Optimal control design for linear-invariant linear singular systems with time using orthogonal functions

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TABATABAEE HAMID; Memari Mahdi

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Journal: DECISIONS AND OPERATIONS RESEARCH Year:2019 | Volume:4 | Issue:3 Page(s): 262-275

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Title

Optimal control design for linear-invariant linear singular systems with time using orthogonal functions

Author(s)

TABATABAEE HAMID | Memari Mahdi | Issue Writer Certificate

Keywords

Optimal control

Orthogonal functions

Singular matrix

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Abstract

The problem of solving Optimal control of Singular problems in the classic method has a complexity that is solved by approximation of the equations in the problem with orthogonal bases instead of solving the dynamic equation system of a set of static problems. In return for a more relaxed solution, it will face some errors in the computation. however, it has an appropriate precision. Legendre and Fourier series are presented using the specifications of the Fourier transform of Legendre and Fourier series. In this algorithm, the state variables, and the state-derivative variables and the control vector are extended by the orthogonal basis of Legendre and Fourier series with unknown coefficients. in order to compute Optimal control vector and optimal path of linear Singular systems with quadratic cost function, we are introduced by using the properties of Orthogonal functions introduced by the coefficients and. using the proposed method, the system dynamics are converted into algebraic equations and the problem of dynamic optimization of dynamic space has been mapped to static space optimization problem with quadratic cost function and linear constraints. First, it is used to solve the problem using an orthogonal basis of raw material and then the problem solving with orthogonal basis of Fourier series is repeated. Finally, the application and effectiveness of the proposed method are presented.

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APA: Copy

TABATABAEE, HAMID, & Memari, Mahdi. (2019). Optimal control design for linear-invariant linear singular systems with time using orthogonal functions. DECISIONS AND OPERATIONS RESEARCH, 4(3 ), 262-275. SID. https://sid.ir/paper/268888/en

Vancouver: Copy

TABATABAEE HAMID, Memari Mahdi. Optimal control design for linear-invariant linear singular systems with time using orthogonal functions. DECISIONS AND OPERATIONS RESEARCH[Internet]. 2019;4(3 ):262-275. Available from: https://sid.ir/paper/268888/en

IEEE: Copy

HAMID TABATABAEE, and Mahdi Memari, “Optimal control design for linear-invariant linear singular systems with time using orthogonal functions,” DECISIONS AND OPERATIONS RESEARCH, vol. 4, no. 3 , pp. 262–275, 2019, [Online]. Available: https://sid.ir/paper/268888/en

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