Tuesday, 16:15 - 16:40 h, Room: H 2035

 

Laurent Pfeiffer
Sensitivity analysis for relaxed optimal control problems with final-state constraints

Coauthors: Joseph Frédéric Bonnans, Oana Silvia Serea

 

Abstract:
We consider a family of relaxed optimal control problems with final-state constraints, indexed by a perturbation variable y. Our goal is to compute a second-order expansion of the value V(y) of the problems, near a reference value of y. We use relaxed controls, i.e., the control variable is at each time a probability measure. Under some conditions, a constrained optimal control problem has the same value as its relaxed version.
The specificity of our study is to consider bounded strong solutions [2], i.e., local optimal solutions in a small neighborhood (for the L\infty-distance) of the trajectory. To obtain a sharp second-order upper estimate of V, we derive two linearized problem from a wide class of perturbations of the control (e.g., small perturbations for the L1-distance). Relaxation permits a very convenient linearization the problems. Using the decomposition principle [1], we prove that the upper estimate is an exact expansion.



  1. J.F. Bonnans, N.P. Osmolovski\u\i. Second-order analysis of optimal control problems with control and final-state constraints. 2010.
  2. A.A. Milyutin, N.P. Osmolovski\u\i. Calculus of variations and optimal control. 1998.


 

Talk 3 of the invited session Tue.3.H 2035
"Control and optimization of impulsive systems II" [...]
Cluster 24
"Variational analysis" [...]

 

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