Abstract
Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.
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Communicated by G. Leitmann
This research has been partially supported by the Canada Council, Grant No. S.741122X2, and by the Programme FCAC de la DGES, Ministère de l'Education du Québec, Québec, Canada.
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Haurie, A. Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems. J Optim Theory Appl 31, 515–533 (1980). https://doi.org/10.1007/BF00934475
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DOI: https://doi.org/10.1007/BF00934475