A Strictly Predefined-Time Convergent Neural Solution to Equality- and Inequality-Constrained Time-Variant Quadratic Programming

Abstract

Aiming at time-variant problems solving, a special type of recurrent neural networks, termed zeroing neural network (ZNN), has been proposed, developed, and validated since 2001. Although equality-constrained time-variant quadratic programming (TVQP) has been well solved using the ZNN approach, TVQP problems with inequality constraints involved have not been satisfactorily handled by the existing ZNN models. To overcome this issue, this paper designs a ZNN model with exponential convergence for solving equality- and inequality-constrained TVQP problems. Considering a fast convergence is preferred in some time-critical applications in practice, a predefined-time stabilizer is for the first time utilized to endow the ZNN model with predefined-time convergence, leading to a predefined-time convergent ZNN (PTCZNN) model that exhibits an antecedently- and explicitly-defined convergence time. Theoretical analysis is performed with the convergence of the two ZNN models including the predefined-time convergence of the PTCZNN model rigorously proved. Validations are comparatively conducted to verify the effectiveness and superiority of the PTCZNN model in terms of convergence performance. To demonstrate the potential applications, the PTCZNN model is applied to image fusion and kinematic control of two robotic arms with joint limits considered. The efficacy and applicability of the PTCZNN model are validated by the illustrative examples. This is the first time to develop a ZNN model working as a quadratic programming solver that is applicable to kinematic control of robotic arms with joint constraints handled since the emergence of ZNNs.