Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TIME-OPTIMAL BANG-BANG TRAJECTORIES USING BIFURCATION RESULT

  • Published : 1997.08.01
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Abstract

This paper is concerned with the control problem $$ \dot{x}(t) = F(x) + u(t)G(x), t \in [0,T], x(0) = 0, $$ where F and G are smooth vector fields on $R^n$, and the admissible controls u satisfy the constraint $$\mid$u(t)$\mid$ \leq 1$. We provide the sufficient condition that the bang-bang trajectories having different switching orders intersect.

Keywords

References

  1. Controlled Dynamical Systems Nilpotent approximations and optimal trajectories A. Bressan
  2. SIAM J. Control & Opt. v.24 The generic local timeoptimal stabilizing control in dimension 3 A. Bressan
  3. SISSA Lecture notes on the Mathematical Theory of Control A. Bressan
  4. Geometry of Manifolds R. L. Bishop;R. J. Crittenden
  5. Optimization Theory and Applications L. Cesari
  6. Methods of Bifurcation Theory S. N. Chow;J. K. Hale
  7. SIAM J. Control & Opt. v.27 The structure of small time reachable sets in low dimensions A. Krener;H. Schattler
  8. Applied Mathematics J. D. Logan
  9. Proceedings of the 28th Conference on Decision and Control (1989) Conjugate points and intersections of bang-bang trajectories H. Schattler
  10. SIAM J. Control & Opt. v.26 On the local structure of time-optimal bang-bang trajectories in R³ H. Schattler
  11. Proceedings of the 28th Conference on Decision and Control Envelopes, high-order optimality conditions and Lie brackets H. Sussmann