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Control Systems with Jumps in the State Variables

Karl Vind

Abstract

Pontryagin's Principle can be and has been used in inventory theory, production theory, capital theory and growth theory. The idea presented in this paper shows how the principle can be used also when a firm operates in a market economy or a country in a world market. The resulting jumps in the state variables--amount of capital, amount sold of a commodity, etc.--will disappear through a reinterpretation of the system. The idea is that time is one of the variables and the speed of time can be controlled. By stopping time and letting the other variables change, one can get jumps with respect to time.