CONTROL OF SYSTEMS ON SPATIAL DOMAINS WITH MOVING BOUNDARIES: 3D PRINTING AND TRAFFIC

Until roughly the year 2000, control algorithms (of the kind that can be physically implemented and provided guarantees of stability and performance) were mostly available only for systems modeled by ordinary differential equations. In other words, while controllers were available for finite-dimensional systems, such as robotic manipulators of vehicles, they were not available for systems like fluid flows. With the emergence of the “backstepping” approach, it became possible to design control laws for systems modeled by partial differential equations (PDEs), i.e., for infinite dimensional systems, and with inputs at the boundaries of spatial domains. But, until recently, such backstepping controllers for PDEs were available only for systems evolving on fixed spatial PDE domains, not for systems whose boundaries are also dynamical and move, such as in systems undergoing transition of phase of matter (like the solid-liquid transition, i.e., melting or crystallization). In this invited article we review new control designs for moving-boundary PDEs of both parabolic and hyperbolic types and illustrate them by applications, respectively, in additive manufacturing (3D printing) and freeway traffic

Analiza propisa o radu beogradske policije iz 1831. godine

After the Second Serbian Uprising in Serbia, a mixed Serbian-Turkish Administration was established, based on the agreement of Prince Milos and Marasli-Ali Pasha in 1815. Essentially, this meant that the Turkish authorities had jurisdiction over the Turks, while the newly established national authorities had jurisdiction over the Serbs. The so-called Kadi and Muselim had the power of a judge for the Turks, while the Duke was the chief of police - as a separate authority. The headquarters of the Turkish police commanding officers were in the administrative units called Nahiyah (or Nahia), and there was one Duke in Belgrade and one in Grocka. Even though the Dukes were formally subordinated and exclusively responded to the Vizier in Belgrade for their work, in practice they paid much more attention to the opinion of the Serbian Prince, who they were financially dependent on. The National Princes had the power of a judge for the Serbs, and simultaneously were in charge of policing. They usually arbitrated 'in the field', and carried out the sentences themselves with the assistance of armed young men. In Belgrade, these jobs were mainly performed by the Princes of the National Office (the Court). Due to the constant presence of the Turks in Belgrade and their sensitivity to any independent decisions made by the Serbian authorities, the conditions of their work were much more complex than those in somewhere up country. This is the reason why the Princes of the National Office did not dare to bring verdicts and carry out sentences themselves, so in each spe­cific case they would first ask for the instructions of Prince Milos. Realizing that one Bulibasha with about 15 policemen (which formed the Belgrade police at the time) objectively was not able to serve the National office, guard the Palace in Topcider and maintain order in the Serbian part of Belgrade, Prince Milos decided to introduce changes - a decision which resulted from his incredible pre­sentiment of the events that Serbia was yet to face. In 1826 Prince Milos turned the National office into the Belgrade court (so-called Magistrate) and appointed its employees himself. In mid-1828 Prince Petar Lazarevic was appointed by the Prince Milos to be the first Director of the Belgrade police, which was part of the court at the time. Three years later, a regulation