Doctor of Technical Sciences

"No calculation no proof"


Graduated from Bauman Moscow State Technical University (BMGTU) specialization - “Automatic Control Systems”.


Candidate thesis on “Synthesis of Structurally Stable Control System for Flight Vehicles” was presented at Bauman Moscow State Technical University.


The medal “In the 850-th anniversary of Moscow” was awarded.


Doctoral thesis on “Development of the Numerical Method for Solving NP-hard Discrete Optimization Problems Based on the Lawler-Bell method”, in which their decomposition into the difference of two monotonically non-decreasing functions is used to estimate the values of the objective and limiting functions was presented at Dorodnicyn Computing Centre of RAS. Specialty - “System Analysis, Management and Processing of Information”.


Academic title Professor was awarded.


The Korkyt Ata gold medal in honor of the 80th anniversary of Korkyt Ata Kyzylorda State University.


1. Lecture courses for bachelors and masters of the direction “Management in technical systems”:

  • “Modern Problems of Control Theory”,
  • “Modern Tools of Intelligent systems”, “Mathematical Modeling of Objects and Control Systems”,
  • “Management of Uncertain Systems”.

2. For postgraduate students of the direction “Computer Science and Engineering”:

  • “System Analysis, Management and Processing of Information”.


  • Research on the development of numerical methods for the synthesis of intelligent control systems for robotic products and group interaction of robots. The results are used in the field of algorithmization and programming. 
  • The method of the network operator, which is designed to solve the problems of structural parametric synthesis of control systems and structural parametric identification of mathematical models was developed. It allows to build algorithms to search using a computer structure and optimal parameters of mathematical expressions. It belongs to the class of new methods of symbolic regression, which appeared at the end of the XX century and are designed to find optimal non-numeric solutions, structures, graphs, algorithms, programs, formulas. 
  • The principle of small variations of the basic solution, which is a generalized principle that allows you to create computational algorithms to find optimal solutions to non-numerical optimization problems was formulated. The principle can be applied in the problem of control synthesis, etc.
  • The variational genetic programming method was developed. Advanced symbolic regression method is a genetic programming method that, unlike the network operator method, encodes a mathematical expression as an ordered set of character codes that define elementary functions.
  • The variational method of analytic programming was developed. It is an improved method of symbolic regression of the method of analytical programming based on the use of the principle of small variations of the basic solution in the known method.
  • The method of binary variation genetic programming was developed. In contrast to the method of symbolic regression, the new method uses only function with one or two arguments, the encoding of mathematical expressions in the form of a composition of functions using the graph complete binary tree in which functions with one argument associated with the arcs of the graph, and the function with two arguments associated with the nodes of the graph, leaves the graph connected with parameters, arguments and single elements are functions with two arguments. The variational genetic algorithm is used to find the solution.

Scientific interests

  • Efficient computational methods for the solution of management tasks, including the solution of optimal control problems, control design, identification of the mathematical model of the control object and the creation of intelligent control systems.
  • Methods of synthesis of intelligent control systems of robotic devices.
Problems of control of group of robots consists in considering of dynamic restrictions which arise because of the requirement of avoiding of collisions of robots among themselves. For the solution of a problem of optimum control of group of robots we use a two-stage method of synthesis. At the first stage, we solve a problem of stabilization of each robot for any point of state space. The system of stabilization will be identical for homogeneous robots. At the second stage, we find coordinates of points of state space for the stabilization of each robot. At search of points of stabilization, we consider conditions of collisions of robots among themselves and violation of other phase restrictions. For the solution of a problem of stabilization we use one of methods of symbolical regression, a method of binary variational genetic programming. The method allows to find the coded mathematical expression for function of control by the evolutionary genetic algorithm. At the second stage by search of points of stabilization of optimum trajectories we use evolutionary computation methods and gradient algorithms of nonlinear programming. The example of the solution of a problem of synthesis of control of group for three mobile robots is given. For search of points of state space, we use a genetic algorithm, a particle swarm optimization method, bee algorithm, and algorithm of the fastest gradient descent.
Experimental analysis of the most popular evolutionary and gradient-based algorithms for the optimal control problem is presented. For correct comparison, the multisolution search is included in the gradient-based methods and the parameters of all algorithms are chosen so that the number of fitness function calculations in the search process by each algorithm is approximately equal. The computational experiment of the optimal control search with four phase constraints is carried out using mobile robot model. As criteria for comparison of algorithms the best found value of the fitness function, the mean value and standard deviation are used.
In the known methods of symbolical regression by search of the solution with the help of a genetic algorithm, there is a problem of crossover. Genetic programming performs a crossover only in certain points. Grammatical evolution often corrects a code after a crossover. Other methods of symbolical regression use excess elements in a code for elimination of this shortcoming. The work presents a new method of symbolic regression on base of binary computing trees. The method has no problems with a crossover. Method use a coding in the form of a set of integer numbers like analytic programming. The work describes the new method and some examples of codding for mathematical expressions.
The universal method for the solution of problems of non-numerical optimization is considered. Concepts of basic element, small and elementary variations were defined. Definitions of norm and metric distance on the code's space of non-numerical elements were introduced. A genetic algorithm on the basis of small variations for basic solution was presented. Examples of solutions of travelling salesman problem and synthesis of control were presented.
The problem of synthesis of the spacecraft control system is considered for the spacecraft descent onto the Moon surface. In the problem, it is necessary for the spacecraft from the given domain of initial values to fall into the vicinity of terminal states for the limited time. To solve the problem, a numerical method of network operator is applied, which allows both structure and parameters of multidimentional function to be found. The search for control function is performed over the set of multidimentional functions described in the form of integer matrices of network operators. The elements of matrices indicate the numbers of elements in the sets of unary and binary operations. The domain of initial values is replaced with the finite set of points. Initial functionals are substituted by the sum of functionals that are calculated for each point. The obtained control system is investigated. It is shown that the synthesized nonlinear control system provides a high precision of the spacecraft falling into the specified domain with different variations of initial values and parameters of the object of control.