In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

A method for synthesizing the laws of terminal control of uniaxial movement of nonlinear dynamic objects is proposed. The problem is solved for the case when the control action is included in the scalar additive component of the nonlinear equations of the object. Target control laws meet the requirement to transfer an object from an arbitrary initial state toa specified final position with a specified final speed. The other parameters of the object’s state at the end time are generally not controlled. When assigning a zero final speed, the object’s "soft" transition to the specified position is achieved, which is necessary for many terminal systems. Due to the fundamental complexity of optimal synthesis in conditions where the control object has nonlinear properties, a purely terminal formulation of the problem is preferable. One of the most effective means of solving this problem is the methods of trajectory planning and solving inverse dynamics problems. This approach is adopted in this study. Using it together with additional analysis allowed us to write the control law in the feedback form for the case of a nonlinear mathematical model of the object. The developed synthesis method is characterized by simplicity of form and ease of practical implementation, for example, using embedded microcontrollers. Known general approaches are usually associated with a significant expenditure of time and technical resources of the control system in this case. The specified efficiency of the method is achieved by taking into account the features of scalar and additive control in the system. The use of the method is illustrated by an example of "soft" turn of the sequential excitation electric motor shaft at a given angle with zero final speed, which does not require the use of rigid stop. The latter circumstance means a significant improvement in the quality of terminal control. Under this condition, the organization of positioning of mobile executive bodies of various industrial equipment is significantly simplified.

The paper proposes a new approach as an alternative to full automation of processes that meets current economic trends — collaborative multi-agent systems. In this concept, people and robots are considered as agents in a single sensory-information field, who perform tasks to achieve the goals of the collaborative multi-agent system. The urgency of collaborative multi-agent systems results from the fact that the industrial use of fully automated multi-component systems is limited by the financial and infrastructural unavailability of various industries to switch to completely unmanned technologies. The proposed approach combines the latest, but remaining quite recouped, technological advances along with highly skilled human labor. The use of collaborative multi-agent systems will be economically justified in the manufacture of products in small batches, in the conditions of rapid change of product lines, as well as the presence of staff shortages. The article shows that such an approach can significantly reduce automation costs, while ensuring that the specified production indicators are met. This approach allows taking a fresh look at a human, considering him and a robot as equal partners within a collaborative system. The basic concepts and distinctive characteristics of collaborative multi-agent systems are formulated and presented in the work, justifications for their use are given. Creating a new class of collaborative multi-agent systems requires solving a number of problems associated with the interaction of man and robot. The article considers issues related to the work of a person within a collaborative system, with a rational separation of human functions and an automated production system, in accordance with the necessary level of collaboration. The inclusion of a person with his psychoemotional and physical characteristics as an equivalent agent of a multi-agent system causes difficulties in formalizing collaborative multi-agent systems associated with the need to take these features into account and create a sensory-information system. The inclusion of a person with his psychoemotional and physical characteristics as an equivalent agent of a multi-agent system causes difficulties in formalizing collaborative multi-agent systems associated with the need to take these features into account and create a sensory-information system. The paper discusses ways to formalize a collaborative multi-agent system and management approaches.

The swing-up control of the electromechanical systems is considered. Electromechanical system is the cascade system. The input subsystem is a mechanical plant. The output subsystem is the actuator which dynamics cannot be neglected in particular oscillation control problem. The energy-based objective function is used to design the energy efficient virtual control law of output subsystem. The control objectives are achieving the mechanical subsystem’s reference energy and boundedness of closed-loop cascade system trajectories.In parametric uncertainty, both energy and the control objective depends on unknown parameters of a mechanical subsystem. That complicates the design procedure. The modified Speed bi-gradient method (SBGM) to identify unknown parameters, achieve a desired energy and provide boundedness of the trajectories is proposed. Modifications of SBGM are the introduction of the output subsystem tunable model, and indirect adaptive control design. Swing-up control is calculated based on current estimation performed by the adaptation loop that is without preliminary identification. The design procedure, conditions of applicability and stability analysis are presented. The proposed method is used to design the swing-up control of pendulum under parametric uncertainty. The experimental results coтfirming the performance of a closed-loop system are demonstrated.

Collision avoidance is very important problem in the domain of multi-robot interaction. In this paper we propose a new approach of collision avoidance in the context of the optimal control system synthesis problem definition with minimal information available. It is assumed that robots have a certain scope within which they can interact with static and dynamic phase constraints. A group of robots is considered to be homogeneous, and control system unit for reaching terminal states already available to robots. The control system which is responsible for collision avoidance is only activated when the nearest neighbor is located in the scope of the considered robot. The first important feature of this work is the fact that the collision avoidance between two robots is reciprocal with joint control system, without assigning priorities. Another key feature of this work is the complete absence of information about the environment and the current state of other robots at given time. Robots only share information with nearest neighbors if they locate in the scope of each other. We also present a computational experiment with mobile robots as control objects. A multilayer perceptron was used to approximate the control function. Weights of the perceptron were optimized in unsupervised paradigm by an algorithm belonging to the evolutionary strategies class. At the beginning of each epoch we generate a sample of collision scenarios for optimization, while the quality criterion of the achieved weights at the end of epoch is evaluated on a fixed test sample. Experimental results demonstrate strong ability of the optimized multilayer perceptron to map the relative state of two mobile robots to controls in order to avoid collisions.

The paper presents a solution to the problem of optimal control of a quadrocopter under phase constraints by the numerical method of a network operator based on multi-point stabilization. According to this approach, the task of control system synthesis is initially solved. As a result, the quadrocopter is stabilized with respect to a certain point in the state space. At the second stage, a sequence of stabilization points is searched in the state space such that switching the stabilization points at fixed times ensures the movement of the quadrocopter from the initial state to the terminal state with an optimal value of the quality criterion taking into account phase constraints. To solve the problem of stabilization system synthesis, the network operator method is used. The method is numerical and, unlike the well-known analytical methods, allows to synthesize a control system automatically without a specific analysis of the right parts of the model. The method allows to find the structure and parameters of a mathematical expression in the encoded form using the genetic algorithm. The network operator code is an integer upper-triangular matrix. At the stage of solving the synthesis problem, the mathematical model of quadrocopter motion is decomposed into angular and spatial motions in order to separate control components for angular and spatial motions, respectively. The synthesized stabilization system consists of two subsystems connected in series for spatial and angular motion. As controls for spatial motion, moments around the axes and the total thrust of all quadcopter propellers were used. And the inputs for the angular motion stabilization system are the desired angles of inclination of the quadrocopter. The stabilization problem is considered as a general synthesis task for a control system. Using the network operator method, one control function is searched that provides stabilization of the object at a given point in the considered state space from the set of initial conditions. At the stage of the search for equilibrium points, the evolutionary particle swarm algorithm is used. A numerical example of solving the problem of optimal control of a quadrocopter with four phase constraints is given.