Why use fuzzy logic for control ?

Controlling a system means that some characteristics of this system are monitored, and, depending on

the values of these characteristics, different controls are applied. An algorithm that transforms sensor

inputs into corresponding control values is called a control strategy. The previous chapters deal with the

traditional approach of control systems design that consists of the following:

• First, one tries to to describe the behaviour of the system in precise mathematical terms, i.e., one

comes up with the exact model of the system.

• Second, one tries to describe in precise terms what one wants to achieve. One wants the control

that is the best in the sense of some criterion.

• Now that the controlled system is described in precise mathematical terms, and the objective

function is described in the same manner, it can be determined for each control strategy and for

each initial state how exactly the system will change and what the resulting value of the control will

be. The main goal is then to find the control strategy for which the resulting value of the objective

function is the largest possible one. This is a well-defined mathematical optimisation problem, and

traditional control theory has developed many methods for solving this problem and designing the

corresponding control strategies.

Traditional control theory has many important applications. There are, however, practical cases when

this theory is not applicable. Indeed, to apply the traditional control theory, one must

• know the model of the controlled system,

• know the objective function formulated in precise terms, and

• be able to solve the corresponding mathematical design problem.

If one of these conditions is not satisfied, then traditional control methodology is not applicable, as in

the following cases:

• Sometimes, the model and the objective function is known, but the design problem cannot be

solved. This is when the design problem is very complicated, time consuming or when the problem

is new and algorithms for solving it have not yet been developed. For example, parking a car is an

example of a problem that traditional control theory has not considered until recently.

• Sometimes, the model is known, but the objective function is unknown. For example, if a control

system for a vehicle is designed, the intended goal is to make the ride most comfortable, but there

is no well-accepted formalism of what comfortable means.

• Sometimes, one does not even know the model of the controlled system. In many practical applications

one can in principle measure all the possible variables and determine the model exactly, but

this will increase the cost drastically. In other practical situations, the main goal of the controlled

system is to explore the unknown, e.g., to control a rover over a terrain of unknown type, or to

control surgery instruments. In such situations, the entire objective of the control is to learn as

much about the system, and one cannot have a precise model of this system before the control is

over.

If traditional control methodology cannot be applied, how can one control? Often, there is an additional

expert knowledge available, for example, expert operators who successfully control the desired system.

Expert operators know how to operate a plant. Therefore it is desirable to extract the control rules from

the expert and use this knowledge in an automatic control system. At first glance, the problem seems

very simple. Since the person is a real expert, one simply ask her multiple questions like “suppose that

x1 is equal to 1.2, x2 is equal to -2.7, ..., what is u ?” After asking all these questions, one will get many

pattern, from which one will be able to extrapolate the function f(x1, ..., x2) using one of the known

methods. Alas, there are two problems with this idea:

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