242
A. V. Panteleev and M. M. S. Karane
Table 16.8 Results of solving task 3
Optimization method
Coordinates of points
(x 1 (1.6), x 2 (1.6))
Switching point
coordinate
The value of the
functional I
Hybrid multi-agent
optimization method of
interpolation search
(3.45449, 12.87062)
1.25
−2.98082
Multi-agent optimization
algorithm using linear
regulators for agents
motion control
(3.45949, 12.87562)
1.25
−2.97832
Known solution [15]
(3.46114, 12.884)
1.26
−2.98086
Table 16.9 Results of solving task 3
Optimization method
Coordinates of points
(x 1 (1.6), x 2 (1.6))
Coefficients in
expansion c i
The value of the
functional I
Hybrid multi-agent
optimization method of
interpolation search
(3.45449, 12.87062)
0.22, 1.15
−2.98082
Multi-agent optimization
algorithm using linear
regulators for agents
motion control
(3.48523, 13.44901)
0.36, 0.99
−2.87218
The results of solving Task 3 by the search algorithm of optimal open-loop control
using switching points are presented in Table 16.8.
Solving Task 3 by the search algorithm of optimal open-loop control using expansion in a system of basis functions. The best number of coefficients in expansion:
L = 2.
Optimization method and its parameters: hybrid multi-agent optimization method
of interpolation search (N P = 30, I max = 50, M 1 = 2, M 2 = 5, P RT = 0.01,
nstep = 5, and b 2 = 8) and multi-agent optimization algorithm using linear regulators for agents motion control (N P = 101, N M AX = 50, P max = 10, k s = 1,
k l = 5, and h = 0.0001).
The results of solving Task 3 by the search algorithm of optimal open-loop control
using expansion in a system of basis functions are presented in Table 16.9.
Graphs of optimal trajectories and controls are shown in Fig. 16.9.
16.4 Conclusions
Two new multi-agent algorithms are proposed to search for optimal open-loop control
of one class of deterministic systems: the hybrid multi-agent method of interpolation search and the multi-agent method based on the use of linear regulators of
A. V. Panteleev and M. M. S. Karane
Table 16.8 Results of solving task 3
Optimization method
Coordinates of points
(x 1 (1.6), x 2 (1.6))
Switching point
coordinate
The value of the
functional I
Hybrid multi-agent
optimization method of
interpolation search
(3.45449, 12.87062)
1.25
−2.98082
Multi-agent optimization
algorithm using linear
regulators for agents
motion control
(3.45949, 12.87562)
1.25
−2.97832
Known solution [15]
(3.46114, 12.884)
1.26
−2.98086
Table 16.9 Results of solving task 3
Optimization method
Coordinates of points
(x 1 (1.6), x 2 (1.6))
Coefficients in
expansion c i
The value of the
functional I
Hybrid multi-agent
optimization method of
interpolation search
(3.45449, 12.87062)
0.22, 1.15
−2.98082
Multi-agent optimization
algorithm using linear
regulators for agents
motion control
(3.48523, 13.44901)
0.36, 0.99
−2.87218
The results of solving Task 3 by the search algorithm of optimal open-loop control
using switching points are presented in Table 16.8.
Solving Task 3 by the search algorithm of optimal open-loop control using expansion in a system of basis functions. The best number of coefficients in expansion:
L = 2.
Optimization method and its parameters: hybrid multi-agent optimization method
of interpolation search (N P = 30, I max = 50, M 1 = 2, M 2 = 5, P RT = 0.01,
nstep = 5, and b 2 = 8) and multi-agent optimization algorithm using linear regulators for agents motion control (N P = 101, N M AX = 50, P max = 10, k s = 1,
k l = 5, and h = 0.0001).
The results of solving Task 3 by the search algorithm of optimal open-loop control
using expansion in a system of basis functions are presented in Table 16.9.
Graphs of optimal trajectories and controls are shown in Fig. 16.9.
16.4 Conclusions
Two new multi-agent algorithms are proposed to search for optimal open-loop control
of one class of deterministic systems: the hybrid multi-agent method of interpolation search and the multi-agent method based on the use of linear regulators of