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The Value Function of Singularly Perturbed Control Systems

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Abstract.

The limit as ɛ→ 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton—Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton—Jacobi equation are applicable in cases where the reduction of order, namely setting ɛ = 0 , does not yield an optimal behavior.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel zvika@wisdom.weizmann.ac.il , , , , , , IL

    Z. Artstein

  2. School of Mathematics, University of South Australia, The Levels, Pooraka, South Australia 5095, Australia mavg@lux.levels.unisa.edu.au , , , , , , AU

    V. Gaitsgory

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  1. Z. Artstein
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  2. V. Gaitsgory
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Accepted 18 November 1999

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Artstein, Z., Gaitsgory, V. The Value Function of Singularly Perturbed Control Systems . Appl Math Optim 41, 425–445 (2000). https://doi.org/10.1007/s002459911022

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  • DOI: https://doi.org/10.1007/s002459911022

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