scholarly journals Control Synthesis as Machine Learning Control by Symbolic Regression Methods

2021 ◽  
Vol 11 (12) ◽  
pp. 5468
Author(s):  
Elizaveta Shmalko ◽  
Askhat Diveev
Keyword(s):  
Machine Learning ◽  
Genetic Programming ◽  
Mathematical Formulation ◽  
Small Variation ◽  
Learning Control ◽  
Symbolic Regression ◽  
Control Technique ◽  
Control Synthesis ◽  
Basic Solution ◽  
Regression Methods

The problem of control synthesis is considered as machine learning control. The paper proposes a mathematical formulation of machine learning control, discusses approaches of supervised and unsupervised learning by symbolic regression methods. The principle of small variation of the basic solution is presented to set up the neighbourhood of the search and to increase search efficiency of symbolic regression methods. Different symbolic regression methods such as genetic programming, network operator, Cartesian and binary genetic programming are presented in details. It is shown on the computational example the possibilities of symbolic regression methods as unsupervised machine learning control technique to the solution of MLC problem of control synthesis for obtaining the stabilization system for a mobile robot.

scholarly journals Synthesis of a mobile robot spatial stabilization system based on machine learning control by symbolic regression

2021 ◽  
Vol 22 (2) ◽  
pp. 129-138
Author(s):  
Askhat I. Diveev ◽  
Neder Jair Mendez Florez
Keyword(s):  
Machine Learning ◽  
Mobile Robot ◽  
Initial Conditions ◽  
Symbolic Regression ◽  
Synthesis Problem ◽  
Terminal Point ◽  
Control Synthesis ◽  
Stabilization System ◽  
Nonlinear Feedback ◽  
Regression Methods

The spatial stabilization system synthesis problem of the robot is considered. The historical overview of methods and approaches for solving the problem of control synthesis is given. It is shown that the control synthesis problem is the most important task in the field of control, for which there are no universal numerical methods for solving it. As one of the ways to solve this problem, it is proposed to use the method of machine learning based on the application of modern symbolic regression methods. This allows you to build universal algorithms for solving control synthesis problems. Several most promising symbolic regression methods are considered for application in control tasks. The formal statement of the control synthesis problem for its numerical solution is given. Examples of solving problems of synthesis of system of spatial stabilization of mobile robot by method of network operator and variation Cartesian genetic programming are given. The problem required finding one nonlinear feedback function to move the robot from thirty initial conditions to one terminal point. Mathematical records of the obtained control functions are given. Results of simulation of control systems obtained by symbolic regression methods are given.

scholarly journals Machine Learning Control Based on Approximation of Optimal Trajectories

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 265
Author(s):  
Askhat Diveev ◽  
Sergey Konstantinov ◽  
Elizaveta Shmalko ◽  
Ge Dong
Keyword(s):  
Machine Learning ◽  
Control Function ◽  
Mathematical Formulation ◽  
Quality Criterion ◽  
Learning Control ◽  
Supervised Machine Learning ◽  
Training Set ◽  
Initial State ◽  
Regression Methods ◽  
General Synthesis

The paper is devoted to an emerging trend in control—a machine learning control. Despite the popularity of the idea of machine learning, there are various interpretations of this concept, and there is an urgent need for its strict mathematical formalization. An attempt to formalize the concept of machine learning is presented in this paper. The concepts of an unknown function, work area, training set are introduced, and a mathematical formulation of the machine learning problem is presented. Based on the presented formulation, the concept of machine learning control is considered. One of the problems of machine learning control is the general synthesis of control. It implies finding a control function that depends on the state of the object, which ensures the achievement of the control goal with the optimal value of the quality criterion from any initial state of some admissible region. Supervised and unsupervised approaches to solving a problem based on symbolic regression methods are considered. As a computational example, a problem of general synthesis of optimal control for a spacecraft landing on the surface of the Moon is considered as supervised machine learning control with a training set.

scholarly journals Universal Approach to Solution of Optimization Problems by Symbolic Regression

2021 ◽  
Vol 11 (11) ◽  
pp. 5081
Author(s):  
Elena Sofronova ◽  
Askhat Diveev
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Small Variation ◽  
Search Space ◽  
Search Algorithms ◽  
Symbolic Regression ◽  
Basic Solution ◽  
Potential Solution ◽  
Regression Methods ◽  
Universal Approach

