A simple, fast and robust Passive Velocity Field Control (PVFC) scheme for contour tracking in 2D and 3D is presented. A model-free and chattering-free second order sliding mode controller is proposed, which enforces an invariant manifold for all time such that the generalized velocity tracks the spatial velocity field. A constructive simple and intuitive method to design this velocity field is built upon a fuzzy aggregation of orthogonal vectors to guide the end-effector subject to a dissipative map. Stability properties in the sense of Lyapunov establish the fast and yet smooth tracking with typical robustness of sliding modes. In this way, the closed-loop system exhibits the mildness of PVFC but it evades the subtle complexities of the original approach PVFC. A simulation study is discussed, and experimental results highlight the characteristics of the proposed approach.

The adaptive controller for a class of nonlinear discrete-time systems based on Multi-Input Fuzzy Rules Emulated Network (MIFREN) is introduced in this article. MIFREN is assigned to identify the unknown plant under control, then a novel control law is introduced based the previously identified plant with another MIFREN. All control parameters, including the learning rates are selected to guarantee bounded close-loop signals, via Lyapunov stability criteria. The performance of the proposed control algorithm is demonstrated by computer simulation results.