Generalized Hamilton-Jacobi equations for nonholonomic dynamics

Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the action is actually minimized (not just extremized)

Exact controllability of non-Lipschitz semilinear systems

We present sufficient conditions for exact controllability of a semilinear infinite-dimensional dynamical system. The system mild solution is formed by a noncompact semigroup and a nonlinear disturbance that does not need to be Lipschitz continuous. Our main result is based on a fixed point-type application of the Schmidt existence theorem and illustrated by a nonlinear transport partial differential equation

Lagrange Lemma and the optimal control of diffusions II : nonlinear Lagrange functionals

In (Kosmol, 1991; Kosmol and Pavon, 1993) a new elementary approach to optimal control problems relying on the Lagrange lemma was described which appears to be technically, and conceptually, much simpler than existing methods, and, furthermore, provides a unified variational approach. In (Kosmol and Pavon, 1992) this method was further clarified and developed for linear Lagrangefunctionals. We devote this second paper to nonlinear Lagrangefunctionals. The power of this approach is here clearly demonstrated. In particular, it is shown that the nonlinear Lagrange functional induced by the value function of the problem is just one of the many functionals which may effectively be employed to solve control problems, see Examples 1 and 2 in Section 3. Moreover, in our approach, we can deal in the same framework with problems with state constraints, or nonsmooth problems. Hence, the Lagrange functionals approach provides new tools to solve control problems which may be readily applied even when existing approaches fail

Comparision of optimisation methods basing on primitives and initiall geometric models

W artykule przedstawiono porównanie dwóch metod optymalizacji korpusów maszyn. Obie metody wykorzystują zarówno metodę elementów skończonych jak i algorytm ewolucyjny. Pierwsza z nich zakłada, że znany jest model wstępny obiektu i wówczas należy użyć tylko optymalizacji parametrycznej. Natomiast w drugim przypadku, kiedy nie ma żadnych informacji o modelu obiektu należy zastosować zarówno optymalizacje topologiczną jak i parametryczną. Ta druga metoda wykorzystuje prymitywy, jako modele wstępne obiektu. W artykule zamieszczono wyniki porównania obu metod dla wybranego korpusu obrabiarki. Porównaniu podlegały optymalne rozwiązania w postaci: wskaźników sztywności, ich rozrzutu, masy korpusów i częstotliwość drgań własnych. Wyniki tych porównań są dosyć oczywiste: metoda optymalizacji, bazująca na prymitywach daje korzystniejsze efekty niż metoda bazująca na projekcie wstępnym. Dotyczy to w szczególności masy zoptymalizowanego korpusu, która może być nawet o 10 mniejsza.The paper presents comparison of two optimisation methods of machine frames. Both methods use Finite Element Methods and Evolutionary Algorithm simultanously. The first of the method assumes that the initail model of the body is known and in such situation the parametric optimisation should be applied only. In the second case when one has no information about the object’s model, the Topology optimisation and Parametric optimisation should be applied. The second method uses Prymitives as preliminary model of object. The paper presents results of comparision of both metof applied to an example frame. Such parameters were compared: coefficients of stiffness, dispersion of stiffness, masses od frames, free frequency of vibration. Results of comparision are very obviousness: method of optimisation based on primitives gives better results than method based on initialy project. First of all it concerns on the mass of opimised frame, which may be even 10% smaller

Solving optimal control problems by means of general Lagrange functionals

The method of Lagrange functionals is applied to the optimal control of systems with quadratic and implicit dynamics

Lagrange Approach To the Optimal-control of Diffusions

A new approach to the optimal control of diffusion processes based on Lagrange functionals is presented. The method is conceptually and technically simpler than existing ones. A first class of functionals allows to obtain optimality conditions without any resort to stochastic calculus and functional analysis. A second class, which requires Ito's rule, allows to establish optimality in a larger class of problems. Calculations in these two methods are sometimes akin to those in minimum principles and in dynamic programming, but the thinking behind them is new. A few examples are worked out to illustrate the power and simplicity of this approach

Experimental verification of polymer concrete frames

W artykule przedstawiono wstępne wyniki badań eksperymentalnych korpusu belki suportowej niewypełnionej i wypełnionej polimerobetonem w postaci odpowiedzi impulsowej i charakterystyk widmowych. Celem tych badań była ocena poprawy niektórych właściwości dynamicznych korpusów obrabiarek, poprzez wypełnienie ich polimerobetonem.The paper presents preliminary experimental results of a machine tool beam filled up and not filled up with Polymer Concrete (PC) as a transient response and amplitude spectrum. The main goal of the experiments was evaluation of improving selected dynamic properties of machine tool frames through filled them Polymer Concrete