CONTROL AND COORDINATION OF ECONOMIC AND INTELLECTUAL ACTIVITIES BY INTEGRATED COMPLEX STRUCTURES

Transcription

1 DEZVOLTAREA DURABILĂ FAVORABILĂ INCLUZIUNII CONTROL AND COORDINATION OF ECONOMIC AND INTELLECTUAL ACTIVITIES BY INTEGRATED COMPLEX STRUCTURES Constantn MARIN,2 Correspondng Member of the Academy of Techncal Scences of Romana 2 Unversty of Craova Abstract: Ths paper belongs to the category of research for the development and mplementaton of heterogeneous structures they apply favorable ncluson of the human factor for control and coordnaton of complex actvtes from varous felds: economc, ntellectual, bologcal, mltary, etc. It can be consdered as a new drecton for the development and applcaton of modern concept CPS (Cyber Physcal Systems) where actvtes of the above areas are treated as physcal processes specfc to CPS. The proposed structure hghlghts the nteracton between the human control factor and physcal processes represented by the control numercal equpments and controlled processes. In ths closed loop control structure, the nformaton s represented n three forms namely:. Numbers n dgtal equpments; 2. Physcal sgnals n controlled processes (economc or ntellectual); 3. Documents n whch the human factor s part of the control structure. The bodes composed of human factors (board, councl, offce, manager, etc.) nteract wth each other and wth other components of the heterogeneous system by exchange of nformaton that have the document as physcal support. For the documents creaton, transmsson and operaton, as a carrer of nformaton, specfc tools are used: workflow,.net development platform. vrtualzaton procedures sharepont envronment. A partcular problem for the control systems of the economc actvtes s the breaks exstence defned as tme perods of nactvty when all or some state components are kept constant so that classcal models are not generally avalable. They appear as a specfc category of systems called State Blockng Systems (SBS). Examples of controllng an economc process, based on the law of supply and demand modelng the prce evoluton and an ntellectual process for coordnaton of monetary polcy are presented. The results obtaned by numercal smulaton pont out the advantages of ths approach. Keywords: Control structures; Mathematcal models; Control algorthms; Fnte tme response; Blockng systems.. INTRODUCTION The control and coordnaton of economc and ntellectual actvtes are complex problems because at the stage of concevng and mplementaton of control decsons, the human actons are combned wth a realty expressng the evoluton of controlled economc or ntellectual processes. In most cases these processes are descrbed by dynamc models, n partcular hgher order dfferental or dfferences equatons. No matter how traned and capable a human operator can be, he can not successfully handle actvtes that are dynamc nterrelated up to maxmum of second order. For example, for an n order dscrete tme process, the human operator must ntutvely perceve the effect of the current decson over a tme nterval of n tme unts. Informaton carrer "n a human operator", as an object n the controllng process, s the document. A responsble control s perfotmed on the bass of documents. The document s an entty n the form presented both on paper "hard" and n "soft", vrtual. The system for control and coordnaton of economc and ntellectual actvtes, developed n ths paper, can be appled to a wde range of economc and ntellectual processes. Specfc examples are lmted to economc processes where the law of supply and demand s true. Such processes are descrbed by dfferental equatons. In the studed economc lterature, a few appled control solutons are based on dfferental equatons. Generally, the proposed mathematcal models are n the form of expressonsns. Often they are functons of tme that n the background actually represent partcular solutons of some lnear or 8 Buletnul AGIR Suplment 2 / 25

