A Fuzzy Sliding-Mode Control Based on Z-Numbers and LAMDA

Abstract

Z-Numbers is a recent concept related to fuzzy logic where the restriction and reliability criteria are characterized as fuzzy sets. Due to the potential of Z-numbers, this paper presents the development of a fuzzy controller that combines the fundamentals of LAMDA (Learning Algorithm for Multivariate Data Analysis) with the concepts of the Total Utility of Z-numbers, to establish an inference method to improve the performance in a control system. The controller uses criteria from the sliding mode control (SMC) and the Lyapunov concepts to guarantee robustness and stability respectively. The LAMDA method is applied to compute a chattering-free control action which is applied to systems with model uncertainties and variable dynamics. The fuzzy controller has been tested by simulation in two different tasks: 1) Control of a process that consists of a mixing tank with variable dynamics, and 2) Trajectory tracking of a mobile robot. The proposed approach provides suitable results at runtime and outperforms the results of the other tested controllers in terms of performance, minimizing the deviation between the current system output and the reference. Finally, a complexity analysis is presented to evaluate the feasibility in the implementation of the proposal. The obtained results prove the suitability of using a LAMDA Z-number-based controller in the tested systems.

Hybrid Approaches-Based Sliding-Mode Control for pH Process Control

“…A new methodology that combines fuzzy logic with SMC is presented in refs ( 45 ) and ( 46 ). This technique uses the LAMDA (learning algorithm for multivariable data analysis).…”