Controllability and extremality in nonconvex differential inclusions

  • H. D. Tuan
Contributed Papers


LetF:[0, T]×R n →2 R n be a set-valued map with compact values; let η:R n →R m be a locally Lipschitzian map,z(t) a given trajectory, andR the reachable set atT of the differential inclusion\(\dot x(t) \in F(t,x(t))\). We prove sufficient conditions for η(z(T))∈intR and establish necessary conditions in maximum principle form for η(z(T))∈(R). As a consequence of these results, we show that every boundary trajectory is simultaneously a Pontryagin extremal, Lagrangian extremal, and relaxed Lagrangian extremal.

Key Words

Differential inclusions η-local controllability η-extremality Kaskosz maximum principle 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • H. D. Tuan
    • 1
  1. 1.Department of Electronic and Mechanical EngineeringNagoya UniversityNagoyaJapan

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