Dynamic optimization of a system with input-dependant time delays

This paper studies one example of dynamic optimisation of systems subject to hydraulic transportation delays. Properly taking into account the variability of the delay in optimisation is a challenging problem, of importance in several applications. While stationary conditions have been derived in earlier works, here we investigate practical numerical aspects and propose a direct resolution method using an orthogonal collocation approach and a state of the art interior point solver. On the basis of the benchmark process considered here, we compute optimal solutions, discuss their surprisingly rich structure and explore the relevance of different numerical schemes.