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Dynamic Optimization for Reachability Problems

Author

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  • A. B. Kurzhanski
  • P. Varaiya

Abstract

This paper uses dynamic programming techniques to describe reach sets andrelated problems of forward and backward reachability. The original problemsdo not involve optimization criteria and are reformulated in terms ofoptimization problems solved through the Hamilton–Jacobi–Bellmanequations. The reach sets are the level sets of the value function solutionsto these equations. Explicit solutions for linear systems with hard boundsare obtained. Approximate solutions are introduced and illustrated forlinear systems and for a nonlinear system similar to that of theLotka–Volterra type.

Suggested Citation

  • A. B. Kurzhanski & P. Varaiya, 2001. "Dynamic Optimization for Reachability Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 227-251, February.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:2:d:10.1023_a:1026497115405
    DOI: 10.1023/A:1026497115405
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    Cited by:

    1. Yurilev Chalco-Cano & Valeriano A. Oliveira & Geraldo N. Silva, 2015. "Description of the Attainable Sets of One-Dimensional Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 138-153, January.

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