2 COMPUTING SYSTEMS MULTI-OBJECTIVE OPTIMIZATION USING DOMAIN-KNOWLEDGE nonlnear dfferental equatons. A specal work n ths area s the book [], but n whch the models, based on the law of supply and demand, are of the frst order [2]. In ths paper we use hgher order models that express the nterdependence between the varous operators. Unfortunately the practcal evoluton of of such processes s characterzed by ntervals of rest, so that the classcal models are not generally avalable. A contrbuton of ths paper s the applcaton to economc and ntellectual processes of the Fnte Tme Response (FTR) control algorthms [3]. Many fnancal and economc processes have sgnfcant benefts f t succeeds to obtan, n the the shortest tme, the desred values of the controlled varables. After that these varables have to reman constant. In contrast to techncal processes, n most economc processes descrbed by state equatons, eg that manpulate stocks (stocks of materal, fnancal, ntellectual deposts) or processes governed by the law of supply and demand, the system state s avalable for measurements. Practcally, based on observatons, t can delmt a number of economc agents that nteract n a specfc envronment, such as the sale of products market, fnancal market, market development projects etc. Based on these observatons s defned the mathematcal model structure, but wth unknown parameters. Another contrbuton of ths paper s to use dentfcaton method based on dstrbutons to determne the parameters of system state equatons. In lterature, dstrbutons based dentfcaton s performed on parameters of an nput-output model. In the present case of economc processes, because the state s avalable, we can actually determne the parameters showng the nteracton weghts of dfferent economc agents. In ths paper we amed to acheve an automated or at least part of helpng automated decson makng n the feld of ntellectual and economc actvtes. The am s to combne, n the control process of economc and ntellectual actvtes, the systemc mathematcal descrpton of the behavor and the nformaton representaton n the form of documents. These documents are produced automatcally, but they are managed and modfed by the human operator nvolved n the process of coordnaton and control. The am s to desgn and mplement these deas through varous software applcatons. These applcatons wll manage the resources of enterprse, nonproft organzatons or commercal organzatons as complementary solutons from SAP-AG. An dea of the research conssts n combnng the best of the varous resources wthn the platforms and technques namely.net platform; SharePont platform; technques based on the method workflow and vrtualzaton. As any sgnal that carres nformaton s modfed, processed, operated, so the document s subjected to such operatons. For example, data entry, approval, submsson for executon, etc. 2. THE INTEGRATED STRUCTURE OF THE SCCEIA (SYSTEM FOR CONTROL AND COORDINATION OF ECONOMIC AND INTELLECTUAL ACTIVITIES) A system of control and coordnaton of economc and ntellectual actvtes, accordng to ths paper, s composed of three man aspects, namely:. Controlled process (CPr); 2. System for processng and transmsson of documents (SPTD); 3. Numercal control equpment (NCE). It s proposed the structure of the as n Fg.. Ths structure comples wth the general structure of a control system hghlghtng the human factor n the process of nformaton and decson. Ths human factor has the document as nformatonal support. 2.. Controlled process (CPr) It conssts of economc actvty or ntellectual actvty characterzed by a number of varables (quanttes, attrbutes, characterstcs) that have an evoluton over tme [3], [4]. On the set of these varables a causal relatonshp s defned, so that the process can be systemcally defned as an orented system [5]. There are a wde varety of mathematcal models for economc actvtes and ntellectual actvtes such as: dfferental equatons, dfference equatons, tables, lngustc representatons, representatons by fuzzy etc., [6]. It can be determned a pror only the structure of the mathematcal model, remanng as ts parameters values to be determned by dentfcaton based on measurements of the nput, output and state varables. Buletnul AGIR Suplment 2 / 25 8

