Machine Learning Control by Symbolic Regression

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