Optimal control over a second-order dynamical system
DOI:
https://doi.org/10.15407/dopovidi2015.05.035Keywords:
method of Lagrange multipliers, necessary conditions of optimality, optimal control, quadratic functional, system of differential Riccati equationsAbstract
The problem of minimization of the quadratic functional on solutions of the system of differential equations of the second order is considered. The method of Lagrange multipliers is applied to research the formulated optimization problem. Such approach has given a chance to obtain necessary conditions of optimality. On the basis of these conditions, the system of differential Riccati equations is deduced. The solution of this system permits us to write the closed formula for optimal control.
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