Evolution of a Controller with a Free Variable Using Genetic Programming

A mathematical formula containing one or more free variables is "general" in the sense that it provides a solution to an entire category of problems. For example, the familiar formula for solving a quadratic equation contains free variables representing the equation's coefficients. Previous work has demonstrated that genetic programming can automatically synthesize the design for a controller consisting of a topological arrangement of signal processing blocks (such as integrators, differentiators, leads, lags, gains, adders, inverters, and multipliers), where each block is further specified ("tuned") by a numerical component value, and where the evolved controller satisfies user-specified requirements. The question arises as to whether it is possible to use genetic programming to automatically create a "generalized" controller for an entire category of such controller design problems  instead of a single instance of the problem. This paper shows, for an illustrative problem, how genetic programming can be used to create the design for both the topology and tuning of controller, where the controller contains a free variable.