Optimization problems and their solution by symbolic regression methods are considered. The search is performed on non-Euclidean space. In such spaces it is impossible to determine a distance between two potential solutions and, therefore, algorithms using arithmetic operations of multiplication and addition are not used there. The search of optimal solution is performed on the space of codes. It is proposed that the principle of small variations of basic solution be applied as a universal approach to create search algorithms. Small variations cause a neighborhood of a potential solution, and the solution is searched for within this neighborhood. The concept of inheritance property is introduced. It is shown that for non-Euclidean search space, the application of evolution and small variations of possible solutions is effective. Examples of using the principle of small variation of basic solution for different symbolic regression methods are presented.

scholarly journals Ensemble modeling approach for rainfall/groundwater balancing

2007 ◽  
Vol 9 (2) ◽  
pp. 95-106 ◽  
Author(s):  
D. Laucelli ◽  
O. Giustolisi ◽  
V. Babovic ◽  
M. Keijzer
Keyword(s):  
Machine Learning ◽  
Genetic Programming ◽  
Empirical Evidence ◽  
Averaging Method ◽  
Total Error ◽  
Ensemble Methods ◽  
Real Data ◽  
Symbolic Regression ◽  
Ensemble Modeling ◽  
Physical Phenomena

This paper introduces an application of machine learning, on real data. It deals with Ensemble Modeling, a simple averaging method for obtaining more reliable approximations using symbolic regression. Considerations on the contribution of bias and variance to the total error, and ensemble methods to reduce errors due to variance, have been tackled together with a specific application of ensemble modeling to hydrological forecasts. This work provides empirical evidence that genetic programming can greatly benefit from this approach in forecasting and simulating physical phenomena. Further considerations have been taken into account, such as the influence of Genetic Programming parameter settings on the model's performance.

scholarly journals Closed-loop separation control using machine learning

2015 ◽  
Vol 770 ◽  
pp. 442-457 ◽  
Author(s):  
N. Gautier ◽  
J.-L. Aider ◽  
T. Duriez ◽  
B. R. Noack ◽  
M. Segond ◽  
...  
Keyword(s):  
Machine Learning ◽  
Feedback Control ◽  
Genetic Programming ◽  
Closed Loop ◽  
Recirculation Zone ◽  
Low Frequency ◽  
Learning Control ◽  
Separation Control ◽  
Periodic Forcing ◽  
Model Free

We present the first closed-loop separation control experiment using a novel, model-free strategy based on genetic programming, which we call ‘machine learning control’. The goal is to reduce the recirculation zone of backward-facing step flow at $\mathit{Re}_{h}=1350$ manipulated by a slotted jet and optically sensed by online particle image velocimetry. The feedback control law is optimized with respect to a cost functional based on the recirculation area and a penalization of the actuation. This optimization is performed employing genetic programming. After 12 generations comprised of 500 individuals, the algorithm converges to a feedback law which reduces the recirculation zone by 80 %. This machine learning control is benchmarked against the best periodic forcing which excites Kelvin–Helmholtz vortices. The machine learning control yields a new actuation mechanism resonating with the low-frequency flapping mode instability. This feedback control performs similarly to periodic forcing at the design condition but outperforms periodic forcing when the Reynolds number is varied by a factor two. The current study indicates that machine learning control can effectively explore and optimize new feedback actuation mechanisms in numerous experimental applications.

scholarly journals EVOLUTIONAL METHODS FOR CREATING ARTIFICIAL INTELLIGENCE OF ROBOTIC TECHNICAL SYSTEMS

2018 ◽  
Vol 16 (2) ◽  
pp. 148-152 ◽  
Author(s):  
Askhat I. Diveev ◽  
Sabit Ibadulla
Keyword(s):  
Artificial Intelligence ◽  
Genetic Programming ◽  
Control Systems ◽  
Intelligent Control ◽  
Symbolic Regression ◽  
Robotic Systems ◽  
Basic Solution ◽  
Intelligent Control Systems ◽  
Intellectual Control ◽  
Technical Systems

This paper considers evolutionary methods of symbolic regression for the creation of artificial intelligence of robotic systems. Methods of symbolic regression are reviewed and the features of their application to the solution of the problem of synthesis of control of robotic systems are indicated. The measure of the complexity of artificial intelligence is determined and the advantage of using the principle of small variations of the basic solution is shown, while creating intelligent control systems. A method of variational genetic programming is described and an example of its use for the synthesis of intellectual control is given.

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