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Controllability of a nonholonomic macroeconomic system. (English) Zbl 1257.49022
Summary: This paper studies optimal control problems and sub-Riemannian geometry on a nonholonomic macroeconomic system. The main results show that a nonholonomic macroeconomic system is controllable either by trajectories of a single-time driftless control system (single-time bang-bang controls), or by nonholonomic geodesics or by sheets of a two-time driftless control system (two-time bang-bang controls). They are strongly connected to the possibility of describing a nonholonomic macroeconomic system via a Gibbs-Pfaff equation or by four associated vector fields, based on a contact structure of the state space and our isomorphism between thermodynamics and macroeconomics that praises three laws of a nonholonomic macroeconomic system.
MSC:
49K30Optimal solutions belonging to restricted classes
53C17Sub-Riemannian geometry
91B64Macro-economic models (monetary models, models of taxation)
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