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|Title||Solving Quadratic Optimal Control Problems Using Legendre Scaling Function and Iterative Technique|
During the last three decades several approximation techniques based on the property of functions orthogonality were proposed to solve different classes of optimal control problems (OCPS). The methods used to solve OCPS are classified into two types: the direct methods are discretization and parameterization while indirect methods are Caley-Hamilton and Euler-Lagrange. The direct parameterization methods are classified into three ways control parameterization, state parameterization, and state-control parameterization. The proposed method in this thesis uses state-control parameterization via Legendre scaling function in which OCPS is converted into quadratic programming. In addition, when OCP in quadratic form, it is easy to solve it by using any software package like MATLAB, Mathmatica, or Maple. The optimal control problems investigated in this thesis deals with linear time invariant (LTI) systems, linear time varying (LTV) systems, and nonlinear systems. The LTI and LTV problems were parameterized based on the Legendre scaling function such that the cost function and the constraints are casted in terms of state and control parameters while, complex nonlinear OCPS can be solved by proposed method after converted to a sequence of time varying problem using iterative technique. To demonstrate applicability and effectiveness of the proposed technique various numerical examples are solved and the results are better when compared with other methods.
|Publisher||the islamic university|
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