3 DEZVOLTAREA DURABILĂ FAVORABILĂ INCLUZIUNII Numerc nputs (NI) Numercal control equpment (NCE) System for processng and transmsson of documents (SPTD) Model structure Settngs n (NCE) Numerc outputs (NO) Dsturbances Control decsons (DC) Informat Controlled processs (CPr) Program Restrctons Approvals Measured dsturbances Superor decson makng body (SDMB) Measured process Process measurabl e Qualty varable Measured dsturbances Echpament numerc de conducere IN Identfcare parametrcă Adaptarea leg de conducere Lege de conducere Structura modelulu matematc EN Fg.. Structure of the System for Control and Coordnaton of Economc and Intellectual Actvtes (SCCEIA). Fg. 2. Sefltunng adaptve control structure of (SCCEIA) 2.2. System for processng and transmsson of documents (SPTD) The central element of ths control structure s the block System for processng and transmsson of documents (SPTD), subordnate to Superor decson makng body (SDMB). SPTD s composed of dfferent organzatonal structures that nvolve human factors, but whose actvty s based on documents. It s proposed to use nformatcs platforms. NET and Sharepont for generatng, dstrbutng, updatng these documents. The varety of the organzatonal structure s large, dependng on the concrete applcaton. Usng the platform accordng to ths research has the advantage that structures can be confgured easly to represent a realty. One can magne two ways of achevng and mplementng the SCCAEI namely: a. The controlled process (CPr) exsts, t functoned wth a control based exclusvely on the human factor. To ncrease the qualty of control, an advanced structure as n Fg.. s proposed. In ths structure, the control decsons are elaborated by the Numercal control equpment (NCE) where numercal control algorthms are mplemented. In ths control structure, NCE acts as operator gude, a gude for human factors that can make, accordng to socal and human crtera, correctons on decsons developed by NCE. What s new n the approach of ths paper s that t proposes a closed loop fnte tme response control (FTR) structure. In ths structure, t takes nto account the nterventons and correctons appled by the operator, so that n the shortest tme system to reach a desred state, requred by Superor decson makng body (SDMB). Obvously, n ths varant, f desred or f NCE fals, the control can be acheved only through the decsons developed by human factors. b. The controlled process (CPr) s desgned and developed from the begnnng to be controlled by numercal computng equpment, wth all physcal facltes for the transmsson and processng of nformaton. In ths varant, the flow of nformaton n SPTD and SDMB, namely ssuance, movement and handlng of documents, s fully automatc performed but the documents can be nstantly ssued, crculated and manpulated by the human factor n the system wthout generatng shocks. Of course one can magne and ntermedate versons. SPTD receve programs and restrctons from SDMB from whch the desred values of the system state are deducted. SPTD has ncorporated nto ts structure some bodes and structures for collectng nformaton about CPr (nformaton "on the ground") namely the measured process varables and the measured process dsturbances. Because SPTD delver control decsons (CD), that means t knows the appled nputs to CPr so that t s able to evaluate a seres of qualty varables of the CPr. In specal ntalzaton crcumstances or f the control qualty s worsenng, by specalzed bodes of analyss, SPDT apprecate the mathematcal model structure underlyng the CPr behavor. For example for an economc process, the observable economc agents whch nteract wth the own system are delmted. Also the type of nforma- 82 Buletnul AGIR Suplment 2 / 25

4 COMPUTING SYSTEMS MULTI-OBJECTIVE OPTIMIZATION USING DOMAIN-KNOWLEDGE tonal lnks s consdered, for example lnear or nonlnear dfferental equatons, dfference equatons, systems wth fnte number of values for the nput, output and state, etc. SPDT s nformed of the rest perods (pause tmes) of CPr components. All such nformaton s teratvely submtted for approval SDMB. In case of denal of SDMB, SPDT resume unapproved actons to obtan approval. After ths stage, SPDT transmt nformaton to NCE n a format compatble wth t Numercal control equpment (NCE) As any numercal control equpment, t has nput ports through whch are fnally nserted n the numercal equpment numbers that we call "numerc nputs (NI)" and output ports through whch are delvered to the outsde numbers for use n one form or another that we call " numerc outputs (NO)". The nput varables NI nto the NCE, delvered by SPDT, contan n a format compatble wth the numerc equpment, all necessary nformaton for control actvty. We propose a specfc control structure, namely Adaptve control structure wth self tunng (ACSS)", as shown n Fg.2. Ths structure s approprate for control of economc processes and ntellectual actvtes because the system structure can well enough be apprecated. To dentfy the parameters of the state equatons an orgnal algorthm was conceved based on the theory of dstrbutons. Ths dentfcaton method has been appled prevously [7], for nput output models only. 3. PLATFORMS AND TOOLS TO ACHIEVE SPDT It ams to acheve SPDT n the control structure of Fg, as a software applcatons, n the software category of ERP (Enterprse Resource Plannng) or MRP (Materal Requrement Plannng). They wll manage the resources of a enterprses, non-proft or commercal processes wth a hgh degree of complexty. All the SAP features can be used. Makng SPTD s based on a seres of concepts wdely used n software as:workflow,prmary and secondary processes, plannng, carryng out control, transt vsblty, etc. It s noted WF (Wndows Workflow), a Mcrosoft technology ncluded n the.net framework that facltates the development of specfc applcatons, emulaton and mplementng processes as workflows. In the central concept s the noton WF actvty. There s a ready-bult lbrary actvtes. Essental s the engne performance of workflows. It ncludes servces such as schedulng servce executon unusual about servce management, servce tax rules. Accessble mplementaton possbltes are represented by the Mcrosoft platform MOSS 27 and by the Sharepont 2 famly of technologes. Sharepont s composed of a collecton of products and software elements where remarks: modules of processes management, search modules, platform for document management, collaboraton functonaltes based on web browser. Another tool for creatng applcatons from scratch of any knd s th e.net platform.ths s ndependent of the software archtecture so that a large part of.net assembles can be recreated and executed on non-mcrosoft operatng systems (MacOS X, Lnux, Solars) [8]. 4. MATHEMATICAL MODELS FOR ECONOMIC AND INTELLECTUAL PROCESSES Concernng the development of mathematcal models for economc and ntellectual processes were consdered two types of processes, namely:. Economc proceses based on supply and demand law and 2. Intellectual procese of monetary polcy coordnaton. The economc lterature [, 4, 9, ], presents the problem of the evoluton of prces n a market economy n general for a sngle operator. In these approaches the prce of a product s governed by the law of supply and demand, n the dea that the prce remans constant f the demand s equal to supply. It s noted the paper [] n whch economc models are presented as dfferental or dfference equatons, but only for a sngle operator. By an economc agent we understand an entty E (a product on the market) at the prce P, provded, handled by an economc agent A or by a couple (A, Ej). There s an optmum value P* of Buletnul AGIR Suplment 2 / 25 83

5 DEZVOLTAREA DURABILĂ FAVORABILĂ INCLUZIUNII the prce P whch they would lke an economc agent, for whch the effcency s maxmzed. The approach of ths paper s consdered that there n economc agents that nteract drectly or ndrectly through the market reacton (the set of the economc agents benefcares and partcularly of ther buyers). We consder the evoluton of economc processes n contnuous tme, so that dynamc processes are expressed by dfferental equatons. From these we can deduce the dscrete tme models expressed by dfference equatons. We consder n economc agents, E, :n, each characterzed by ts actvty value prce P(t), :n, of the economc agent P (t) [D (t) S (t)], :n,where D(t), P(t), :n at the current tme t. It s consdered the prce E, :ngoverned by the law of supply and demand S (t), express the equvalent varables related to the demand and offer respectvely, regardng the product of the economc agent E. The factor allows to adjust the response speed