An exponential turnpike theorem for dissipative discrete time optimal control problems

Tobias Damm (1) , Lars Grüne (2) , Marleen Stieler (2) , Karl Worthmann (2)

1 Mathematical Institute
2 Mathematisches Institut [Bayreuth]

We investigate the exponential turnpike property for nite horizon undercounted 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.

Domaines: Optimisation et contrôle [math.OC]

Tobias Damm, Lars Grüne, Marleen Stieler, Karl Worthmann. An exponential turnpike theorem for dissipative discrete time optimal control problems. SIAM Journal on Control and Optimization, 2014, 52 (3), pp.1935-1957. ⟨10.1137/120888934⟩. ⟨hal-00944266⟩