Abstract
In a simplified version of the pollution subsystem of Forrester's world dynamics model, it is proposed to choose the capital investment policy for maximizing the integral of the quality of life. The optimization is carried out by using Green's theorem and the maximum principle. The optimal control is characterized by a combination of bang-bang and singular control, with the singular are forming a turnpike, corresponding to a global equilibrium policy.
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References
Forrester, J. W.,World Dynamics, Wright-Allen Press, Cambridge, Massachusetts, 1971.
Cuypers, J. G. M.,World Dynamics: Two Simplified Versions of Forrester's Model, Automatica, Vol. 9, No. 3, 1973.
Meadows, D. M., Meadows, D. L., Randers, J., Behrens, W. W.,The Limit to Growth, Potomac Associates/Universe Books, New York, New York, 1972.
Miele, A.,Extremization of Linear Integrals by Green's Theorem, Optimization Techniques, Edited by G. Leitmann, Academic Press, New York, New York, 1962.
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Communicated by J. V. Breakwell
This research was supported by the Consiglio Nazionale delle Ricerche (CNR-GNAS), Roma, Italy.
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Mariani, L., Nicoletti, B. World dynamics: An optimization study of the pollution subsystem. J Optim Theory Appl 17, 251–271 (1975). https://doi.org/10.1007/BF00933879
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DOI: https://doi.org/10.1007/BF00933879