Fuzzy modeling and control of a class of non‐differentiable multi‐input multi‐output nonlinear systems

Abstract

This paper presents a new approach in modeling and control of multi‐input multi‐output (MIMO) systems that have non‐differentiable operating points. A circle criterion is introduced at the non‐differentiable operating points to divide the entire operating region into two parts. Takagi‐Sugeno fuzzy models are developed in each part, and a switching framework is introduced to model the operating region. Accordingly, a sliding mode controller (SMC) is developed. The proposed modeling and controller are implemented on the benchmark quadruple tank process (QTP). It is demonstrated that the proposed modeling and controller design provides simplicity and universality in a set of nonlinear systems; it is robust with respect to various internal and external disturbances and model uncertainties which allows for accurate regulation and tracking; and it converges in finite time, is capable of controlling nonlinear systems with coupling dynamic, and enables fuzzy modeling of continuous‐time systems without imposing differentiability.

A third‐order sliding mode controller for nonlinear multivariable systems

“…Theorem 1. Under Assumption 1, if the controller is defined as (7) and the sliding surface is designed as Equation ( 6), then the sliding variables and the tracking errors are ultimately uniformly bounded.…”

“…Many methods have now been developed to control nonlinear dynamical systems. Some examples of the robust control techniques that have been proposed include sliding mode control (SMC) [1], adaptive control [2][3][4][5], fuzzy control [6][7][8], backstepping [9], model predictive control [10], integral-type saturated control [11], proportional-derivative control [12], and observer-based quantized output feedback control [13].…”

A novel fixed‐time sliding mode control for nonlinear manipulator systems based on adaptive disturbance observer

“…However, since the robotic manipulator is a system with nonlinear and complex perturbations, the actual control is susceptible to modeling errors, friction, and external disturbances, which all increase the difficulty of control. In response to the problems of nonlinear systems, scholars have developed different control methods to improve them, such as neural network control [3,4], fuzzy control methods [5][6][7][8][9], backstepping control methods [10][11][12], and sliding mode control (SMC) methods [13][14][15][16][17][18].…”

Rational entropy‐based fuzzy fault tolerant control for descriptor stochastic distribution networked control systems with packet dropout

“…When the nonlinear term of the system does not meet the Lipschitz condition, it is difficult to use the existing research methods. The T-S fuzzy model can use multiple local linear system models to approximate the global nonlinear system model [17,18], which provides a novel idea for the investigation of nonlinear SDC systems. The tracking control problem of fuzzy stochastic distribution sampled-data systems is studied in [19].…”