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Turnpike theorems deal with the optimality of trajectories reaching a
singular solution, in calculus of variations or
optimal control problems.
For scalar calculus of variations problems in infinite horizon, linear with
respect to the derivative, we use the theory of viscosity solutions of
Hamilton-Jacobi equations to obtain a unique characterization of the value
function.
With this approach, we extend for the scalar case the classical result based on
Green theorem, when there is uniqueness of...
This work deals with a non linear inverse problem of reconstructing
an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type,
by using boundary measurements. The problem is turned into an optimal shape design one, by constructing
a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary.
Furthermore, we prove that the derivative of this cost function with respect to a direction θ
depends only on the state u0, and not...
We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump
set A or a controlled jump set C where controller can choose to jump or not. At each jump, trajectory can move to a different Euclidean space.
We allow the cost functionals to be unbounded with certain growth and hence...
This paper analyzes the relation of viability kernels and control
sets of control affine systems. A viability kernel describes
the largest closed viability domain contained in some closed subset
Q of the state space. On the
other hand, control sets are maximal regions of the state space
where approximate controllability holds. It turns out that
the viability kernel of Q can be represented by the union of
domains of attraction of chain control sets, defined relative
to the given set Q.
In particular,...
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