Adaptive fuzzy logic control of discrete-time dynamical systems
The aim of this paper is to describe an approach to tracking control for a class of nonlinear dynamical systems with unknown properties using a discrete-time fuzzy logic controller. The discrete-time feature is important because fuzzy logic controllers are most often implemented on digital computers. The authors present a design algorithm and provide a stability proof for an adaptive, model free, universal fuzzy logic controller that uses basis vectors derived from the fuzzy system. By contrast, most approaches with standard adaptive control use basis vectors that depend on the unknown plant, and are often very tedious to compute. To adapt the fuzzy system parameters, the authors use an approach based on \(\varepsilon\)-modification. With very modest assumptions about the class of discrete-time nonlinear systems, the authors use Lyapunov methods to show that their adaptive fuzzy logic controller guarantees uniform boundedness of the closed-loop signals, and the controller achieves the desired tracking control. Although passivity cannot ordinarily be guaranteed in adaptive fuzzy logic control, the authors' approach does guarantee desirable passivity properties. The authors also provide simulation results that show good tracking of nonlinear dynamics without any a priori information.
scientific article; zbMATH DE number 1394977