A Recurrent Neural Network With Explicitly Definable Convergence Time for Solving Time-Variant Linear Matrix Equations

Abstract

Time-variant linear matrix equations (TVLMEs) are ubiquitous in engineering. To solve TVLMEs, various zeroing neural network (ZNN) models have been developed. These ZNNs globally converge to the solution of TVLMEs either in infinity long time or in finite time. However, even the convergence time of a finite-time convergent ZNN is implicit and closely dependent on the initial condition of a problem. This may reduce its applicability to time-critical applications in practice. To overcome this problem, this paper for the first time accelerates a ZNN to fixed-time convergence using a novel activation function. The convergence time of the proposed ZNN can be antecedently defined as an explicit parameter. Theoretically, its fixed-time convergence and robustness properties are rigorously proved. Comparative numerical results substantiate the superior convergence and robustness performance of the fixed-time convergent ZNN for TVLMEs solving. Additionally, the fixed-time convergent ZNN is applied to motion planning of a redundant robotic arm.