Developing an Interval Type-2 TSK Fuzzy Logic Controller

Abstract

Type-2 Fuzzy Logic Controllers offer great capabilities in modeling and handling the effects of real world uncertainties from sensors, actuators and the environment. Nevertheless, the general Type-2 Fuzzy Logic Controllers enormously suffer from high computation cost. To overcome this problem, in this paper, we present a computationally effective Type-2 Fuzzy Logic Controller which uses Interval Type-2 fuzzy sets to capture the control inputs and utilizes the Takagi-Sugeno-Kang technique to render the control outputs. It is shown that the proposed technique greatly reduces the computation cost since only the lower and upper bounds of the input fuzzy sets suffice to calculate the control output.

Interval Type-2 TSK+ Fuzzy Inference System

“…Given an observation Opà 1 ,¨¨¨,à k q, the intermediate resultc i led by rule R i needs to be calculated first. As intervals are usually used as the parameters of the polynomial function in the consequence of IT2 TSK rules and the domains of input variables are normalized, each sub-consequencec i from rule R i in the IT2 TSK+ system is therefore a crisp interval [26], [27]. The minimum and maximum values ofc i can be obtained based on the given observation and the corresponding IT2 polynomial function of the rule consequence:…”

“…Many type-1 fuzzy systems have been extended to support IT2 fuzzy systems, including the TSK approach [26], [27]. Generally speaking, the inputs and all the fuzzy sets in the rule antecedents can but not necessarily be IT2 fuzzy sets in a IT2 fuzzy systems; and the consequence of IT2 TSK rules are zero or first order of polynomial functions, where the parameters can be either crisp values or a crisp interval.…”

“…In this experiment, the well-known cart centering problem, which has been considered in [26], was used for system evaluation. In this particular problem, a cart can only move along a line on a frictionless plane, and the goal is to drive the cart to the center position of the line from a given initial position on the line, which forms a typical control problem.…”

“…The inputs of the controller for this problem are the current position coordinates of the cart x and the current velocity of the cart v; and the output of this fuzzy model is the force F that should be applied on the cart. In [26], the domain of cart position x was restricted from´0.75m to 0.75m; the range of cart velocity v was restricted from´0.75m{s to 0.75m{s; the output force F was defined between´0.18m{s and 0.18m{s; and the sampling time used was t " 0.1s. This set of parameters and constraints were also utilized in this experiment reported herein.…”

“…This set of parameters and constraints were also utilized in this experiment reported herein. Based on the problem described above, a 0-order IT2 TSK fuzzy model has been designed and created in [26]. In particular, five linguistic values, represented as IT2 fuzzy sets, were used to cover every domain of input variables x and v, which are negative large (NL), negative small (NS), zero (0), positive small (PS) and positive large (PL), as shown in Figure 2.…”