Core Concepts
The turnpike property is crucially connected to system theoretical properties, providing insights into optimal control solutions.
Abstract
This paper explores necessary conditions for the turnpike property in generalized linear-quadratic optimal control problems. The turnpike property signifies that optimal trajectories and controls remain close to a steady state over a large time horizon. Various notions of the turnpike property have been studied extensively in connection with stability and control systems. The exponential turnpike property is highlighted as a significant concept, reflecting hyperbolicity around the steady state. Necessary conditions are derived for measure and exponential turnpike properties, emphasizing stabilizability and detectability of the system. The equivalence between different types of turnpike properties is established, offering structural insights into optimal solutions.
Stats
Over a sufficiently large time horizon, optimal trajectories stay close to steady state.
Exponential stabilizability and detectability are crucial for the turnpike property.
Equivalence between different types of turnpike properties.
Quotes
"The term 'generalized' means both quadratic and linear terms are considered in the running cost."
"Turnpike phenomena provide structural insights into optimal solutions."
"Exponential turnpike property naturally appears when exploiting hyperbolicity around the steady state."
"The occurrence of turnpike property is closely linked to some structural-theoretical properties of the system."
"The monographs present a complete overview on turnpike properties in various optimal control problems."