Title data
Grüne, Lars ; Guglielmi, Roberto:
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems.
Bayreuth
,
2017
.  20 S.


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Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract
We investigate turnpike behaviour of discrete time optimal control problems with linear dynamics and linearquadratic cost functions including state and control constraints. We give necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. As important tools we use the concepts of strict dissipativity and a new property called strict predissipativity of a system at an equilibrium point and link these properties to the turnpike behaviour of the optimal control problem. Moreover, we give further conditions to ensure that the turnpike behavior is of exponential type, i.e., the optimal trajectories are exponentially close to a steadystate of the system for all but finitely many time instants whose number is bounded independently of the optimization horizon.