Abstract
The main purpose of viability theory is to explain the evolution of the state of a control system governed by nondeterministic dynamics and subjected to viability constraints, reveal the concealed feedbacks which allow the system to be regulated and provide selection mechanisms for implementing them. It assumes implicitly an “opportunistic” and “conservative” behavior of the system: a behavior which enables the system to keep viable solutions as long as its potential for exploration (or its lack of determinism) — described by the availability of several evolutions — makes its regulation possible. It also happens that these results can be used to study infinite horizon optimal control problems, with in-tergenerational constraints, with nonstandard inter-temporal optimality criteria bearing not only on the evolutions of the states and the controls, but also on the velocities of the controls, allowing us in particular to minimize maximal inertia. We illustrate these points with simplified Greenhouse Gas models, where we minimize the worst transition cost of changing the short-term pollution rate (or economic growth) in order to maintain the concentration of greenhouse gases bounded.
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Aubin, JP., Bernado, T., Saint-Pierre, P. (2005). A Viability Approach to Global Climate Change Issues. In: Haurie, A., Viguier, L. (eds) The Coupling of Climate and Economic Dynamics. Advances in Global Change Research, vol 22. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3425-3_5
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DOI: https://doi.org/10.1007/1-4020-3425-3_5
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