Unified Model Solving Nine Types of Time-Varying Problems in the Frame of Zeroing Neural Network

MNTZNN for Solving Hybrid Double-Deck Dynamic Nonlinear Equation System Applied to Robot Manipulator Control

Compared with conventional dynamic nonlinear equation systems, a hybrid double-deck dynamic nonlinear equation system (H3DNES) not only has multiple layers describing more different tasks in practice, but also has a hybrid nonlinear structure of solution and its derivative describing their nonlinear constraints. Its characteristics lead to the ability to describe more complicated problems involving multiple constraints, and strong nonlinear and dynamic features, such as robot manipulator tracking control. Besides, noises are inevitable in practice and thus strong robustness of models solving H3DNES is also necessary. In this work, a multilayered noise-tolerant zeroing neural network (MNTZNN) model is proposed for solving H3DNES. MNTZNN model has strong robustness and it solves H3DNES successfully even when noises exist in both the two layers of H3DNES. In order to develop the MNTZNN model, a new zeroing neural network (ZNN) design formula is proposed. It not only enables equations with respect to solutions to become equations with respect to the second-order derivatives of solutions but also makes the corresponding model have strong robustness. The robustness of the MNTZNN model is proved when parameters in the model satisfy a loose constraint and the error bounds are programmable via setting appropriate parameter values. Finally, the MNTZNN model is applied to the tracking control of the six-link planar robot manipulator and PUMA560 robot manipulator with hybrid nonlinear constraints of joint angle and velocity.

A Novel Swarm-Exploring Neurodynamic Network for Obtaining Global Optimal Solutions to Nonconvex Nonlinear Programming Problems

A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CDNN) as a local quadratic programming (QP) solver and combining it with a two-timescale model design method, a two-timescale convergent-differential (TTCD) model is exploited, and its stability is analyzed and described in detail. Second, swarm exploration neurodynamics are incorporated into the TTCD model to obtain an SENN with global search capabilities. Finally, the feasibility of the proposed SENN is demonstrated via simulation, and the superiority of the SENN is exhibited through a comparison with existing collaborative neurodynamics methods. The advantage of the SENN is that it only needs a single recurrent neural network (RNN) interact, while the compared collaborative neurodynamic approach (CNA) involves multiple RNN runs.

Zeroing Neural Network With Coefficient Functions and Adjustable Parameters for Solving Time-Variant Sylvester Equation

To solve the time-variant Sylvester equation, in 2013, Li et al. proposed the zeroing neural network with sign-bi-power function (ZNN-SBPF) model via constructing a nonlinear activation function. In this article, to further improve the convergence rate, the zeroing neural network with coefficient functions and adjustable parameters (ZNN-CFAP) model as a variation in zeroing neural network (ZNN) model is proposed. On the basis of the introduced coefficient functions, an appropriate ZNN-CFAP model can be chosen according to the error function. The high convergence rate of the ZNN-CFAP model can be achieved by choosing appropriate adjustable parameters. Moreover, the finite-time convergence property and convergence time upper bound of the ZNN-CFAP model are proved in theory. Computer simulations and numerical experiments are performed to illustrate the efficacy and validity of the ZNN-CFAP model in time-variant Sylvester equation solving. Comparative experiments among the ZNN-CFAP, ZNN-SBPF, and ZNN with linear function (ZNN-LF) models further substantiate the superiority of the ZNN-CFAP model in view of the convergence rate. Finally, the proposed ZNN-CFAP model is successfully applied to the tracking control of robot manipulator to verify its practicability.

A Novel Neural Approach to Infinity-Norm Joint-Velocity Minimization of Kinematically Redundant Robots Under Joint Limits

Generally, the infinity-norm joint-velocity minimization (INVM) of physically constrained kinematically redundant robots can be formulated as time-variant linear programming (TVLP) with equality and inequality constraints. Zeroing neural network (ZNN) is an effective neural method for solving equality-constrained TVLP. For inequality-constrained TVLP, however, existing ZNNs become incompetent due to the lack of relevant derivative information and the inability to handle inequality constraints. Currently, there is no capable ZNN in the literature that has achieved the INVM of redundant robots under joint limits. To fill this gap, a classical INVM scheme is first introduced in this article. Then, a new joint-limit handling technique is proposed and employed to convert the INVM scheme into a unified TVLP with full derivative information. By using a perturbed Fisher-Burmeister function, the TVLP is further converted into a nonlinear equation. These conversion techniques lay a foundation for the success of designing a capable ZNN. To solve the nonlinear equation and the TVLP, a novel continuous-time ZNN (CTZNN) is designed and its corresponding discrete-time ZNN (DTZNN) is established using an extrapolated backward differentiation formula. Theoretical analysis is rigorously conducted to prove the convergence of the neural approach. Numerical studies are performed by comparing the DTZNN solver and the state-of-the-art (SOTA) linear programming (LP) solvers. Comparative results show that the DTZNN consumes the least computing time and can be a powerful alternative to the SOTA solvers. The DTZNN and the INVM scheme are finally applied to control two kinematically redundant robots. Both simulative and experimental results show that the robots successfully accomplish user-specified path-tracking tasks, verifying the effectiveness and practicability of the proposed neural approach and the INVM scheme equipped with the new joint-limit handling technique.