of the prce P(t). As result from economc lterature, the most dffcult problem s to determne expressons for varables "demand" D(t) and "supply" S (t). Each component P(t), :n, depend also on the values of other prces that nteract wth P(t),j j :n. The demand D and the supply S of P (t) depend also on ts own factors (t), (t) and on some external factors w(t), q(t) respectvely. D D [P,..,P j,..,p n,,w ] ; S S[ P,,P, j,p n,,q ]. Partcularly an affne model can be obtaned, n a form wth nput u(t), the state x(t), the output z(t) and the dsturbance p(t) x(t) A x(t) B u(t) p(t), y(t) C x(t) D u(t), where x(t) P(t) P T, P(t) [P (t) P(t) P n(t)]. Here u(t) ncorporates the control parameters of ts own subsystem and p (t) ncorporates the control parameters of the external subsystems. The matrces A, B can be determned through an dentfcaton process as proposed n the next secton. In ths paper we consder two categores of economc agents namely proper and external economc agents. The proper economc agents A, IP are agents that can be nfluenced n the control process. Ths can be done by delberately modfyng some parameters, such as the free parameters (t), (t), IP defnng the prce P(t), IP. The set of proper agents defne a so-called proper subsystem S P, composed of state equatons components P(t), I P. The external economc agents A, IEare agents that can not be nfluenced n the control process but whose prce P(t), IE affects all prces ncludng of the own agents. The set of external agents defne a so-called external subsystem S E, composed of state equatons components P(t), IE. Another example where applcable SCCEIA (System for Control and Coordnaton of Economc and Intellectual Actvtes), s the ntellectual process of coordnaton of monetary polcy, [4, ]. Here the mportance of control, partcularly wth FTR s great, amng to stablze fnancal markets by monetary acton. Ths example s presented n detal n the book []. 5. STATE BLOCKING SYSTEMS Into practce, there are systems that can be found n two nstances (two status), namely: the system can be actve or system can be blocked (locked or pause). A partcular problem for the control systems of the economc actvtes s the breaks exstence defned as tme perods of nactvty when all or some state components are kept constant, []. Throughout the consulted lterature, there s no evdence of ths phenomenon for the control purposes, [2], Such structures are commonly found n economc, fnancal, ntellectual processes due to of break tme perods when only some components of the state vector reman constant (partal break), or when all state vector components reman constant durng breaks (total break). For example, bankng, purchasng, sales actvtes, producton actvtes are characterzed by these phenomena. 84 Buletnul AGIR Suplment 2 / 25

6 COMPUTING SYSTEMS MULTI-OBJECTIVE OPTIMIZATION USING DOMAIN-KNOWLEDGE Also many ntellectual actvtes: tranng, desgn, consultancy etc., whose tme evoluton s descrbed by dynamcal systems, are characterzed by tme perods of partal or total break. Of course numerous examples of techncal systems can be gven where such tme perods of rest, more specfcally called blockng perods, can appear due to physcal phenomena: dry frcton, mechancal stffness, nterruptons of electrcal crcuts, etc. Physcally the phenomena are the same as n common systems, they have the same mathematcal models, but n the blockng system pauses can appear. All these systems are referred n the paper as a specal category of systems, called State Blockng Systems (SBS), []. Descrpton of the system n the physcal tme, where the breaks are taken nto account, makes descrpton more complcated, whch means ts nterpretaton as a dfferental system wth dscontnuty on the rght. If break ntervals are removed we obtan a fctve tme, called the actvty tme. Durng the actvty tme, mathematcal models are smple. They are ones gven by physcal (economcal) relatons. A system s SBS, f there s a tme nterval, called the blockng perod, where at least one component of the state vector remans constant over ths perod, whchever s the appled nput to the system. x ( ) x(t, ] x(, ] 2 x(, ] 2 3 x(, ) 3 t 2 3 Fg. 3. Example of the x component evoluton