**Tuesday, 15:45 - 16:10 h, Room: H 2035**

**Elena Goncharova**

Impulsive systems with mixed constraints

**Coauthor: Maxim Staritsyn**

**Abstract:**

We consider an optimal control problem for an impulsive hybrid system. Such a dynamical system can be described by a nonlinear measure differential equation under mixed constraints on a state trajectory and a control measure. The

constraints are of the form

\begin{gather*}

Q_{-}\big(x(t-)\big) =0, Q_{+}\big(x(t)\big)=0, \

Ψ\big(x(t-)\big) ≤ 0, Ψ\big(x(t)\big) ≤ 0 ν -a.e. on *[0, T]. *

\end{gather*}

Here, *x(t-)*, *x(t)* are the left and right limits of a state trajectory *x* at time *t*, a non-negative scalar measure * ν * is the total variation of an "impulsive control'', and * ν ([0, T]) ≤ M* with *M>0*. Such conditions can be also regarded as state constraints of equality and inequality type qualified to hold only over the set where * ν * is localized. A time reparameterization technique is developed to establish a result on the problem transformation to a classical optimal control problem with absolutely continuous trajectories. Based on this result, a conceptual approach is proposed to design numerical methods for optimal impulsive control. We give some results on numerical simulation of a double pendulum with a blockable degree of freedom.

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*Talk 2 of the invited session Tue.3.H 2035

**"Control and optimization of impulsive systems II"** [...]

Cluster 24

**"Variational analysis"** [...]