Elizaveta Shmalko

The paper presents new results of applying symbolic machine learning methods to automate the development of a control system as applied to a collaborative multi-agent system. The article proposes an original mathematical formulation of the problem of optimal control of a collaborative multi-agent system, where collaboration implies joint activity of robots and humans in a single complex phase space to achieve the control goal with the optimal value of a given quality criterion. The presented formulation proposes to consider the role of a human in the form of phase constraints with uncertainty and an additional control vector, with the help of which the influence of these phase constraints is reduced in terms of minimizing the functional. The solution to the problem is a multidimensional control function that transfers a technical object, a group of mobile robots, to the target state, taking into account possible uncertainties in the state of the object, while minimizing the specified quality criterion of the process. The task is to automatically find both the optimal structure and the parameters of the control function. Such a general statement of the control problem cannot be solved directly by existing analytical methods due to its complexity and requires a lot of manual work to select the appropriate controllers and optimally adjust their parameters. The paper proposes an approach based on symbolic machine learning using symbolic regression and evolutionary optimization to solve such a generalized problem. The effectiveness of the approach is demonstrated by numerical experiments. An example of an optimal control problem for three mobile robots with two controlled phase constraints is given. The applied problem is considered in a general mathematical statement, which allows using universal methods of symbolic machine learning to automatically find a solution.

Symbolic regression methods are becoming increasingly popular and they are a worthy competitor to neural networks in many tasks. However, symbolic regression methods have the greatest promise in those problems where there is no training sample and it is necessary to search for a solution to a machine learning problem only on the basis of some given general quality criterion. A wide class of such problems includes control synthesis problems. Machine learning control tasks consist in searching for a vector- function of control according to some criterion. As a rule, there is no training sample for such tasks, except to approximate the operator's actions. However, this approach is unlikely to satisfy the given criterion. Some symbolic regression methods have already shown good results in control problems. But the complexity of the tasks reveals the need to develop new approaches and modifications of existing methods. In this regard, a benchmark of machine learning control problems is proposed to test symbolic regression methods. Problem formulations and reference solutions are presented.

The development of artificial intelligence systems assumes that a machine can independently generate an algorithm of actions or a control system to solve the tasks. To do this, the machine must have a formal description of the problem and possess computational methods for solving it. This article deals with the problem of optimal control, which is the main task in the development of control systems, insofar as all systems being developed must be optimal from the point of view of a certain criterion. However, there are certain difficulties in implementing the resulting optimal control modes. This paper considers an extended formulation of the optimal control problem, which implies the creation of such systems that would have the necessary properties for its practical implementation. To solve it, an adaptive synthesized optimal control approach based on the use of numerical methods of machine learning is proposed. Such control moves the control object, optimally changing the position of the stable equilibrium point in the presence of some initial position uncertainty. As a result, from all possible synthesized controls, one is chosen that is less sensitive to changes in the initial state. As an example, the optimal control problem of a quadcopter with complex phase constraints is considered. To solve this problem, according to the proposed approach, the control synthesis problem is firstly solved to obtain a stable equilibrium point in the state space using a machine learning method of symbolic regression. After that, optimal positions of the stable equilibrium point are searched using a particle swarm optimization algorithm using the source functional from the initial optimal control problem statement. It is shown that such an approach allows for generating the control system automatically by computer, basing this on the formal statement of the problem and then directly implementing it onboard as far as the stabilization system has already been introduced.

The development of artificial intelligence systems assumes that a machine can independently generate an algorithm of actions or a control system to solve the tasks. To do this, the machine must have a formal description of the problem and possess computational methods for solving it. The article deals with the problem of optimal control, which is the main task in the development of control systems, insofar as all systems being developed must be optimal from the point of view of a certain criterion. However, there are certain difficulties in implementing the resulting optimal control modes. The paper considers an extended formulation of the optimal control problem, which implies the creation of such systems that would have the necessary properties for its practical implementation. To solve it, an adaptive synthesized optimal control approach based on the use of numerical methods of machine learning is proposed. The method moves the control object, optimally changing the position of the stable equilibrium point in the presence of some initial position uncertainty. As a result, from all possible synthesized controls, he chooses one that is less sensitive to changes in the initial states. As an example, the optimal control problem of quadcopter with complex phase constraints is considered. To solve this problem? according to the proposed approach, the control synthesis problem is firstly solved to obtain a stable equilibrium point in the state space by a machine learning method of symbolic regression. After that optimal positions of the stable equilibrium point are searched according to source functional from the optimal control problem by particle swarm optimization algorithm. It is shown that such approach allows generating the control system automatically by computer basing on the formal statement of the problem and then directly implementing it onboard as far as they have already had a stabilization system inserted.

Autonomous navigation is one of the key tasks in the development of control systems for real autonomous mobile objects. This paper presents the developed technology for accurately determining the position of a mobile robot in an autonomous operating mode without an external positioning system. The approach involves using a high-precision model of a real robot identified by a neural network. The robot adjusts its position, determined using odometry and video camera, according to the position of the robot, obtained using an accurate model. To train the neural network, a training set is used that takes into account the features of the movement of a wheeled robot, including wheel slip. In the experimental part, the problem of autonomous movement of a mobile robot along a given trajectory is considered.

This paper considers the difficulties that arise in the implementation of solutions to the optimal control problem. When implemented in real systems, as a rule, the object is subject to some perturbations, and the control obtained as a function of time as a result of solving the optimal control problem does not take into account these factors, which leads to a significant change in the trajectory and deviation of the object from the terminal goal. This paper proposes to supplement the formulation of the optimal control problem. Additional requirements are introduced for the optimal trajectory. The fulfillment of these requirements ensures that the trajectory remains close to the optimal one under perturbations and reaches the vicinity of the terminal state. To solve the problem, it is proposed to use numerical methods of machine learning based on symbolic regression. A computational experiment is presented in which the solutions of the optimal control problem in the classical formulation and with the introduced additional requirement are compared.