Infinite Horizon Optimal Control pp 97-123 | Cite as

# Asymptotic Stability with a Discounted Criterion; Global and Local Analysis

Chapter

## Abstract

In this chapter, the global asymptotic stability (G.A.S.) property of optimal controlled systems with an infinite time horizon will be further explored by considering the case where the criterion has the following form:
The term e

$$ {J_8}\left( {x,u} \right) = \int\limits_0^8 {{e^{ - pt}}{t_0}\left( {x\left( t \right),u\left( t \right)} \right)dt} $$

(5.1)

^{-ρt}is a discount factor and*ρ*is the discount rate. If*ρ*is positive and f_{o}(x,u) is bounded then the integral converges when*8→∞*. A positive discount rate is used when the future earnings have to be discounted due to an interest rate*ρ*. In that case the relative weighting given to a distant future makes it negligible, hence one may suppose that high positive values of*ρ*can have a destabilizing effect on the optimal trajectories.## Keywords

Stationary Point Discount Rate Hamiltonian System Optimal Trajectory Global Asymptotic Stability
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## References

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## Additional Reference

- 10.C. D. Feinstein and S. S. Oren, A “funnel” turnpike theorem for optimal growth problems with discounting, Journal of Economic Dynamics and Control Vol. 9, pp. 25–39, 1985.CrossRefGoogle Scholar
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1987