Chapter 16
Application of Multi-agent Optimization
Methods Based on the Use of Linear
Regulators and Interpolation Search
for a Single Class of Optimal
Deterministic Control Systems
Andrei V. Panteleev and Maria Magdalina S. Karane
Abstract Two new multi-agent algorithms for controlling one class of deterministic
systems are proposed: the hybrid multi-agent method of interpolation search and
multi-agent method based on the use of linear regulators of agent movement control.
Detailed descriptions of the strategies of these methods are given, and step-by-step
algorithms for each multi-agent method are described. Since multi-agent algorithms
are used to find optimal control of dynamic systems, step-by-step algorithms for
finding optimal open-loop control using multi-agent methods are also given. Two
approaches to the search for optimal open-loop control are considered: when control
is sought in relay form with a certain number of switches and when control is sought
in the form of an expansion in a system of basis functions. In this chapter, cosine
curves were considered as basis functions. Based on the above algorithms, software
has been formed that allows finding the optimal open-loop control. Recommended
parameters are given for each multi-agent algorithm. To study the effectiveness of
the above algorithms, a specially selected set of test problems for finding the optimal
open-loop control is solved, where the model of the control object is described by
an ordinary differential equation linear in bounded control. During the study, it was
shown that the described algorithms successfully cope with the task and can find a
solution close to the exact one.
A. V. Panteleev · M. M. S. Karane (B)
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow
125993, Russian Federation
e-mail: mmarselina@mail.ru
A. V. Panteleev
e-mail: avpanteleev@inbox.ru
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_16
217
Application of Multi-agent Optimization
Methods Based on the Use of Linear
Regulators and Interpolation Search
for a Single Class of Optimal
Deterministic Control Systems
Andrei V. Panteleev and Maria Magdalina S. Karane
Abstract Two new multi-agent algorithms for controlling one class of deterministic
systems are proposed: the hybrid multi-agent method of interpolation search and
multi-agent method based on the use of linear regulators of agent movement control.
Detailed descriptions of the strategies of these methods are given, and step-by-step
algorithms for each multi-agent method are described. Since multi-agent algorithms
are used to find optimal control of dynamic systems, step-by-step algorithms for
finding optimal open-loop control using multi-agent methods are also given. Two
approaches to the search for optimal open-loop control are considered: when control
is sought in relay form with a certain number of switches and when control is sought
in the form of an expansion in a system of basis functions. In this chapter, cosine
curves were considered as basis functions. Based on the above algorithms, software
has been formed that allows finding the optimal open-loop control. Recommended
parameters are given for each multi-agent algorithm. To study the effectiveness of
the above algorithms, a specially selected set of test problems for finding the optimal
open-loop control is solved, where the model of the control object is described by
an ordinary differential equation linear in bounded control. During the study, it was
shown that the described algorithms successfully cope with the task and can find a
solution close to the exact one.
A. V. Panteleev · M. M. S. Karane (B)
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow
125993, Russian Federation
e-mail: mmarselina@mail.ru
A. V. Panteleev
e-mail: avpanteleev@inbox.ru
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_16
217