Solving information constrained control problem for quasi-linear stochastic systems and the robotic arm control example

Mathematics. Physics. Mechanics


Аuthors

Rumyantsev D. S.1*, Tsarkov K. A.2**

1. Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4, M. Khariton'evskii per., Moscow, 101990, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: dima_rum@mail.ru
**e-mail: k6472@mail.ru

Abstract

In the paper, we present a constructive algorithm for synthesis of the suboptimal information constrained control law for quasi-linear stochastic dynamical systems. This algorithm can be used directly for solving applied control problems. The information constraints are described as follows. We suppose that each control vector component depends on a prespecified set of precisely measured state vector components.
The aim of this article is to concretize our new results for the efficient practical usage. We propose to construct the stochastic quasi-linear system control laws as a linear in state function such that the linear parameter and the constant term of this function are polynomial in time. This control law is called suboptimal. If an optimal control can not be constructed for some reason, then the suboptimal one can be used. So, it is very important to have an algorithm for synthesis of the suboptimal control law. In the paper, we present the algorithm based on gradient descent numerical method.
The algorithm is used to construct the suboptimal control of a two-link robotic arm. The robotic arm control process is considered as a mechanical manipulator plane movement. The goal of control is to move the manipulator to a known state. The goal must be achieved in a specified time period. In addition, the control cost must be minimized.We show that the suboptimal control can be effectively used for this problem. Despite the fact that the result is not an optimal solution, it has a simple linear regulator structure, which can be directly used to control the robotic arm. The comparison of the suboptimal performance index with the optimal one shows that the difference between these solutions is very small.

Keywords:

stochastic optimal control, quasi-linear dynamical system, information constraints, suboptimal control, two-link robotic arm

References

  1. Khrustalev M.M., Rumyantsev D.S., Tsarkov K.A. Izvestiya RAN. Teoriya i sistemy upravleniya, 2014, no. 1, pp. 74-86.
  2. Pugachjov V.S., Sinicin I.N. Stokhasticheskie differentsial’nye sistemy. Analiz i fil’tratsiya (Stochastic differential systems. Analysis and filtration), Moscow, Fizmatlit, 1990, 642 p.
  3. Rumyantsev D.S., Khrustalev M.M. Izvestiya RAN. Teoriya i sistemy upravleniya, 2006, no. 5, pp.43-51.
  4. Rumyantsev D.S., Khrustalev M.M.,Izvestiya RAN. Teoriya i sistemy upravleniya, 2007, no. 3, pp.27-38.
  5. Panteleev A.V., Letova T.A. Metody optimizatsii v primerakh i zadachakh (Optimization Methods in Examples and Tasks), Moscow,Vysshaja shkola, 2005, 544 p.
  6. Lutmanov S.V. Lineinye zadachi optimizatsii (Linear Optimization Problems), Perm, Permskii universitet, 2005, part 2, 195 p.

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