Controllability of a nonholonomic macroeconomic system. (English) Zbl 1257.49022

Udrişte, C.; Ferrara, M.; Zugrăvescu, D.; Munteanu, F.

J. Optim. Theory Appl. 154, No. 3, 1036-1054 (2012).

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:

49K30	Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
53C17	Sub-Riemannian geometry
91B64	Macroeconomic theory (monetary models, models of taxation)

Keywords:

nonholonomic economic system; extremals with nonholonomic constraints; controllability; sub-Riemannian geometry; simulations of economic paths

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