A.M. Abbasov, F.A. Aliev, N.S. Hajiyeva.
Sweep method for solution of linear quadratic optimization problem with constraint in the form of equalities on control
In the article the linear quadratic optimization problem with boundary condition is investigated. Here in a certain part of time interval some coordinates of control action are known constants. An extended functional corresponding to the given quadratic functional is constructed and the Euler-Lagrange equation with boundary conditions is obtained. Using sweep method the given linear quadratic optimization problem has been solved and the control actions and the corresponding program trajectory on each part of the time interval have been constructed. The results are illustrated using the example of the vertical motion of a flying vehicle.
Keywords: Linear quadratic optimization problem, Euler-Lagrange equation, Sweep method, Control action, Optimal program trajectory, The system of linear algebraic equation, Matrix algebraic Riccati equations, Flying object, AMS Subject Classification: 49M25, 49N20
DOI: https://doi.org/10.54381/icp.2024.1.01
Sweep method for solution of linear quadratic optimization problem with constraint in the form of equalities on control
In the article the linear quadratic optimization problem with boundary condition is investigated. Here in a certain part of time interval some coordinates of control action are known constants. An extended functional corresponding to the given quadratic functional is constructed and the Euler-Lagrange equation with boundary conditions is obtained. Using sweep method the given linear quadratic optimization problem has been solved and the control actions and the corresponding program trajectory on each part of the time interval have been constructed. The results are illustrated using the example of the vertical motion of a flying vehicle.
Keywords: Linear quadratic optimization problem, Euler-Lagrange equation, Sweep method, Control action, Optimal program trajectory, The system of linear algebraic equation, Matrix algebraic Riccati equations, Flying object, AMS Subject Classification: 49M25, 49N20
DOI: https://doi.org/10.54381/icp.2024.1.01