Machine Learning Control by Symbolic Regression

This book provides comprehensive coverage on a new direction in computational mathematics research: automatic search for formulas. Formulas must be sought in all areas of science and life: these are the laws of the universe, the macro and micro world, fundamental physics, engineering, weather and natural disasters forecasting; the search for new laws in economics, politics, sociology. Accumulating many years of experience in the development and application of numerical methods of symbolic regression to solving control problems, the authors offer new possibilities not only in the field of control automation, but also in the design of completely different optimal structures in many fields. For specialists in the field of control, Machine Learning Control by Symbolic Regression opens up a new promising direction of research and acquaints scientists with the methods of automatic construction of control systems.For specialists in thefield of machine learning, the book opens up a new, much broader direction than neural networks: methods of symbolic regression. This book makes it easy to master this new area in machine learning and apply this approach everywhere neural networks are used. For mathematicians, the book opens up a new approach to the construction of numerical methods for obtaining analytical solutions to unsolvable problems; for example, numerical analytical solutions of algebraic equations, differential equations, non-trivial integrals, etc. For specialists in the field of artificial intelligence, the book offers a machine way to solve problems, framed in the form of analytical relationships.

Auteur

Prof., Dr. Diveev is a renowned specialist in the field of control and a leading researcher in Russia in evolutionary computation and symbolic regression. He received the Ph.D. degree in technical science from Bauman Moscow State Technical University, in 1989, and Doctor of Sciences in 2001 in Dorodnitsyn Computing Center of the Russian Academy of Sciences, in 2009 he became a professor. Presently, he works as a Director of Robotic Center of Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences. He is also a Professor at the RUDN University, Engineering Department. He is the author of five books, more than 300 articles. Prof. Diveev is a member of the editorial board of the RUDN journal of Engineering Researches and journal of Instrument Engineering of the Bauman Moscow State Technical University, a general chair of the INTELS Symposium. Dr. Shmalko is a former student and follower of Prof. Diveev, received the B.S. and M.S. degrees in Computer Science and Cybernetics from RUDN University, Engineering Dept. and the Ph.D. degree from Dorodnicyn Computing Center of the Russian Academy of Sciences, Moscow, Russia, in 2009. From 2007 to 2010, she was with IBM East Europe/Asia. Since 2010, she is a Senior researcher with the Computing Center of the Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences. The authors' current research interests are computational methods in control, symbolic regression and evolutionary computation with applications to model identification, optimization and control system synthesis. The authors conduct theoretical research and implement applied tasks on the basis of the Robotics Center of the Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences.

Contenu

1 Introduction1.1 About modern control systems1.2 About machine learning control1.3 About symbolic regression methodsReferences2 Mathematical Statements of MLC Problems2.1 Machine Learning Problem2.2 Optimal Control Problem2.3 Control Synthesis Problem2.4 Synthesized Optimal Control Problem2.5 Model Identification ProblemReferences3 Numerical Solution of Machine Learning Control Problems3.1 Artificial Neural Networks3.2 General Approach of Symbolic Regression3.3 The principle of small variations of the basic solution3.4 Genetic Algorithm for Multicriterial Structural-Parametric Search of Functions3.5 Space of Machine-Made Functions AppendixReferences4 Symbolic Regression Methods4.1 Genetic Programming4.2 Grammatical Evolution4.3 Cartesian Genetic Programming4.4 Inductive Genetic Programming4.5 Analytic Programming4.6 Parse-Matrix Evolution4.7 Binary Complete Genetic Programming4.8 Network Operator Method4.9 Variational Symbolic Regression Methods4.9.1 Variational Genetic Programming4.9.2 Variational Analytic Programming4.9.3 Variational Binary Complete Genetic Programming4.9.4 Variational Cartesian Genetic Programming4.10 Multilayer Symbolic Regression MethodsReferences5 Examples of MLC Problem Solutions5.1 Control Synthesis as Unsupervised MLC5.1.1 Ponryagin's Example5.1.2 Mobile Robot5.1.3 Quadcopter5.2 Control Synthesis as Supervised MLC5.3 Identification and Control Synthesis for Multi-link Robot5.4 Synthesized Optimal Control Example5.4.1 Synthesized optimal control5.4.2 Direct solution of the optimal control problem5.4.3 Experimental analysis of sensitivity to perturbations5.5 Machine learning in Synergetic controlReferences