Lyapunov stability theory and Barbalat’s lemma are used to guarantee the synchronization of response and drive systems. Finally, an illustrative example is given to demonstrate the effectiveness of the presented synchronization scheme.
AN APPROACH FOR SOLVING NONLINEAR PROGRAMMING PROBLEMS
Hadi Basirzadeh,Ali Vahidian Kamyad,Sohrab Effati 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.