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Displaying 81 –
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156
This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under...
In this paper we consider the numerical computation of the optimal cost
function associated to the problem that consists in finding the minimum of
the maximum of a scalar functional on a trajectory. We present an
approximation method for the numerical solution which employs both
discretization on time and on spatial variables. In this way, we obtain a
fully discrete problem that has unique solution. We give an optimal estimate
for the error between the approximated solution and the optimal cost
function...
A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.
The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds:
.
We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition:
, ∀y ∈ Y.
However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties...
We consider the variational problem inf{αλ1(Ω) + βλ2(Ω) + (1 − α − β)λ3(Ω) | Ω open in ℝn, |Ω| ≤ 1}, for α, β ∈ [0, 1], α + β ≤ 1, where λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω) and |Ω| is the Lebesgue measure of Ω. We investigate for which values of α, β every minimiser is connected.
We present Z. Naniewicz method of optimization a coercive integral functional 𝒥 with integrand being a minimum of quasiconvex functions. This method is applied to the minimization of functional with integrand expressed as a minimum of two quadratic functions. This is done by approximating the original nonconvex problem by appropriate convex ones.
For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of ; the minimizer is and is such that vanishes at one point.
For a class of 2-D elastic energies we show that a radial equilibrium solution
is the unique global minimizer in a subclass of all admissible maps. The
boundary constraint is a double cover of S1; the minimizer u is C1
and is such that vanishes at one point.
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