One of the main problems of symbolic regression methods is how to encode mathematical expressions to make the structure concise and readable. Here we address to the problem of network operator's matrix scarcity, which we resolve using python's standard types. Our approach allows to get rid of zero elements bellow the main diagonal. Moreover, we introduce new parametric variation, which helps us to tune parameters during structural evolving. We provide a description of the network operator and algorithms for finding the optimal solution using the principle of small variations of the basis solution. Our new encoding scheme and the complex functional for the group control task then described. In the experimental part we introduce a new way to apply network operator with a variable number of arguments to the group control system synthesis problem. Along with this we use for the first time individual network operators for each robot. From the experiment we can see that provided tricks lead to results that are not inferior in the case of usual network operator shared by all robots. (C) 2019 The Authors. Published by Elsevier B.V.

In this paper we consider collision avoidance at swarm regrouping, one of the fundamental problems in the field of mult-agent systems. We give each mobile robot its own optimizer which is able to search in the space of functions from variable number of arguments. Moving towards the target without outside interference a modified network operator of a particular robot represents a control function from discrepancy between current and terminal states. If some another robot arises on his way to the target, the argument base of the control function extends to the discrepancy between considering and neighboring robot's states. We use modified network operator to synthesize the control function which encoding scheme of mathematical expression is more concise compared with classical version of the method. The experimental part demonstrates strong result for a swarm of 18 robots.

Some common properties of violation of object function unimodality in optimal control problems are considered. Phase constraints and control object models for special symmetric systems are considered. It is shown that for a control problem of a group of objects, given in the form of a symmetric system of equations, for certain initial and terminal conditions the functional is not unimodal. It is claimed that for optimal control problems with non-unimodal functionals it is efficient to use evolutionary algorithms. An example of an optimal control problem for a group of symmetric objects with phase constraints resolved by evolutionary and gradient algorithms is provided.

This article is devoted to the desription of аpython library based on symbolic regression methods for control systems synthesis problem. Control sysnthesis is becoming more and more relevant, gaining particular importance in view of the rapid development of robotics. Usually, practicians and engineers apply template-type regulators when modeling, and then select optimal parameters for them. At a time when the computing power of PC’s has reached its peak, and programming languages have become extremely expressive due to the high level of abstraction and the vastness of libraries, it is better to implement the synthesis in the form of a library. Python was chosen as the language for synthesis implementation. According to the authors of the article, Python is a convenient language for programming matrix and vector calculations thanks to the numpy package. Moreover, the share of projects written in Python in the web service for hosting Github has been steadily increasing recently, which indicates the support of the language from the developer community. This article describes how to use the package to solve the problem of control synthesis. The authors provide the description of the symbolic regression method, the network operator and algorithms for finding the optimal solution using the principle of small variations of the basic solution. In the experimental part of the article, an example of how to use the library to solve the problem of synthesis of control of a mobile robot moving on a planewith obstacles is considered.