9.4 Review/Preview

This chapter introduced the concept of time-varying systems and the need for adaptive controllers. Specifically, a time-varying cart-pole system was introduced in which system parameters such as the cart mass, the pole length, and the coefficients of friction could change. The effect of changing a parameter was illustrated by changing the mass of the cart. An adaptive control system was developed to control such time varying systems. This adaptive control system included three elements: (1) a control element, (2) an analysis element, and (3) a learning element.

The control element consists of a fuzzy controller much like those described in previous chapters. It receives information about the current state of the system, and based on these values, prescribes an action to be taken on the problem environment. The analysis element recognizes when and to what extent the problem environment changes. It accomplishes this task by tracking the real-world system with a computer simulation. It then uses a GA to tune the parameters in a computer model until the response of the model matches the response of the real-world system. The learning element adjusts the control strategy being used by the control element based on information supplied by the analysis element. The learning element develops its updated strategy in the same way as the fuzzy systems were designed using GAs earlier in this book.

The adaptive control system described requires a computer model of the real-world system. For the cart-pole system, obtaining such a model was no problem because its physics lead to equations of motion which can be integrated numerically leading directly to a first principles model. However, there are systems for which acquiring or developing a computer model is a daunting task. Thus, we feel it is necessary to provide the reader with some approaches to computer modeling that we found to be effective. Thus, in the next section, we will introduce neural networks for modeling, further discuss the idea of using GAs for curve fitting, and present methods for data management.

The next section of the book deals with the development of computer models. However, it is important for the reader to keep in mind the software architecture presented for adaptive control presented in this chapter; it will be used in later applications we present.

References

Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley.

Karr, C. L. (1991). Genetic algorithms for fuzzy controllers, AI Expert, 6 (2), 26–31.