The small parameter method for solving the problem of optimal stabilization
of systems with random structure and random jumps of the phase vector
Author(s):
Tatyana Viktorovna Zavyalova
National Research Technological University (MISiS),
Moscow, Leninsky Prospect, 6, bld. 7
cand. phys.-mat. sciences, associate professor
tzava@yandex.ru
Abstract:
The paper considers a linear-quadratic optimal control problem
for a system with a random structure. System parameters are exposed
to a purely discontinuous Markov process with given transition probabilities.
It is assumed that at a random time, structural state of the system changes
and its phase vector changes abruptly. Earlier, the conditions
for finding the optimal control in the form of integral matrix equations
were obtained by V.Buhalev. But these equations are cumbersome for practical use.
In this paper we consider the construction of optimal control using the small
parameter method, which allows us to construct tyhe control in the form of
a convergent series in powers of a small parameter.
Keywords
- jumps of the phase vector
- Markov random process
- optimal control
- random structure systems
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