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

Abstract

In this paper, the stability of polynomial fuzzy-model-based (PFMB) observercontrol system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy-model-based (FMB) control strategy, it leads to non-convex stability conditions. Therefore, the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares (SOS) with less manually designed parameters. In addition, the membership functions of the polynomial observer-controller are optimized by the improved gradient descent method, which outperforms the widely applied parallel distributed compensation (PDC) approach according to a general performance index. Simulation examples are provided to verify the proposed design and optimization scheme.

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

“… B = 0 . 6 and g = 10 m / s 2 . The polynomial fuzzy model of the ball-and-beam system can be described via a two-rule polynomial fuzzy model, as shown in the work by Liu et al (2016a)…”

“…This scenario is presented to compare the results of this paper with the newly published work by Liu et al (2016a); Vafamand et al (2016). Since the approach of Liu et al (2016a) is derived for disturbance-free nominal polynomial fuzzy models, we consider the same assumption and use the system and controller without any uncertainties. And, only the saturation constraint affects the controller.…”

An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning

“…The stability of the fuzzy control is recommended to be taken into consideration in order to set the domain D ρ , and useful approaches are reported in [23,[27][28][29][31][32][33][34][35][36]. The objective function J α j (ρ) is referred to as the weighted sum of the absolute value of the control error and of the squared output sensitivity function, but the state sensitivity functions can be included as well.…”

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

“…Along the line of PDC design concept, stability conditions in terms of SOS were obtained in [60]. Since then, a lot of research on stability analysis of PFMB control systems have been carried on and variations of SOS-based stability conditions have been obtained for different control problems, just to name a few, such as observer-based control problems [63,64,65,66,67], output-feedback control problems [68], positive control problems [69], regulation control problems [70], sampled-data control problems [71], stabilization control problems [60,72,61,73,74,75,76,77,78,79,80,81,82,83,84,85,86,11,87,88], switching control problems [79], tracking control problems [89] and etc.…”