Cartesian Genetic Programming for Synthesis of Optimal Control System

Abstract

The problem of general synthesis of optimal control system of mobile robot is considered. In the problem it is necessary to find a feedback control function such that a mobile robot can achieve the set terminal position from any point of area of initial conditions. The solution of this problem is a mathematical expression of control function. For solution of this problem Cartesian genetic programming (CGP) is used. CGP is one of symbolic regression methods. The methods of symbolic regression allow numerical with the help of computer to find analytical form of mathematical expression. CGP codes multi-dimension function in a form of integer matrix on the base of the sets of arguments and elementary functions. Every string of this matrix is a code of one call of a function. For search of optimal solution, a variation genetic algorithm is used that realizes the principle of small variation of basic solution. The algorithm searches for a mathematical expression of the feedback control function in the form of code and at the same time value of parametric vector that is one of arguments of this function. An example of numerical solution of the control system synthesis problem for mobile robot is presented. It is introduced a conception a space of machine made functions. In this space functions can’t have value is infinity, and all function can be presented in the form of Taylor’s series only with a finite number of members.