Control of systems to sets and their interiors

  • F. H. Clarke
  • P. R. Wolenski
Contributed Papers


For a closed target setS⊏ℝ n and a control system (formulated as a differential inclusion and defined nearS), the present paper considers a sufficient condition for the property that every point nearS can be steered toS in finite time by some trajectory of the system. Estimates are obtained revealing how fast some such trajectory is nearing the target. A strong form of this condition is shown to imply that every trajectory of the system hits the target. With a further assumption on the target setS, we also consider conditions that guarantee that some trajectories enter the interior ofS.

Key Words

Weak and strong attainability control systems penetrative systems minimum time function 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • F. H. Clarke
    • 1
  • P. R. Wolenski
    • 2
  1. 1.Centre de Recherches Mathématiques (CRM)Université de MontréalMontréalCanada
  2. 2.Department of MathematicsLouisiana State UniversityBaton Rouge

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