Abstract
We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Highlights
The first works on infinite horizon optimal control problems are due to Pontryagin and his school 1
We consider in this paper an infinite horizon Optimal Control problem in the discrete time framework
Boltianski 12 shows that in the discrete time case, a convexity condition is needed to guarantee a strong Pontryagin Principle while this last one can be obtained without such condition in the continuous time setting
Summary
We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones.
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