Zhang Neural Network Model for Time-Variant Convex Optimization Involving Nonlinear Inequality Constraints With Robotic Application
提出一种可微变换函数，结合拉格朗日乘子和KKT条件，将含非线性不等式约束的时变凸优化问题转化为等式系统，并设计张神经网络模型，集成滑模控制以抑制噪声，在机器人路径跟踪中验证有效性。
Time-variant convex optimization involving nonlinear inequality constraints (TVCOINICs) is a challenging problem due to the nonlinearity and time-variant nature of its objective function and multitype constraints. Differing from traditional slack variables and projection operator methods, this article proposes a novel differentiable transform function that is continuous and differentiable everywhere, while eschewing the need for additional tunable hyperparameters. On the basis of the Lagrange multiplier technique and Karush–Kuhn–Tucker (KKT) conditions, the initial time-variant optimization problem is converted into a time-variant nonlinear system comprising both equalities and inequalities. By employing the proposed differentiable transform function, this system is then further refined into an equivalent time-variant nonlinear system of equalities. Subsequently, the comprehensive design process of the differentiable transform function-based Zhang neural network (DTFZNN) model is delineated, which, through the comprehensive utilization of the time derivatives and error feedback information, is capable of adeptly addressing the TVCOINICs problem. Moreover, sliding mode control (SMC) is integrated into the proposed model to endow it with verified noise-suppression capability. The relevant theorems prove its convergence and robustness, and corresponding numerical experiments verify its effectiveness. Ultimately, to evaluate the practical efficacy of the proposed model, the proposed model is implemented to address the path tracking and repetitive motion problem associated with a robotic arm, thereby illustrating its superiority in solving practical problems.