Computational Optimal Control of the Saint-Venant PDE Model Using the Time-scaling Technique

TL;DR

This paper introduces a novel time-scaling technique for optimal control of the Saint-Venant PDE system, improving computational efficiency and accuracy through nonuniform time discretization.

Contribution

It develops a new time-scaling approach, derives gradient formulas via variational methods, and demonstrates its effectiveness through simulations.

Findings

Time-scaling improves control optimization accuracy.

The method effectively handles distributed parameter systems.

Simulation results show enhanced computational performance.

Abstract

This paper proposes a new time-scaling approach for computational optimal control of a distributed parameter system governed by the Saint-Venant PDEs. We propose the time-scaling approach, which can change a uniform time partition to a nonuniform one. We also derive the gradient formulas by using the variational method. Then the method of lines (MOL) is applied to compute the Saint-Venant PDEs after implementing the time-scaling transformation and the associate costate PDEs. Finally, we compare the optimization results using the proposed time-scaling approach with the one not using it. The simulation result demonstrates the effectiveness of the proposed time-scaling method.