scholarly journals Solution of the optimal control problem by symbolic regression method

2021 ◽  
Vol 186 ◽  
pp. 646-653
Author(s):  
A.I. Diveev ◽  
S.V. Konstantinov ◽  
A.M. Danilova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Symbolic Regression ◽  
Regression Method

Solving the Problem of the Optimal Control System General Synthesis Based on Approximation of a Set of Extremals using the Symbol Regression Method

2020 ◽  
pp. 59-74
Author(s):  
S.V. Konstantinov ◽  
A.I. Diveev
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Symbolic Regression ◽  
Regression Method ◽  
Synthesis Problem ◽  
Optimal Control System ◽  
Initial States

A new approach is considered to solving the problem of synthesizing an optimal control system based on the extremals' set approximation. At the first stage, the optimal control problem for various initial states out of a given domain is being numerically sold. Evolutionary algorithms are used to solve the optimal control problem numerically. At the second stage, the problem of approximating the found set of extremals by the method of symbolic regression is solved. Approach considered in the work makes it possible to eliminate the main drawback of the known approach to solving the control synthesis problem using the symbolic regression method, which consists in the fact that the genetic algorithm used in solving the synthesis problem does not provide information about proximity of the found solution to the optimal one. Here, control function is built on the basis of a set of extremals; therefore, any particular solution should be close to the optimal trajectory. Computational experiment is presented for solving the applied problem of synthesizing the four-wheel robot optimal control system in the presence of phase constraints. It is experimentally demonstrated that the synthesized control function makes it possible for any initial state from a given domain to obtain trajectories close to optimal in the quality functional. Initial states were considered during the experiment, both included in the approximating set of optimal trajectories and others from the same given domain. Approximation of the extremals set was carried out by the network operator method

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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