A three-dimensional optimal control problem in determining the boundary control heat fluxes

A three-dimensional optimal control algorithm in determining the strength of the unknown optimal boundary control heat fluxes utilizing the Conjugate Gradient Method (CGM) and a general purpose commercial code CFX4.2 is applied successfully in the present study based on the desired domain temperature distributions at the final time of heating. Results obtained by using the conjugate gradient method to solve this three-dimensional optimal control problems are justified based on the numerical experiments. Two different computational domains and two different desired temperature distributions are given and the corresponding optimal control heat fluxes are to be determined. Results show that the optimal control heat fluxes can always be obtained with any arbitrary initial guesses of the boundary fluxes.     

Optimal control of structures governed by variational and hemiva-riational inequalities and applications

The optimal control problem for broad classes of structures is studied, including those structures having as state relations variational equalities, variational inequalities and hemivariational inequalities. The optimal control problem consists in the minimization of a functional (performance index) having the state relation, enlarged by the control actions, as side condition. Certain new results are given of the optimal control of structures governed by variational and hemivariational inequalities.Some propositions are proved on the existence and the approximation of the solution of the static optimal control problem of structures having a variational inequality as state relation. Then a regularization procedure is proposed for the treatment of corresponding dynamic problem, as well as for the case of hemivariational inequalities. The theory is illustrated by applications concerning convex elastoplasticity and convex and nonconvex unilateral contact problems.     

A control problem for Burgers' equation with bounded input/output

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to illustrate the theoretical results.     

Special cases in a control problem

A number of control problems for mechanical systems with feedback are reduced to a matrix algebraic Riccati equation. The exact solutions of matrix algebraic Riccati equations with singularities are presented. These singularities do not permit the use of standard solution procedures. Asymptotic solutions of these equations are found in the neighborhood of the singular points. These results can be used as test examples in developing new solution algorithms for matrix algebraic Riccati equations __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 113–120, February 2006.     

On the control problem for a compound wheeled vehicle

A compound transport vehicle with one steerable wheel is considered as a controlled mechanical system with nonholonomic constraints. A control system for this system is synthesized within the framework of the kinematic approximation. A procedure is proposed to synthesize a robust controller for the system. The efficiency of this procedure is demonstrated with an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 105–112, November 2007.     

Mixed testing strategies in the quality check problem for stabilization algorithms

The maximin testing problem for the stabilization quality of linear systems with discrete initial and parametric disturbances is considered. A testing procedure is implemented by reducing the original dynamic game to a geometric game. The transition to a mixed expansion of the geometric game is proposed in the absence of saddle points. An optimal mixed disturbance strategy is shown to be applicable.     

Construction of an asymptotic solution of one optimal control problem

We construct an asymptotic solution of a singularly perturbed optimal control problem in the case of a regular pencil of boundary matrices.     

A class of quasilinear differential inequalities whose solutions are ultimately constant

Let be a domain in R ⁿ with compact complement and let T be a quasilinear elliptic or degenerate elliptic operator associated with functions u C ²(). This paper is a study of solutions of (sgn u) Tuf(¦u¦, ¦ grad u¦) where f belongs to a class of functions here termed bifurcation functions. The main condition on f is that uniqueness fails for the ordinary differential equation y'=f(y, y) with the initial condition y(0)=y(0)=0. The conclusion is that u is constant for large ¦x¦ and hence, under mild supplementary hypotheses, u has compact support. Examples show that the results fail if the assumptions on f are only slightly weakened, so that the class of f is, essentially, the largest class for which the results can be stated truly.To James Serrin, in celebration of his 60^th birthday     

A simple vorticity diffusion problem

Summary In the present note a simple extension of the Rayleigh problem in the theory of viscous flows is considered. The situation is shown in fig. 1. The problem has two unusual features. In the first place a discontinuity in the velocity of the viscous fluid occurs along thez-axis, owing to the discontinuity in the wall velocity and the no-slip condition. In the second place the vorticity associated with the velocity discontinuity diffuses in the direction of the vorticity vector. Although this type of diffusion is included in the general vorticity diffusion equation the author is unaware of simple, reasonably realistic situations where it can be clearly demonstrated. The problem may be of some interest for the flow in machines where moving parts are adjacent to parts at rest.     

A bifurcation problem involving elastica

Summary A flexible inextensible elastica has been considered, with fixed end points and fixed equal end slopes, and varying length. The existence of at least one elastic curve has been proved when the elastica length is greater than the distance between the end points. A critical value of the length has been found, as a function of the given end slope only, corresponding to some elastic curves. From each of them two new elastic curves branch when the length is greater than the critical value.

---

Sommario Si consideri un filo flessibile ed inestensibile di lunghezza assegnata, vincolato agli estremi con angoli prefissati , – ; 0<<.Vengono determinate le infinite configurazioni del filo aventi momento nullo agli estremi; ognuna di queste è caratterizzata dal numero di volte con cui la curva elastica attraversa il segmento congiungente gli estremi del filo. Allorché la lunghezza del filo viene perturbata si dimostra che in corrispondenza di ogni configurazione con momento nullo agli estremi (denominata «inflexional elastica» in [4]) nascono due nuove configurazioni del filo aventi agli estremi momento diverso da zero (denominate «non inflexional elastica» in [4]).

---

---

Member of Consiglio Nazionale delle Ricerche of Italy — Gruppo di Informatica Matematica.

---

Member of Consiglio Nazionale delle Ricerche of Italy — Gruppo di Informatica Matematica — Professor at Istituto Matematico del Politecnico di Torino.     

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without con-vexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the sys-tems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vec-tor quasi-optimization problems.     

Minimum area of revolution as a state constrained optimal control problem

The classical variational problem of determining the meridian curve for the rotational surface of smallest area is solved using optimal control theory in the presence of control and state constraints The Goldschmidt solution is found to be an optimal solution under certain conditions.