Terminal zeroing neural network for time-varying matrix computing under bounded noise

To improve the convergence performance of zeroing neural network (ZNN) for time-varying matrix computation problems solving, a terminal zeroing neural network (TZNN) with noise resistance and its logarithmically accelerated form (LA-TZNN) were proposed. The terminal attraction of the error dynamic equation were analyzed, and the results showed that the neural state of the proposed networks can converge to the theoretical solution within a fixed time when subjected to bounded noises. In addition, the LA-TZNN could achieve logarithmical settling-time stability, and its convergence speed was faster than the TZNN. Considering that the initial error was bounded in actual situations, an upper bound of the settling-time in a semi-global sense was given, and an adjustable parameter was set to enable the network to converge within a predefined time. The two proposed models were applied to solve the time-varying matrix inversion and trajectory planning of redundant manipulators PUMA560. The simulation results further verified that compared with the conventional ZNN design, the proposed methods have shorter settling-time, higher convergence accuracy, and can effectively suppress bounded noise interference.