Title data
Grüne, Lars ; Krügel, Lisa:
Local turnpike analysis using local dissipativity for discrete time discounted optimal control.
Bayreuth
,
2021
.  22 pages
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Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
Recent results in the literature have provided connections between the socalled turnpike property, near optimality of closedloop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with discounted stage cost are of great interest. In contrast to nondiscounted optimal control problems, it is more likely that several asymptotically stable optimal equilibria coexist. Due to the discounting and transition cost from a local to the global equilibrium, it may be more favourable staying in a local equilibrium than moving to the global  cheaper  equilibrium. In the literature, strict dissipativity was shown to provide criteria for global asymptotic stability of optimal equilibria and turnpike behavior. In this paper, we propose a local notion of discounted strict dissipativity and a local turnpike property, both depending on the discount factor. Using these concepts, we investigate the local behaviour of (near)optimal trajectories and develop conditions on the discount factor to ensure convergence to a local asymptotically stable optimal equilibrium.