on Belgrade policing was brought by the prince, which tasked the police forces with the following: to maintain the peace, order and cleanliness of the town, to make proposals to the Magistrate and be at hand for its every need, to monitor the local people and the foreigners, to control and verify passports, and to carry out sentences upon the offenders ordered by the Magistrate. This regulation for the first time clearly separated the executive and the judicial power: the Director of the police had no authority to sentence the offenders - instead he delivered them before the court and waited for the verdict; while the right for punishment was limited to 25 blows with a stick (more serious penalty could only be imposed by the Magistrate). The director of police was at the same time a full member of the Magistrate with the voting right during pronouncing sentences. However, he was directly subordinated only to the Prince.Nakon Drugog srpskog ustanka u Srbiji je uspostavljena mešovita, srpsko-turska uprava, zasnovana na usmenom sporazumu kneza Miloša i Marašli-Ali paše iz 1815. godine. U osnovi, to je značilo da nadležnost nad Turcima imaju turski organi vlasti, dok su za Srbe bili nadležni novoformirani domaći organi. Turcima su sudili kadija i muselim, a na čelu policije kao posebne ustanove bio je vojvoda. Sedište turskih policijskih starešina bilo je u nahijskim centrima, a po jedan vojvoda obitavao je u Beogradu i Grockoj. Iako su formalno bile neposredno potčinjene veziru u Beogradu i za svoj rad odgovarale isključivo njemu, vojvode su u praksi mnogo više vodile računa o mišljenju srpskog kneza od koga su finansijski zavisile. Srbima su sudili narodni knezovi, nahijski i knežinski, koji su istovremeno obavljali i policijske dužnosti. Oni su po unutrašnjosti sudili 'na terenu' i svoje presude uz pomoć naoružanih momaka sami i izvršavali. U tom pogledu izdvajao ce Beograd, y kome su maj posao uglavnom obavljali knezovi Narodne kancelarije (suda). Imajući u vidu stalno prisustvo Turaka u Beogradu i njihovu osetljivost na svako samostalno rešenje srpskih organa, uslovi njihovog rada bili su mnogo složeniji od onih u unutrašnjosti. Upravo zato knezovi Narodne kancelarije i nisu smeli sami presuđivati i kažnjavati, već su u svakom konkretnom slučaju najpre tražili uputstva za rad od kneza Miloša. Sa neverovatnom osobinom tačnog predosećanja događaja kojima je Srbija išla u susret, a i uviđajući da jedan buljubaša sa petnaestak pandura koji su činili beogradsku policiju objektivno ne može da opslužuje Narodnu kancelariju, čuva konak u Topčideru i pazi i održava red u srpskom delu beogradske varoši, knez Miloš se rešio na promene. Narodna kancelarija je 1826. pretvorena u Beogradski sud (magistrat), čiji je personal odredio knez Miloš. Polovinom 1828. Miloš je postavio kneza Petra Lazarevića za prvog 'direktora' beogradske policije, koju je istovremeno uključio u sastav suda. Tri godine kasnije beogradska policija je od kneza dobila 'propis' o radu, kojim joj je u zadatak stavljeno: da motri na mir, red i čistoću u varoši, da čini predloge Magistratu i bude mu pri ruci za svaku potrebu, da nadgleda domaće ljude i strance, da pregleda i overava pasoše i da izvršava kazne nad prestupnicima koje Magistrat izrekne. Ovim propisom prvi put su jasnije razdvojene izvršna i sudska vlast: direktor policije nije imao pravo kažnjavanja krivaca, već ih je predavao sudu i očekivao njegovu presudu, a i pravo kažnjavanja podređenih mu je ograničeno na 25 udaraca štapom (kazne veće od ove mogao je izreći Magistrat). Direktor policije je istovremeno bio punopravni član Magistrata sa pravom glasa pri izricanju presuda. Ipak, neposredno je bio podređen samo knezu

Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs

Deep neural networks that approximate nonlinear function-to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as backstepping, so that, for each new functional coefficient of a PDE plant, the backstepping gains are obtained through a simple function evaluation. These initial results have been limited to single PDEs from a given class, approximating the solutions of only single-PDE operators for the gain kernels. In this paper we expand this framework to the approximation of multiple (cascaded) nonlinear operators. Multiple operators arise in the control of PDE systems from distinct PDE classes, such as the system in this paper: a reaction-diffusion plant, which is a parabolic PDE, with input delay, which is a hyperbolic PDE. The DeepONet-approximated nonlinear operator is a cascade/composition of the operators defined by one hyperbolic PDE of the Goursat form and one parabolic PDE on a rectangle, both of which are bilinear in their input functions and not explicitly solvable. For the delay-compensated PDE backstepping controller, which employs the learned control operator, namely, the approximated gain kernel, we guarantee exponential stability in the $L^2$ norm of the plant state and the $H^1$ norm of the input delay state. Simulations illustrate the contributed theory

Preparation of Ni/diatomite hydrogenation catalyst precursors: Effect of counter ions on textural characteristics

Diatomite supported nickel catalyst precursors (Ni/D) were prepared by the precipitation-deposition (PD) method using different nickel salts such as nitrate, chloride, acetate and formate. The effect of counter ions (NO3-, Cl-, CH3COO-, and HCOO-) on the texture of prepared samples was studied. For determination of the textural characteristics mercury intrusion porosimetry (MIP) and N2 physisorption techniques were used. MIP and physisorption data (pore volume, pore size distribution, porosity as well as N2 adsorptiondesorption isotherms and BET surface area) showed that counter ions were found to have a profound effect on the microstructure and porosity characteristics of Ni/D precursors. An order of the counter ions effect on the textural characteristics of prepared precursors was determined

Burgers' equation with nonlinear boundary feedback: H

We consider the viscous Burgers' equation under recently proposed nonlinear boundary conditions and show that it guarantees global asymptotic stabilization and semiglobal exponential stabilization in H1 sense. Our result is global in time and allows arbitrary size of initial data. It strengthens recent results by Byrnes, Gilliam, and Shubov, Ly, Mease, and Titi, and Ito and Yan. The global existence and uniqueness of classical solutions follows from the general theory of quasi-linear parabolic equations. We include a numerical result which illustrates the performance of the boundary controller

Application of Multi-Criteria Decision-Making Methods for Supplier Selection in an Agricultural Enterprise

In today's turbulent market conditions, the selection of suppliers in an agricultural enterprise constitutes a primary function, and the entire supply chain with the necessary raw materials and intermediate goods plays an important role in the day-to-day functioning of the economic entity in this field. In order to successfully solve the problem of choosing a supplier, the decision maker uses the methods of multi-criteria analysis, and the corresponding software support. The subject of research in this paper is the selection of mineral fertilizer suppliers in the agricultural enterprise using the AHP methodology, which is one of the most commonly applied methods of multi-criteria analysis today. The aim of the research is to rank suppliers on the basis of the set criteria, and a supplier with the highest rating was selected for the supplier of mineral fertilizer as the observed enterprise

Forecasting wheat and corn production in Republic of Srpska and Bosnia and Herzegovina

The aim of the authors was to create an adequate model for forecasting the production of wheat and corn in Republic of Srpska and throughout B&H based on the twenty-two-year time series (1996-2017) by applying the trend analysis and other quantitative methods of research. After selecting a square model, as the most appropriate model, an analysis of movement tendency of basic production indicators of the observed crop cultures was carried out. The forecast was carried out for a five-year period (2018-2022). The results showed that wheat in the next five-year period (2018-2022) will show a decrease in production in Republic of Srpska, and an increase in the whole of B&H. Wheat yield will grow in both Republic Srpska and B&H. In the prediction period, there will be a decline in production and yield of corn. The contribution of this research is reflected in making timely and rational decisions concerning the further development of crop production and agriculture

