|1Kopets, MM |
1National Technical University of Ukraine "Kyiv Polytechnic Institute"
|Dopov. Nac. akad. nauk Ukr. 2015, 5:35-39|
|Section: Information Science and Cybernetics|
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.
|Keywords: method of Lagrange multipliers, necessary conditions of optimality, optimal control, quadratic functional, system of differential Riccati equations|
- Letov A.M. Flight dynamics and control, Moscow: Nauka, 1969 (in Russian)
- Kopets M.M. The optimal control problem by process of vibration of string, in Theory of Optimal Solutions, Kyiv: Istitute of Cybernatics of the NAS of Ukraine, 2014: 32–38 (in Ukrainian).
- Chikrii A.A. Conflict-controlled processes, Kyiv: Naukova Dumka, 1992 (in Russian).
- Chikrii A.A., Eidel'man S.D. Cybernetics and Systems Analysis, 2012, No 6: 66–99.
- Eidel'man S.D., Chikrii A.A. Ukr. Math. J., 2000, 52, No 11: 1566–1583. https://doi.org/10.1023/A:1010439422856