Optimal Control of Systems Subject to Input-Dependent Hydraulic Delays

In this article, we study the optimal control of systems subject to input-varying hydraulic delays, i.e., systems where the delay on the input depends on the past values of the input through a specific integral relation. The calculus of variations of this problem reveals its nondifferentiable nature. Then, a smooth relaxation is proposed to derive an iterative optimization algorithm. A convergence proof is detailed. The practical interest of the algorithm is evidenced on a numerical example.

Automated summary

This article discusses the optimal control of systems subject to input-varying hydraulic delays, revealing its nondifferentiable nature through the calculus of variations. A smooth relaxation method is proposed to derive an iterative optimization algorithm, with a detailed proof of convergence. The practical interest of the algorithm is demonstrated through a numerical example.