The problem of multi-robot formation is prevalent in scientific and engineering applications, where robots must adapt to uncertain and dynamic behaviors due to real-time environmental or task changes. Traditional methods struggle to meet the demand for high-precision solutions within finite time frames. Zeroing Neural Networks (ZNNs), which utilize the time derivatives of time-varying coefficients, outperform other networks in handling dynamic system behaviors. This paper marks the first attempt to extend the ZNN approach to address finite-time multi-robot through optimization modeling. We introduce an innovative strategy that employs complex number structures to map robot coordinates, simplifying the computation needed for dynamic formation tasks. Additionally, we present a multi-robot formation strategy that minimizes the distance between neighboring robots while adhering to bias-type center constraint. This is effectively reformulated as a complex-valued time-varying matrix equation. Based on this, two complex-type Finite-Time Zeroing Dynamic Controllers (FTZDC) are designed, with their stability and convergence time bounds rigorously analyzed. Finally, in two specific formation tasks, the proposed strategy and FTZDC models achieve precise multi-robot formation, independent of the robots’ initial positions, all within finite time.

Neural dynamics is a powerful tool to solve online optimization problems and has been used in many applications. However, some problems cannot be modelled as a single objective optimization and neural dynamics method does not apply. This paper proposes the first neural dynamics model to solve bi-objective constrained quadratic program, which opens the avenue to extend the power of neural dynamics to multi-objective optimization. We rigorously prove that the designed neural dynamics is globally convergent and it converges to the optimal solution of the bi-objective optimization in Pareto sense. Illustrative examples on bi-objective geometric optimization are used to verify the correctness of the proposed method. The developed model is also tested in scientific computing with data from real industrial data with demonstrated superior to rival schemes.

The computation of matrix pseudoinverses is a recurrent requirement across various scientific computing and engineering domains. The prevailing models for matrix pseudoinverse typically operate under the assumption of a noise-free solution process or presume that any noise present has been effectively addressed prior to computation. However, the concurrent real-time computation of time-varying matrix pseudoinverses holds significant practical utility, while the preemptive preprocessing for noise elimination or reduction may impose supplementary computational overheads on real-time implementations. Different from previous models for solving the pseudoinverse of time-varying matrices, in this paper, a model for solving the pseudoinverse of time-varying matrices using a double-integral structure, called Double-Integral-Enhanced Zeroing Neural Network (DIEZNN) model, is proposed and investigated, which is capable of solving time-varying matrix pseudoinverse while efficiently eliminating the negative effects of linear noise perturbations. The experimental results show that in the presence of linear noise, the DIEZNN model demonstrates better noise suppression performance compared to both the original zeroing neural network model and the Zeroing Neural Network (ZNN) model enhanced with a Li-type activation function. In addition, these models are applied to the control of chaotic system of controllable permanent magnet synchronous motor, which further verifies the superiority of DIEZNN in engineering application.