A multi-constrained zeroing neural network for time-dependent nonlinear optimization with application to mobile robot tracking control

Abstract Because of the strong dynamic behavior and computing power, zeroing neural networks (ZNNs) have been dee different time-dependent issues. However, due to the high nonlinearity and complexity, the research on finding a feasible ZNN to address time-dependent nonlinear optimization with multiple types of constraints still remains stagnant. To simultaneously handle multiple types of constraints for the time-dependent nonlinear optimization, this paper proposes a novel neural-network based model in a unified framework of ZNN. By using leveraging the Lagrange method, the time-dependent nonlinear optimization problem with multiple types of constraints is converted to a time-dependent equality system. The proposed multi-constrained ZNN (termed MZNN) inherently possesses the effectiveness of exponential convergence property by utilizing the time-derivative information. Theoretical analyses on the global stability and exponential convergence property are rigorously provided. Then, three general numerical examples in time-independent and time-dependent cases verify the computational performance of the proposed MZNN. An application based on the mobile robot for nonlinear optimization control sufficiently demonstrates the physical effectiveness of the proposed MZNN for the control of mobile robot with both performance-index optimization and multiple physical-limit constraints. Finally, comparisons with existing neural networks such as gradient neural network (GNN), and performance tests with investigation on computational complexity substantiate the superiority of the MZNN for the time-dependent nonlinear optimization subject to multiple types of constraints.