**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 *L*^{1}-distance). Relaxation permits a very convenient linearization the problems. Using the decomposition principle [1], we prove that the upper estimate is an exact expansion.

J.F. Bonnans, N.P. Osmolovski\u\i. Second-order analysis of optimal control problems with control and final-state constraints. 2010.

- 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"** [...]