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.

 

Talk 2 of the invited session Tue.3.H 2035
"Control and optimization of impulsive systems II" [...]
Cluster 24
"Variational analysis" [...]

 

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