Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.

This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising....

This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising. ...

We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for...

The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector $(u_1,x_1,...,u_T,x_T)$ on a sample space of $2T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_{\tau }$ given $u_1,x_1,...,u_{\tau -1},x_{\tau -1},u_{\tau }$ are known for $\tau =1,...,T$. Our objective is to determine the remaining conditional probability distributions of $u_{\tau }$ given $u_1,x_1,...,u_{\tau -1},x_{\tau -1}$ such...

In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems....