Quadratic Optimal Control Problems
Theory, Analytical Solutions and Numerical Computation with Conjugate Gradient Method and FICO Xpress Mosel
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This book explores quadratic optimal control problems constrained by ordinary differential equations (ODEs), integrating analytical methods with numerical optimization techniques. The analytical approach employs first-order optimality conditions on the Hamiltonian, solved through the fundamental matrix method and Riccati transformations. For numerical computation, discretization is carried out using Simpson's rule and a fifth-order implicit method, reformulated via the Augmented Lagrangian Method. Solutions are obtained using the Conjugate Gradient Method (CGM) and FICO Xpress Mosel. Comparati...
This book explores quadratic optimal control problems constrained by ordinary differential equations (ODEs), integrating analytical methods with numerical optimization techniques. The analytical approach employs first-order optimality conditions on the Hamiltonian, solved through the fundamental matrix method and Riccati transformations. For numerical computation, discretization is carried out using Simpson's rule and a fifth-order implicit method, reformulated via the Augmented Lagrangian Method. Solutions are obtained using the Conjugate Gradient Method (CGM) and FICO Xpress Mosel. Comparative analysis shows that while CGM is effective but sensitive to parameter choices, FICO Xpress Mosel offers faster and more reliable convergence, making it a robust tool for solving high-dimensional control problems.
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