Fuzzy control turns 50: 10 years later

Abstract

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

Shape-independent model predictive control for Takagi–Sugeno fuzzy systems

“…As discussed in the introduction, well-known LMIs have been developed to synthesise state-feedback controllers for systems in the TS form (2). In particular, this paper will root on the so-called guaranteed-cost results [1,12] and will propose predictive controllers which improve on the obtained cost bounds.…”

“…Subsequently, stability analysis and control design tasks can be carried out on the TS models. Control techniques for TS fuzzy systems based on LMIs [1] have been deeply developed in recent years, see the review paper [2] and references therein. Of course, the TS+LMI approach is conservative with respect to an "ideal" nonlinear control approach [3], but it allows solving the problems via convex optimisation tools, derived from linear systems and related to the linear parameter varying (LPV) approach [4].…”

Robust Stabilization of T–S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes

“…For this reason, non-parallel distributed compensation (Non-PDC) is proposed in [8] and combined with a non-quadratic Lyapunov function to show the superiority of the approach when compared to PDC. Fuzzy controller designs for T-S fuzzy systems have been developed for both PDC and Non-PDC where [5], [9] provide a complete review of T-S fuzzy systems. As nonlinear descriptor systems are often encountered in the real world, stabilisation of T-S fuzzy descriptor systems has been considered [4].…”

Design of polynomial fuzzy observer–controller with membership functions using unmeasurable premise variables for nonlinear systems

“…Polynomial fuzzy model [51,49] is one of the effective tools to model and analyze nonlinear systems, which is a generalization of Takagi-Sugeno (T-S) fuzzy model [45,44] in terms of modeling capability. Both 5 of them are employed in fuzzy-model-based (FMB) control strategies, which means that the stability analysis and control synthesis are carried out based on the fuzzy model instead of the nonlinear system [14]. Several techniques are widely employed under the FMB control scheme.…”