CHAPTER 7

PARALLEL DISTRIBUTED CONTROL WITH TAKAGI–SUGENO FUZZY SYSTEMS

If a plant has a model in the form of a Takagi–Sugeno (T–S) fuzzy system that interpolates linear dynamic systems, which we call the plant fuzzy system, one approach to stabilizing it is called parallel distributed control (PDC) [9,17,29]. The basic philosophy of PDC is to create a controller fuzzy system with rule premises identical to those of the plant fuzzy system. In the controller fuzzy system, each rule’s consequent is a control law designed to control the linear system in the corresponding consequent of the plant fuzzy system. The overall control law is thus a weighted average of the individual control laws, just as the overall nonlinear system is a weighted average of the linear systems in each consequent of the plant fuzzy system.

Parallel distributed control is important because it constitutes a method of controlling nonlinear systems. Furthermore, as will be seen in Chapter 10, a nonlinear system can sometimes be identified online as a T–S fuzzy system. If a parallel distributed controller can then be designed based on this identification, a type of real-time control known as adaptive control can be effected for nonlinear systems.

The control methods utilized in this book in parallel distributed control schemes are the ones contained in Chapter 5, that is pole placement, tracking, and model reference. Pole placement via parallel distributed control has the distinct advantage that there exist mathematical ...