**Seminar on Applied Mathematics**

**PROGRAM**

Matematički fakultet

Fakultet organizacionih nauka

JUPIM

IEEE Computer Chapter, Srbija

MI SANU, Knez Mihailova 36, sala 305

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** Utorak, 03.11.2009. u 14:15, Sala 301f, MI SANU: **

** Srdjan Krco, Fakultet organizacionih nauka FP7 SENSEI - ARCHITECTURE OF A UBIQUITOUS SENSING AND ACTUATION FRAMEWORK IN THE CONTEXT OF THE NETWORK OF THE FUTURE **

** Abstract: Internet and the mobile network infrastructures have become the technological backbone of our society, with a large number of businesses, social interactions and public services such as government, health and education, heavily relying on it on a daily basis. More recently, sensing and interacting with the physical world have gained a lot of attention, which has resulted in a range of useful application proposals that have exploited the context of a person, an object or an area, to provide novel services to users or enterprizes. These applications often served immediate and specialized needs (e.g. maps showing nearby restaurants or busy intersections) and hence were designed as isolated enclaves, i.e. as closed, vertical, stand-alone systems built with one specific purpose in mind. In the realm of the network of the future, people, sensors, objects, and spaces will be intertwined in both virtual and physical realms while collaborating and sharing information in an unobtrusive manner. Wireless sensor and actuator networks will enable inclusion of the physical world context into the new intelligent, invisible and autonomous applications and services as well as enhancement and enrichment of the existing communication services (person-person, person-machine, mobile-machine, person-content, and machine-machine). The role of the sensor networks, and more general of Internet of Things, in the network of the future is thus to provide the missing link between the virtual and the physical world. Therefore, it is necessary to take into account the physical world factors when developing new service and network infrastructures and to embed interfaces to the physical world, regardless of how interaction with the physical world is realized. A number of challenges like design of an open sensor and actuator framework, design of horizontal solutions reusable across multiple applications, platforms and domains, business enablers, scalability, inter-operability, security, have to be overcome before such a ubiquitous communication, computing, sensing and actuation environment can be created. **

** In this presentation the work done in FP7 SENSEI project on architecture of a ubiquitous sensing and actuation framework in the context of the Network of the Future addressing the challenges mentioned above is described. The main user scenarios are presented first, followed by a description of the framework components. Finally, a brief outline of the SENSEI's pan-European test bed is given. **

** Pttak, 10.11.2009. u 14:15, sala 301f, MI: **

** Milica Selmic, Saobracajni fakultet, Beograd BEE COLONY OPTIMIZATION FOR SCHEDULING INDEPENDENT TASKS TO IDENTICAL PROCESSORS **

** Abstract: The problem of static scheduling independent tasks on homogeneous multiprocessor systems is presented. This problem is solved by the Bee Colony Optimization (BCO). The BCO algorithm belongs to the class of stochastic swarm optimization methods inspired by the foraging habits of bees in the nature. Our BCO algorithm was able to obtain optimal value of the objective function in most test examples known from the literature. The CPU times required to find the best solutions by the BCO are significantly smaller than the corresponding times required by the CPLEX optimization solver. **

** This is joint work with dr Tatjana Davidovic and prof. Dusan Teodorovic. **

** Utorak, 17.11.2009. u 14:15, sala 301f, MI SANU: **

** Anastasija Andreevna Vasiljeva, Katedra opstih problema upravljanja, Mehanicko-matematihki fakultet, Moskovski drzavni univerzitet KOLMOGOROV WIDTHS OF WEIGHTED SOBOLEV CLASSES **

** Abstract: For a wide class of weight functions estimates of Kolmogorov n-widths of weighted Sobolev classes in a weighted $L_p$ space are obtained. Using Mayorov method of discretization, Pietcsh - Stesin - Kashin - Gluskin estimates of Kolmogorov widths of finite-dimensional balls and Stepanov's estimates of norms of weighted Riemann - Liouville operators and choosing an appropriate partition of an interval, we can obtain generalization and refinement of known results. In a case of multidimensional domains we obtain some embedding theorems and estimates of Kolmogorov n-widths. **

** Docent PhD Alexandr Saveljevich Kochurov, Katedra opstih problema upravljanja Mehanicko-matematicki fakultet Moskovski drzavni univerzitet **

ON SOLUTIONS OF SOME MULTIVARIATE OPTIMAL CONTROL PROBLEMS

** Abstract. This is still unknown, whether Pontryagin's maximum principle holds for multivariate optimal control problems. We present three examples, where the maximum principle is applicable for solutions. In each of those problems the sharp solution can be computed and analized. **

** Utorak, 24.11.2009. u 14:15, sala 301f, MI SANU: **

** Katica R. (Stevanović) Hedrih THE OPTIMAL CONTROL IN ENGINEERING NONLINEAR SYSTEMS WITH TRIGGER OF COUPLED SINGULARITIES Katica R. (Stevanović) Hedrih **

** Abstract. Short main idea of the phase plane method applied to the optimal control in nonlinear dynamical systems with triggers of a coupled singularities, and with one degree of freedom, is reconsidered. Paper present a short review of the authors previous published results containing series of the special cases of the optimal control in nonlinear dynamical systems with trigger of coupled singularities important for engineering applications. This paper analyses the controllability of motion of conservative or noconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of conservative and no conservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or noconservative system. **

** For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with triggers of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of number eight. Task of the defined dynamical conservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final terminate state of the nonlinear dynamics in the minimal time for that optimal control task. **

** Some research results of fascinating nonlinear dynamics of a heavy material particle along circles with coupled rotations with many different properties of nonlinear dynamics and optimal control of this dynamics are presented. A visualizations of nonlinear dynamical processes in such rheonomic systems were made. **

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** RUKOVODIOCI SEMINARA **

** Vera Kovačević-Vujčić Milan Dražić **