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We consider a model for the control of a linear network flow system with unknown but bounded demand
and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function
that makes robust optimal the policy represented by the so-called linear saturated feedback control.
We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
We consider a model for the control of a linear network flow system with unknown but bounded demand
and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function
that makes robust optimal the policy represented by the so-called linear saturated feedback control.
We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
In the present work, divided in three parts, one considers a real skis-skier system, , descending along a straight-line with constant dry friction; and one schematizes it by a holonomic system , having any number of degrees of freedom and subjected to (non-ideal) constraints, partly one-sided. Thus, e.g., jumps and also «steps made with sliding skis» can be schematized by . Among the Lagrangian coordinates for two are the Cartesian coordinates and of its center of mass, , relative...
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are...
In this paper, we look at a model depicting the relationship of cancer cells in different
development stages with immune cells and a cell cycle specific chemotherapy drug. The
model includes a constant delay in the mitotic phase. By applying optimal control theory,
we seek to minimize the cost associated with the chemotherapy drug and to minimize the
number of tumor cells. Global existence of a solution has been shown for this model and
existence...
The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient...
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
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