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Analysis Study Research Paper | Mathematics and Statistics | Ghana | Volume 12 Issue 7, July 2023 | Popularity: 5.3 / 10
Comprehensive Semi-Analytical Approach to Quadratic Optimal Control Problems Governed by Ordinary Differential Equations
Monica Veronica Crankson, Ayodeji Sunday Afolabi, Solomon Eshun
Abstract: The primary focus of this research is on a semi-analytical method for solving a generalized quadratic optimal control problem constrained by Ordinary Differential Equation (ODE). The solutions are obtained by applying the first order optimality conditions on the Hamiltonian function, which is a necessary condition for optimality. The Adomian Decomposition Method (ADM), which views the approximation of a non-linear equation as an infinite series that typically converges to the exact solution, is used to solve the associated general Riccati differential equation. This leads to the optimal state, control and adjoint variables which yields the optimal objective functional value. Solutions to two examples of optimal control problems constrained by ODE are given.
Keywords: Optimal Control, Semi-analytical Solution, Adomian Decomposition Method, Ordinary Differential Equation, Ricatti Differential Equation
Edition: Volume 12 Issue 7, July 2023
Pages: 2059 - 2068
DOI: https://www.doi.org/10.21275/SR23727003411
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