76 research outputs found
The prospects for blended learning in teaching English for academic purposes to TPU master's and postgraduate students
The article covers the issue of blended learning advantages in teaching English for academic purposes (EAP) within Master's and Postgraduate's programmes. The course is aimed at developing students communicative and professional competences, which will contribute to their high performance and active participation in scientific conferences and academic mobility. Blended learning is chosen as a new perspective model of teaching EAP which satisfies the demands of present day educational paradigm being more flexible, productive and cost efficient
Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations
We consider integer-restricted optimal control of systems governed by
abstract semilinear evolution equations. This includes the problem of optimal
control design for certain distributed parameter systems endowed with multiple
actuators, where the task is to minimize costs associated with the dynamics of
the system by choosing, for each instant in time, one of the actuators together
with ordinary controls. We consider relaxation techniques that are already used
successfully for mixed-integer optimal control of ordinary differential
equations. Our analysis yields sufficient conditions such that the optimal
value and the optimal state of the relaxed problem can be approximated with
arbitrary precision by a control satisfying the integer restrictions. The
results are obtained by semigroup theory methods. The approach is constructive
and gives rise to a numerical method. We supplement the analysis with numerical
experiments
Controllability under positivity constraints of multi-d wave equations
We consider both the internal and boundary controllability problems for wave
equations under non-negativity constraints on the controls. First, we prove the
steady state controllability property with nonnegative controls for a general
class of wave equations with time-independent coefficients. According to it,
the system can be driven from a steady state generated by a strictly positive
control to another, by means of nonnegative controls, when the time of control
is long enough. Secondly, under the added assumption of conservation and
coercivity of the energy, controllability is proved between states lying on two
distinct trajectories. Our methods are described and developed in an abstract
setting, to be applicable to a wide variety of control systems
Control and stabilization of waves on 1-d networks
We present some recent results on control and stabilization of waves on 1-d networks.The fine time-evolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a subtle manner on the topology of the network under consideration and also on the number theoretical properties of the lengths of the strings entering in it. Therefore, the overall picture is quite complex.In this paper we summarize some of the existing results on the problem of controllability that, by classical duality arguments in control theory, can be reduced to that of observability of the adjoint uncontrolled system. The problem of observability refers to that of recovering the total energy of solutions by means of measurements made on some internal or external nodes of the network. They lead, by duality, to controllability results guaranteeing that L 2-controls located on those nodes may drive sufficiently smooth solutions to equilibrium at a final time. Most of our results in this context, obtained in collaboration with R. Dáger, refer to the problem of controlling the network from one single external node. It is, to some extent, the most complex situation since, obviously, increasing the number of controllers enhances the controllability properties of the system. Our methods of proof combine sidewise energy estimates (that in the particular case under consideration can be derived by simply applying the classical d'Alembert's formula), Fourier series representations, non-harmonic Fourier analysis, and number theoretical tools.These control results belong to the class of the so-called open-loop control systems.We then discuss the problem of closed-loop control or stabilization by feedback. We present a recent result, obtained in collaboration with J. Valein, showing that the observability results previously derived, regardless of the method of proof employed, can also be recast a posteriori in the context of stabilization, so to derive explicit decay rates (as) for the energy of smooth solutions. The decay rate depends in a very sensitive manner on the topology of the network and the number theoretical properties of the lengths of the strings entering in it.In the end of the article we also present some challenging open problems
Computational optimization of gas compressor stations: MINLP models versus continuous reformulations
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