Abstract
We consider the information constrained optimization problem for stochastic dynamical systems governed by quasi-linear Ito equations. Let us describe the information constraints. We suppose that each control vector component depends on a prespecified set of precisely measured state vector components. In this article we present an algorithm for synthesis of the suboptimal control law. This control law is the linear feedback regulator. The linear parameter and the constant term of the regulator are polynomial functions of time. The algorithm is successfully applied to the problem of two-link robotic arm optimal control. These manipulators may be effectively used at space stations, e.g. for moving cargo in outer space.
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D. S. Rumyantsev and M. M. Khrustalev, “Numerical methods of synthesis of an optimal control for stochastic dynamical systems of diffusion type,” J. Comput. Syst. Sci. Int. 46, 359–370 (2007).
M. M. Khrustalev, D. S. Rumyantsev, and K. A. Tsarkov, “Galerkin method in optimization of quasi-linear dynamical stochastic systems subject to information constraints,” Trudy MI, No. 66. http://www.mai.ru/science/trudy/published.php (June 27, 2013).
D. S. Rumyantsev and M. M. Khrustalev, “Optimal control of quasi-linear systems of the diffusion type under incomplete information on the state,” J. Comput. Syst. Sci. Int. 45, 718–726 (2006).
M. M. Khrustalev, “Nash equilibrium conditions in stochastic differential games where players information about a state is incomplete: Sufficient equilibrium conditions,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 6, 194–208 (1995).
M. M. Khrustalev, “Nash equilibrium conditions in stochastic differential games where players information about a state is incomplete. II. Lagrange method,” J. Comput. Syst. Sci. Int. 35, 67–73 (1996).
V. S. Pugachev and I. N. Sinitsyn, Stochastic Differential Systems: Analysis and Filtering (Nauka, Moscow, 1990) [in Russian].
A. V. Panteleev and T. A. Letova, Optimization Methods: Examples and Problems (Vysshaya shkola, Moscow, 2005) [in Russian].
P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964; Mir, Moscow, 1970).
S. V. Lutmanov, Linear Optimization Problems. Part 2, Optimal Control of Linear Dynamic Plants (Izd. Permskogo Univ., Perm, 2005) [in Russian].
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Original Russian Text © D.S. Rumyantsev, M.M. Khrustalev, K.A. Tsarkov, 2014, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2014, No. 1, pp. 74–86.
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Rumyantsev, D.S., Khrustalev, M.M. & Tsarkov, K.A. An algorithm for synthesis of the suboptimal control law for quasi-linear stochastic dynamical systems. J. Comput. Syst. Sci. Int. 53, 71–83 (2014). https://doi.org/10.1134/S1064230714010110
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DOI: https://doi.org/10.1134/S1064230714010110