Generating Reachable Set Boundaries for Discrete-Time Systems

  • Walter J. Grantham
  • Michael E. Fisher
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 72)


Computational procedures are presented for determining the reachable set at time k for nonlinear discrete-time control systems, such as a multispecies fishery or other resource management system. In particular, necessary conditions, in the form of a maximum principle, are developed for generating reachable set boundaries at any time k. The maximum principle is analogous to the abnormal case of the discrete-time optimal control maximum principle. However, the results in this paper employ a local maximum principle rather than a global one, and they do not assume convexity of the displacement set. The results are applied to two examples, one of which is a model for a multispecies (krill and Baleen whale) prey-predator fishery.


Maximum Principle Singular Control Resource Management System Baleen Whale Adjoint Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Walter J. Grantham
    • 1
  • Michael E. Fisher
    • 2
  1. 1.Department of Mechanical and Materials EngineeringWashington State UniversityPullmanUSA
  2. 2.Department of MathematicsUniversity of Western AustraliaNedlandsAustralia

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