Optimality Conditions and the Hamiltonian for a Distributed Optimal Control Problem on Controlled Domain
- 201 Downloads
The paper investigates an optimal control problem for a distributed system arising in the economics of endogenous growth. The problem involves a specific coupled family of controlled ODEs parameterized by a parameter (representing the heterogeneity) running over a domain that may dynamically depend on the control and on the state of the system. Existence of an optimal control is obtained and continuity of any optimal control with respect to the parameter of heterogeneity is proved. The latter allows to substantially strengthen previously obtained necessary optimality conditions and to obtain a Pontryagin’s type maximum principle. The necessary optimality conditions obtained here have a Hamiltonian representation, and stationarity of the Hamiltonian along any optimal trajectory is proved in the case of time-independent data.
KeywordsOptimal control Distributed control Controlled domain Pontryagin-type maximum principle Endogenous economic growth
Mathematics Subject Classification49K20 49K21 49J20
This research was funded by the Austrian Science Foundation (FWF) under Grant No I 476-N13.
- 3.Belyakov, A., Haunschmied, J., Veliov, V.M.: General Equilibrium Model with Horizontal Innovations and Heterogeneous Products, Reserch Report 2012–01, ORCOS, TU Wien. http://orcos.tuwien.ac.at/research/research_reports/ (2012)
- 5.Dixit, A.K., Stiglitz, J.E.: Monopolistic competition and optimum product diversity. Am. Econ. Rev. 67(3), 297–308 (1977)Google Scholar
- 6.Grossman, G.M., Helpman, E.: Innovation and Growth in the Global Economy. MIT, Cambridge (1991)Google Scholar