Volume 10, Number 2, August 2009, pp. 157-176
Joël Blot
Key words:
Optimal control, discrete time systems, infinite horizon, Pontryagin principle
Mathematices Subject Classification: 39A05, 49K99, 93C55, 91B62

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	Abstract:
	We give new statements of Pontryagin principles in the setting of infinite-horizon discrete-time optimal control problems with various criteria, when the system is governed by a difference equation or by a difference inequation. In a previous work [3] an invertibility condition of the vector field with respect to the state variable was used. In the present work, after a section devoted to the comparison between the problems governed by difference equations and problems governed by difference inequations, we give new conditions to obtain Pontryagin principles without the using of the above-mentionned invertibility condition: a positivity condition and a partial surjectivity condition.

Infinite-horizon Pontryagin principles without invertibility

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