Prescribed Performance Control for Solving Time-Varying Underdetermined Linear Systems With Bounds on States and Their Derivatives

Abstract

This article addresses the problem of finding online solutions to time-varying underdetermined linear systems with limits on states and their derivatives through a novel zeroing neural network (ZNN) implementation. The proposed model combines zeroing dynamics with user-prescribed performance constraints to ensure that the system achieves desired transient and steady-state behavior. The novelty of this approach lies in a nonlinear invertible mapping that transforms the constrained system to an unconstrained one so that the resulting error remains subsequently bounded by the performance function for all time. In particular, two different ZNN models are synthesized that rely on an exponentially convergent and finite-time convergent performance function to drive the residual error to convergence. The effectiveness of the proposed models is verified through redundancy resolution in path-tracking problems in robotics. A detailed performance comparison study with two leading alternative designs is also undertaken to further illustrate the merits of the proposed schemes.