Impacts of Discretization and Numerical Propagation on the Ability to Follow Challenging Square Wave Commands

Abstract

This study determines the threshold for the computational rate of actuator motor controllers for unmanned underwater vehicles necessary to accurately follow discontinuous square wave commands. Motors must track challenging square-wave inputs, and identification of key computational rates permit application of deterministic artificial intelligence (D.A.I.) to achieve tracking to a machine-precision degree of accuracy in direct comparison to other state-of-art approaches. All modeling approaches are validated in MATLAB simulations where the motor process is discretized at varying step-sizes (inversely proportional to computational rate). At a large step-size (fast computational rate), discrete D.A.I. shows a mean error more than three times larger than that of a ubiquitous model-following approach. Yet, at a smaller step size (slower computational rate), the mean error decreases by a factor of 10, only three percent larger than that of continuous D.A.I. Hence, the performance of discrete D.A.I. is critically affected by the sampling period for discretization of the system equations and computational rate. Discrete D.A.I. should be avoided when small step-size discretization is unavailable. In fact, continuous D.A.I. has surpassed all modeling approaches, which makes it the safest and most viable solution to future commercial applications in unmanned underwater vehicles.

Artificial Intelligence Enhanced UUV Actuator Control

“…As a sequel of Koo [13], multiple propositions are evaluated in Section 2. Validating research is included in Section 3, with direct comparisons between each algorithm based on canonical figures of merit.…”

“…This manuscript continues the investigation of Koo [13] in a deterministic artificial intelligence learning approach following the recommendation provided by Shah [14]. In Section 3, the comparison analysis of computational rate is evaluated for the adaptive and learning methods.…”

“…The development of adaptive and learning systems has a long history that is presently culminating in a very recent, distinguished lineage in the literature [4,11,12,13,14], already bestowing three major publication awards, validating the contemporary interest in continued developments. Many techniques are available from this long lineage as alternatives benchmarks for comparing newly proposed methods.…”

“…The feedback signal was formatted by Koo as an adaptive & learning system (proportional derivative feedback and 2-norm optimal least squares). [13] As a duplication and continuation of Koo's work in [13], this manuscript provides an in-depth comparison between the performance of the deterministic artificial intelligence and declared benchmark approaches with iterated step sizes. The performance evaluation mainly focuses on the ability to track the command signals represented by challenging square wave trajectories.…”

“…A similar phenomenon is revealed in Section 3 of this manuscript for the error distribution comparison of different algorithms. This manuscript describes a duplication and continuation of the work presented in [13], which is also work based on its prequel research by Shah [14], where model-following self-turning regulators [22] are chosen as the comparative benchmark approach.…”