Incremental Correction in Dynamic Systems Modelled with Neural Networks for Constraint Satisfaction

TL;DR

This paper introduces incremental correction techniques for neural network-based dynamic systems to improve constraint satisfaction accuracy at specific time points, especially useful in real-time control applications.

Contribution

It develops linearisation-based incremental correction methods for neural network parameters and control functions to enhance solution accuracy in dynamic systems.

Findings

Effective correction of neural network predictions demonstrated in Mars descent simulation.

Improved constraint satisfaction accuracy at interim points achieved.

Real-time application potential for high-precision control confirmed.

Abstract

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints placed on the performance output variables. The proposed approach is to linearise the dynamics around the baseline values of its arguments, and then to solve for the corrective input required to transfer the perturbed trajectory to precisely known or desired values at specific time points, i.e., the interim points. Depending on the type of decision variables to adjust, parameter correction and control function correction methods are developed. These incremental correction methods can be utilised as a means to compensate for the prediction errors of pre-trained neural networks in real-time applications where high accuracy of the prediction of dynamical systems at prescribed time points is imperative. In this regard, the online update approach can be useful for enhancing overall targeting accuracy of finite-horizon control subject to point constraints using a neural policy. Numerical example demonstrates the effectiveness of the proposed approach in an application to a powered descent problem at Mars.