Beogradska varoška policija u doba uspostavljanja vlasti ustavobranitelja

Prince Mihailo Obrenovic took over the administration of the country in the significantly altered the constitutional situation, created by the adoption of the Constitution of 1838 and the departure of Serbian Prince Milos 1839. Constitution ensured the supremacy of the State Council as an oligarchic body of the prince in the adoption of new legislation expanded and contrary to the constitution. Gradual narrowing and even abolishing competences of prince in the legislative and executive branches Constitutionalists are aimed to ensure the constitutionally established order. One of the measures taken to this aim was the adoption of regulations by which the Belgrade police under the control of Constitutionalist Party. The Belgrade police which in the time of Miloš rule was subordinated directly to the prince, by the Decree of 1840 came under the jurisdiction of the competent ministry. The contents of the this Decree that remained in Serbia in force throughout the nineteenth century shows how wide was the scope of its work. Specifically, the Board took care of law and order, personal safety or property of citizens, conducted surveillance of suspicious persons, travelers, foreigners and idles, worried about traffic safety and the safety of roads, alleys, and cobblestone bridge, followed the proper operation of the innkeepers, butchers and traders worried about neatness squares and product prices, participated in the settlement of disputes between creditors and debtors, secured and numbered the property of deceased persons and fallen into bankruptcy, suppress immorality, watch the correctness water supply, public fountains and street lighting, directing the development of settlements, undertook measures to protect against fire, suppressing the fights, riots and rebellions, took care of the health of citizens and public hygiene, issued an order on line and order in the town, enforce court decisions, took care of the prisoners, carried a list of public and private property at the request of his superiors authorities , state revenues collected from the population, participated in the division of the borough plots for raising houses in the area of Batal mosque, in Sava-waving, Palilula, Terazije, past ponds Venice, and finally led to a variety of correspondence - submitted reports to the competent organs of the state administration and consisted of a number of proposals from the circle of their activity. On the other hand, the Decree on the duties of the administration of the City of Belgrade in 1840 must be seen as part of a comprehensive legislative activities Constitutionalist aimed at establishing a highly branched and durable state organization. As part of the whole legal regulations governing the then ruling political elites govern executive, Regulation confirms the conclusion that the Constitutionalist have achieved a lot in terms of formal legislate lofty police power over the people, but failed to sufficiently develop the system control apparatus of executive power. In addition to subjective, there are objective factors that limited Constitutionalist efforts in this direction. Ideas of modern civil state objectively could not be quickly accepted in the still traditional-patriarchal Serbian society.U radu se analizira sadržina propisa o radu beogradske policije iz 1840. godine u okviru društvenih i političkih prilika u Kneževini Srbiji na početku ustavobraniteljske vladavine. Knez Mihailo Obrenović preuzeo je upravu zemljom u bitno izmenjenoj ustavnoj situaciji, stvorenoj donošenjem Ustava 1838. i odlaskom iz Srbije kneza Miloša 1839. godine. Ustavom obezbeđena prevlast Državnog saveta kao oligarhijskog tela nad knezom u praksi je određenim uredbama proširena i protivno ustavu. Pokušaj kneza u takvoj situaciji da odbrani svoja ustavna ovlašćenja u zakonodavnoj i izvršnoj vlasti i uspostavi ravnotežu u odnosima sa Savetom nije uspeo. O tome svedoči i donošenje propisa kojim beogradska policija, u Miloševo vreme podređena neposredno knezu, dolazi pod nadležnost resornog ministarstva. S druge strane, Uredba o dužnostima uprave varoši Beograda iz 1840. deo je široke zakonodavne aktivnosti ustavobranitelja usmerene na uspostavljanje razgranatije i trajnije državne organizacije. Primenom istorijskog i sociološkog metoda, kao i metoda analize i sinteze, indukcije i dedukcije, autori objašnjavaju motivaciju za izdavanje ovog propisa čija je sadržina bila presudno determinisana interesima tadašnje političke elite u Srbiji

Underactuated Source Seeking by Surge Force Tuning: Theory and Boat Experiments

We extend source seeking algorithms, in the absence of position and velocity measurements, and with tuning of the surge input, from velocity-actuated (unicycle) kinematic models to force-actuated generic Euler-Lagrange dynamic underactuated models. In the design and analysis, we employ a symmetric product approximation, averaging, passivity, and partial-state stability theory. The proposed control law requires only real-time measurement of the source signal at the current position of the vehicle and ensures semi-global practical uniform asymptotic stability (SPUAS) with respect to the linear motion coordinates for the closed-loop system. The performance of our source seeker with surge force tuning is illustrated with both numerical simulations and experiments of an underactuated boat

Errata Corrige: Stress-Induced Phosphorylation of C-Jun-N-Terminal Kinases and Nuclear Translocation of Hsp70 in the Wistar Rat Hippocampus (Vol 61, Pg 1, 2009)

In the paper entitled: Adžić, M., Đorđević, A., Krstić-Demonacos, M., & Radojčić, M. B. (2009). Stress-induced phosphorylation of c-Jun-N-terminal kinases and nuclear translocation of Hsp70 in the Wistar rat hippocampus. Archives of Biological Sciences, 61(1), 1-8. Fig. 1, on page 4, section b, should read "Nucleus" instead of "Cytoplasm