Modeling of nonlinear control object 3-th order with optimal stabilization of the final state
V. V. Afonin1, S. M. Murjumin2, A. V. Muskatinjev3
| Annotation | We consider the problem of optimal stabilization of nonlinear control objects 3-th order, described by ordinary differential equations with constant coefficients. Optimal stabilization is understood in the sense of minimization of a quadratic functional for the linearized control object. The linearization is performed at each step of numerical integration of nonlinear system of differential equations and calculated the matrix of the optimal regulator. Management in the form of state feedback is applied to non-linear object at each step of numerical integration. The results of simulation with plotting transient systems and the closed-loop optimal controller. |
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| Keywords | optimal stabilization, affine control systems, a system of ordinary differential equations, matrix optimal controller, linear-quadratic optimal control problem, feedback, the transition process, Lorenz system |
1Associate Professor in the Department of automated systems of information processing and management, Mordovian State University after N.P. Ogarev, Saransk; korspa@yandex.ru
2Associate Professor in the Department of applied mathematics, differential equations and theoretical mechanics, Mordovian State University after N.P. Ogarev, Saransk; korspa@yandex.ru
3Associate Professor in the Department of electronics and nanoelectronics, Mordovian State University after N.P. Ogarev, Saransk; muskatav@mail.ru
Citation: V. V. Afonin, S. M. Murjumin, A. V. Muskatinjev, "[Modeling of nonlinear control object 3-th order with optimal stabilization of the final state]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:2 (2015) 7–14 (In Russian)
