Machine Learning Control by Symbolic Regression

✍ Scribed by Askhat Diveev, Elizaveta Shmalko

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 162
• Edition: 1
• Category: Library

✦ Synopsis

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 the field 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.

✦ Table of Contents

Preface
Contents
Acronyms
1 Introduction
1.1 About Modern Control Systems
1.2 About Machine Learning Control
1.3 About Symbolic Regression Methods
References
2 Mathematical Statements of MLC Problems
2.1 Machine Learning Problem
2.2 Optimal Control Problem
2.3 Control Synthesis Problem
2.4 Synthesized Optimal Control Problem
2.5 Model Identification Problem
References
3 Numerical Solution of Machine Learning Control Problems
3.1 Artificial Neural Networks
3.2 General Approach of Symbolic Regression
3.3 The Principle of Small Variations of the Basic Solution
3.4 Genetic Algorithm for Multicriterial Structural-Parametric Search of Functions
3.5 Space of Machine-Made Functions
Appendix
References
4 Symbolic Regression Methods
4.1 Genetic Programming
4.2 Grammatical Evolution
4.3 Cartesian Genetic Programming
4.4 Inductive Genetic Programming
4.5 Analytic Programming
4.6 Parse-Matrix Evolution
4.7 Binary Complete Genetic Programming
4.8 Network Operator Method
4.9 Variational Symbolic Regression Methods
4.9.1 Variational Genetic Programming
4.9.2 Variational Analytic Programming
4.9.3 Variational Binary Complete Genetic Programming
4.9.4 Variational Cartesian Genetic Programming
4.10 Multilayer Symbolic Regression Methods
References
5 Examples of MLC Problem Solutions
5.1 Control Synthesis as Unsupervised MLC
5.1.1 Pontryagin's Example
5.1.2 Mobile Robot
5.1.3 Quadcopter
5.2 Control Synthesis as Supervised MLC
5.3 Identification and Control Synthesis for Multi-link Robot
5.4 Synthesized Optimal Control Example
5.4.1 Synthesized Optimal Control
5.4.2 Direct Solution of the Optimal Control Problem
5.4.3 Experimental Analysis of Sensitivity to Perturbations
5.5 Machine Learning in Synergetic Control
References