An Exponential Turnpike Theorem for Dissipative Discrete Time Optimal Control Problems

An Exponential Turnpike Theorem for Dissipative Discrete Time Optimal Control Problems

We investigate the exponential turnpike property for finite horizon undiscounted discrete time optimal control problems without any terminal constraints. Considering a class of strictly dissipative systems, we derive a boundedness condition for an auxiliary optimal value function which implies the e...

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Veröffentlicht in:SIAM journal on control and optimization 2014-01, Vol.52 (3), p.1935-1957
Hauptverfasser: Damm, Tobias, Grune, Lars, Stieler, Marleen, Worthmann, Karl
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Control systems
Controllability
Dissipation
Equilibrium
Mathematical analysis
Mathematics
Optimization
Optimization and Control
Roads & highways
Terminal constraints
Theorems
Time optimal control
Toll roads
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Zusammenfassung:We investigate the exponential turnpike property for finite horizon undiscounted discrete time optimal control problems without any terminal constraints. Considering a class of strictly dissipative systems, we derive a boundedness condition for an auxiliary optimal value function which implies the exponential turnpike property. Two theorems illustrate how this boundedness condition can be concluded from structural properties like controllability and stabilizability of the control system under consideration. [PUBLICATION ABSTRACT]
ISSN:0363-0129
1095-7138
DOI:10.1137/120888934