On Turnpike and Dissipativity Properties of Continuous-Time Optimal Control Problems
For researchers in optimal control theory, this work provides a unified theoretical framework linking three key properties, though it is an incremental extension of existing discrete-time results to continuous-time.
This paper establishes the equivalence between dissipativity, optimal operation at steady state, and the turnpike property for continuous-time optimal control problems, proving both forward and converse implications. Numerical examples illustrate the theoretical results.
This paper investigates the relations between three different properties, which are of importance in optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady state, and the turnpike property. We show in a continuous-time setting that if along optimal trajectories a strict dissipation inequality is satisfied, then this implies optimal operation at this steady state and the existence of a turnpike at the same steady state. Finally, we establish novel converse turnpike results, i.e., we show that the existence of a turnpike at a steady state implies optimal operation at this steady state and dissipativity with respect to this steady state. We draw upon a numerical example to illustrate our findings.