Homeomorphism Mapping Based Neural Networks for Finite Time Constraint Control of a Class of Nonaffine Pure‐Feedback Nonlinear Systems

This paper proposes a new scheme for solving finite time neural networks adaptive tracking control issue for the nonaffine pure‐feedback nonlinear system. The procedure, based on homeomorphism mapping and backstepping, effectively deals with constraint control and design difficulty induced by pure‐feedback structure. The most outstanding novelty is that finite time adaptive law is proposed for training weights of neural networks. Furthermore, by combining finite time adaptive law and Lyapunov‐based arguments, a valid finite time adaptive neural networks controller design algorithm is presented to ensure that system is practical finite stable (PFS) rather than uniformly ultimately bounded (UUB). Because of using the finite time adaptive law to training weights of neural networks, the closed‐loop error system signals are in assurance of bounded in finite time. Benchmark simulations have well demonstrated effectiveness and efficiency of the proposed approach.