Second order optimality conditions in the smooth case and applications in optimal control

@article{Bonnard2007SecondOO,
  title={Second order optimality conditions in the smooth case and applications in optimal control},
  author={B. Bonnard and Jean-Baptiste Caillau and E. Tr{\'e}lat},
  journal={ESAIM: Control, Optimisation and Calculus of Variations},
  year={2007},
  volume={13},
  pages={207-236}
}
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions… Expand
Computation of conjugate times in smooth optimal control: the COTCOT algorithm
Geometric optimal control and applications to aerospace
Optimal control theory and some applications to aerospace problems
Optimal Control and Applications to Aerospace: Some Results and Challenges
  • E. Trélat
  • Mathematics, Computer Science
  • J. Optim. Theory Appl.
  • 2012
Optimal Control of Endoatmospheric Launch Vehicle Systems: Geometric and Computational Issues
Inverse Optimal Control : theoretical study
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 41 REFERENCES
Introduction to nonlinear optimal control
Foundations of optimal control theory
Geometric optimal control of elliptic Keplerian orbits
Control Theory from the Geometric Viewpoint
Singular Trajectories and Their Role in Control Theory
The High Order Maximal Principle and Its Application to Singular Extremals
THE INDEX OF THE SECOND VARIATION OF A CONTROL SYSTEM
Second Order Optimality Conditions
Asymptotics of accessibility sets along an abnormal trajectory
Feedback equivalence for nonlinear systems and the time optimal control problem
...
1
2
3
4
5
...