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.
Highlights
Uncertain systems are characterized by inexact and fuzziness information, making their modeling and control difficult
This paper has formalized a new intelligent controller based on LAMDA, the concepts of Sliding Mode Control (SMC), and the Total Utility of Z-numbers, to establish an inference method that improves the performance of the control system
The controller has used the criteria of restriction given for the Marginal Adequacy Degree (MAD) of LAMDA and the reliability of the measures obtained of the sliding surface and its derivative to compute a more aggressive control action in presence of large errors and smooth control action when the error is close to zero
Summary
Uncertain systems are characterized by inexact and fuzziness information, making their modeling and control difficult. In reference [41], we have proposed and formalized an Adaptive LAMDA for control and modeling of systems, modifying the LAMDA structure with the addition of layers operating similar to neural networks, but with the advantage of having a fixed number of layers whose calibration is not trivial This method has a training phase to set initial values for the controller, and an application phase. Z-number, and can be used to determine the ordering of Z-numbers with the aim to be applied in MCMDs under uncertain environments The advantage of this method is to be able to work with triangular, trapezoidal and Gaussian membership functions, considerably expanding its field of application, which could be used by LAMDA.
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