on the actve tme axes, as a functon () x. x(t) z 2 3 t t z Fg. 4. Example of the x () t component evoluton on the physcal tme t. The mathematcal descrpton s carred out consderng the concepts of blockng functon, blockng process, the process of unblockng that controls the blockng status. The basc dea s to work n another tme, called the actve (workng) tme durng actvty perod of tme. We demonstrate that such a system s descrbed by a smple smooth model easer to handle. Consder a dfferental system wth the state equaton, [] called the actve system. n p x f( x, u, t), x:r R, u:r R, t t, x( t) x, () The blockng operatons of the actve system () can be modeled by multplyng each functon f ( xt ( ), ut ( ), t) of (3) by a tme functon z (), t : n, called blockng functons of the actve system. They take values between and. When z () t, the component x () t s full blocked (locked) and when z () t the component x () t s full actve (unlocked). Buletnul AGIR Suplment 2 / 25 85

7 The SBS equatons are DEZVOLTAREA DURABILĂ FAVORABILĂ INCLUZIUNII x () t z () t f ( x (), t u(),), t t x ( t) x, : n (2) z z z Thus the values or of the components z () t {, }, : n, can represent bnary dgts whch determne the number q, as the value of the bnary functon qt ()(2), specfyng the structure S q at tme t. 2 n n qt () z () t 2 z () t 2 z() t 2 z () t 2 (3) The vector z() t thus defned looks lke a new nput for SBS, some components actng as manpulatng varables and the other act as external dsturbances. 6. DISTRIBUTIONS BASED IDENTIFICATION OF THE STATE EQUATION PARAMETERS FOR ECONOMIC PROCESSES For the economc processes control, the most dffcult problem s to determne the parameters of models, wth specfed structure. Generally, some economc bodes of analyss, are able suffcently well to apprecate the exstence of nteractons between varous operators, but less the strength of these nterdependences. From systemc pont of vew, ths means we are able to know the structure of mathematcal models but not the values of ther parameters. Gven ths stuaton, we propose the use dentfcaton algorthms of mathematcal models parameters, partcularly those descrbed by contnuous tme dfferental equatons. These algorthms must keep the sgnfcance dentfed parameters and not be affected by sample perods used n the dentfcaton process. The best results whch satsfes these requrements are acheved by usng algorthms based on the theory of dstrbutons, specfed by the acronym DBI (Dstrbuton Based Identfcaton). In DBI, all tme functons and ther dervatves are assocated wth dstrbuton, resultng a so-called mathematcal model n dstrbutons. Whether, n dfferental equatons the ndependent varable s the contnuous tme varable t, n dstrbuton the ndependent varable s represented by testng functons as elements of the so-called fundamental space of dstrbutons theory. In dfferental equatons, the unknown varable s a tme functon but for equatons n dstrbuton, the unknown varable s a dstrbuton whch belongs to the fundamental space [7]. Ths algebrac equaton depends on the same parameters both n tme doman dfferental equatons as well as n dstrbuton equatons. The solutons of algebrac equaton n dstrbutons lead to the same values of parameter that cancels both the tme doman dfferental equaton and the equvalent dfferental equaton n dstrbutons. 7. FINITE TIME RESPONSE (FTR) CONTROL OF ECONOMIC SYSTEMS A Fnte Tme Response (FTR) system s a system whose evoluton, wth constant nput, enters steady state after a fnte tme nterval, whatever has been the constant nput value and the evoluton before the tme moment when the nput become constant. [3]. The FTR property s specfc to dscrete-tme systems. Control algorthms wth fnte tme response are well known n the lterature as dead-beat algorthms. State control FTR algorthm obtaned by substtuton method s remarkable. These algorthms are developed for lnear systems only. Because of the blocked components and of the actve subsystem uncontrollable components, an SBS system appears as an affne system wth FTR control procedures unknown n lterature. It s developed a new procedure for the affne systems FTR synthess, called the Equvalent Input Method (EIM). For ths purpose t calculates an equvalent nput whch wll determne, accordng to a quadratc crteron, the best approxmaton of the affne component. In ths way the system s approxmated by an affne system wth an nput varable equals to the sum of the orgnal nput and the equvalent nput, havng a resdual affne component. Ths resdual affne component has a smaller norm than the ntal affne component. 86 Buletnul AGIR Suplment 2 / 25

