Finding an Impulse Response Function Using Genetic Programming

For many practical problems of control engineering, it is desirable to find a function, such as the impulse response function or transfer function, for a system for which one does not have a analytical model. The finding of the function, in symbolic form, that satisfies the requirements of the problem (rather than merely finding a single point) is usually not possible when one does not have an analytical model of the system. This paper illustrates how the recently developed genetic programming paradigm, can be used to find an approximation to the impulse response, in symbolic form, for a linear time-invariant system using only the observed response of the system to a particular known forcing function. The method illustrated can then be applied to other problems in control engineering that require the finding of a function in symbolic form.