What is it about?

Often in dynamic optimal control problems with a long time horizon, in a large neighburhood of the middle of the time interval the optimal control and the optimal state are very close to the solution of a static control problem that is derived form the dynamic optimal control problems by omitting the information about the initial state and possibly a desired terminal state. This is called the *turnpike phenomenon*. This name is motivated by the fact that for all the starting points in a certain neighbourhood of a freeway (turnpike is another name for a freeway) entrance, the fastes way to a fixed target close to a freeway exit often goes through this point on the freeway and then stays on the freeway, regardless of the precise initial state.

Featured Image

Why is it important?

Many systems in engineering evolve in time. However, the corresponding optimal control problems with an evolution equation which is often a partial differential equation are very time-consuming to solve. Therefore it is of interest to reduce the computational time by going to a static optimal control problem where time does not play a role.

Perspectives

Our aim is to use results about the turnpike phenomenon to problems of optimal boundary control with hyperbolic partial differential equations that appear as models for the optimal operation of gas transportation networks. The control variables are on one hand the pressure control by compressor stations and on the other hand control of valves in the network that leads to switching decisions. The aim of the control is to make sure that the customer demands can be sattisfied. The possible demands are fixed by contracts a priori. In this operation, state constraints have to be satisfied: The gas pressure has to be within a prescribed range and the gas velocity has to be suficiently small.

Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg

Read the Original

This page is a summary of: On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems, SIAM Journal on Control and Optimization, January 2019, Society for Industrial & Applied Mathematics (SIAM),
DOI: 10.1137/17m1134470.
You can read the full text:

Read

Resources

Contributors

The following have contributed to this page