3,054 research outputs found
Norm and time optimal control problems of stochastic heat equations
This paper investigates the norm and time optimal control problems for
stochastic heat equations. We begin by presenting a characterization of the
norm optimal control, followed by a discussion of its properties. We then
explore the equivalence between the norm optimal control and time optimal
control, and subsequently establish the bang-bang property of the time optimal
control. These problems, to the best of our knowledge, are among the first to
discuss in the stochastic case
Perturbations of time optimal control problems for a class of abstract parabolic systems
In this work we study the asymptotic behavior of the solutions of a class of
abstract parabolic time optimal control problems when the generators converge,
in an appropriate sense, to a given strictly negative operator. Our main
application to PDEs systems concerns the behavior of optimal time and of the
associated optimal controls for parabolic equations with highly oscillating
coefficients, as we encounter in homogenization theory. Our main results assert
that, provided that the target is a closed ball centered at the origin and of
positive radius, the solutions of the time optimal control problems for the
systems with oscillating coefficients converge, in the usual norms, to the
solution of the corresponding problem for the homogenized system. In order to
prove our main theorem, we provide several new results, which could be of a
broader interest, on time and norm optimal control problems
Exact Controllability of Linear Stochastic Differential Equations and Related Problems
A notion of -exact controllability is introduced for linear controlled
(forward) stochastic differential equations, for which several sufficient
conditions are established. Further, it is proved that the -exact
controllability, the validity of an observability inequality for the adjoint
equation, the solvability of an optimization problem, and the solvability of an
-type norm optimal control problem are all equivalent
Time-optimality by distance-optimality for parabolic control systems
The equivalence of time-optimal and distance-optimal control problems is
shown for a class of parabolic control systems. Based on this equivalence, an
approach for the efficient algorithmic solution of time-optimal control
problems is investigated. Numerical examples are provided to illustrate that
the approach works well is practice
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