Assessment of He's Homotopy Perturbation Method for Optimal Control of Linear Time-Delay Systems
نویسندگان
چکیده
This paper renders an optimal regulator for a system with state time-delay and quadratic performance index. First, by means of Maximum Principle and necessary optimal conditions, a continues-time two-point boundary-value problem (TPBVP) including both time-delay and time-advance is derived. Then, using Homotopy Perturbation Method (HPM), the obtained TPBVP is transformed into a sequence of linear time-invariant TPBVP without any time-delay or timeadvance. Solving the resulted linear TPBVP sequence in a recursive manner, concludes that the optimal control law in the form of rapid convergent series. At the end, an iterative algorithm with low complexity in computation and fast convergence rate is proposed to achieve an accurate enough suboptimal control law. It's worth noting that simulation based on application of a harmonic oscillator is conducted to demonstrate efficiency of this method.
منابع مشابه
Solving the non linear system of third order boundary value problems by using He's homotopy perturbation method
متن کامل
Application of He's homotopy perturbation method for solving Sivashinsky equation
In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient and quite accurateto systems of nonlinear partial differential equations.
متن کاملModified homotopy perturbation method for solving non-linear oscillator's equations
In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...
متن کاملStability Analysis of a Strongly Displacement Time-Delayed Duffing Oscillator Using Multiple Scales Homotopy Perturbation Method
In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...
متن کاملA Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation ethod for Linear and Non-Linear Newell-Whitehead-Segel Equations
In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012