Parameter-Gain Accelerated ZNN Model for Solving Time-Variant Nonlinear Inequality-Equation Systems and Application on Tracking Symmetrical Trajectory

Time-variant nonlinear problems have always been a kind of complex research object in the field of control. The accuracy and efficiency of settling time-variant nonlinear inequality-equation (NIE) systems are often affected by the nonlinearity degree of the systems, and there are currently no complete algorithms to settle the time-variant NIE systems effectively. To settle this class of complex systems effectively, time-variant NIE systems are first equivalently transformed into a time-variant equation by introducing a nonnegative variable. Then, through the idea of zeroing neural network (ZNN) and the role of time-variant parameter-gain functions, a parameter-gain accelerated ZNN (PGAZNN) model is proposed to solve time-variant NIE systems. Theoretically, the stability of the proposed PGAZNN model is proved by strict mathematical analysis. In addition, the PGAZNN model can achieve fixed-time convergence, and the upper-bound of convergence time is estimated. Finally, numerical simulation example and symmetry trajectory tracking are given to verify the validity and correctness of the proposed PGAZNN model.