# American Institute of Mathematical Sciences

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2007, 2007(Special): 456-466. doi: 10.3934/proc.2007.2007.456

## Optimal control of a nonlinear model of economic growth

 1 Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204 2 Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992

Received  September 2006 Revised  January 2007 Published  September 2007

A nonlinear control model of a firm describing the change of production and accumulated $R&D$ investment is investigated. An optimal control problem with $R&D$ investment rate as a control parameter is solved. Optimal dynamics of economic growth of a firm versus the current cost of innovation is studied. It is analytically determined that dependent on the model parameters, the optimal control must be of one of the following types : a) piecewise constant with at most two switchings, b) piecewise constant with two switching and containing a singular arc. The intervals on which switching from regular to singular arcs occur are found numerically. Finally, optimal investment strategies and production activities are compared with econometric data of an actual firm.
Citation: Ellina Grigorieva, Evgenii Khailov. Optimal control of a nonlinear model of economic growth. Conference Publications, 2007, 2007 (Special) : 456-466. doi: 10.3934/proc.2007.2007.456
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