8 COMPUTING SYSTEMS MULTI-OBJECTIVE OPTIMIZATION USING DOMAIN-KNOWLEDGE v k k û q ŵ j k Lnear State Blockng System (L SBS) H qz j f x (k) c x (k) Fg. 5. Block dagram of the FTR control structure for state blockng systems. Q Q f z x (k) The control law avalable for the structure S s c c c c f f z k z x ( k ) ( T ) x ( k ) G u G x ( k ) G x ( k ) The control law avalable for the structure q c f f z k q q q q q q z S j uˆ H x ( k) Q x ( k) Q x ( k) j j j j j j f c f c Q G G, z Q G G G [( G ) G ] ( G ) c c T c c T z c method for the par ( T), G c H s determned by usng classcal deadbeat. Fg. 5, presents the block dagram of the FTR control structure for state blockng systems. Consderng zero the resdual affne component, a FTR lnear system synthess procedure s appled. In the real system, controlled by a FTR control law, the resdual affne component creates at each step a dsturbance that FTR algorthm seeks to cancel. Justfcaton for ths approach s based on fact that the dsturbance resdual affne component s much smaller n norm than the orgnal affne component. Under certan crcumstances ths resdual affne component can be zero. To obtan the FTR control algorthm, the exact dscrete tme model of lnear SBS s obtaned, x c ( k c c c f f z ) ( T ) x ( k ) G u G x ( k ) G x ( k ). k q j z An expermental platform has been desgned n Matlab envronment allowng mplementaton of varous SBS and ther control algorthms. Expermental results are presented to justfy the approached method. 8. EXAMPLE Consder the four agents economc process, based on the law of supply and demand, characterzed by prces of ther products P (), t : 4, wth manpulaton possblty by an attrbute U () t, nterpreted as the nput varable [4]. Usng economc laws between these varables, a lnear or lnearzed dfferental relatonshp can be establshed. The values of these equatons parameters can be obtaned by expermental dentfcaton, usng for example dstrbutons based dentfcaton (DBI) algorthms [7]. A lnear mathematcal model can be obtaned of the form () n varatons wth respect to the steady state values, wth the notatons () () x t P t P, : 4; u () t U () t U. The result s the lnear system (), wth n 4, r, m and matrces, A= It was created a Platform for the Study of Blockng Systems (PSBS), whch allows a number of confguratons through a three elements vector nv [ nv nv2 nv3 ] where: nv s an nteger representng the order n of the system. nv 2 s an nteger that determnes the manner n whch the blockng structure s performed. B=.5 C T = D= Buletnul AGIR Suplment 2 / 25 87

9 DEZVOLTAREA DURABILĂ FAVORABILĂ INCLUZIUNII If nv2, then the blockng vector z() t s composed of n ndependent components based on blockng schedule table. Each component x () t of the state vector s operated by the correspondng blockng component z () t that means, x () t s blocked by. z (), t : n. In Fgure 6, a 4-components blockng vector s consdered. The system responses to a unt step nput appled at the tme t startng from the ntal condton x =x(t )=[ ] T, wthout blockng (natural evoluton) and wth blockng determned by the functon from Fg.6 are shown n Fgure 7. Because n v =[4 ], each component of the state vector was operated by the correspondng blockng functon from Fgure 6. Tme evolutonof the blockng vector z(t) nv=[4 ] z 4 (t) z 3 (t) z 2 (t) z (t) Physcal tme t Fg. 6. Blockng functons z (t), z 2 (t) ), z 3 (t) ), z 4 (t). Economcal process wth 4 agents Evoluton of the control mput u (t).4 u (t)- u (t) appled to the economcal process u (t)- u (t) calculated by feedback Tme (UT) Fg. 8. Evoluton of the FTR control varable u (t). Fg. 7. State vectors for nv = [4 ], x (t) s blcked by z (t), = :4. Economcal process wth 4 agents 2.5 Evoluton of the agent P (t) 2..5 P (t)- P (t) wth FTR P (t)- P (t) wthout FTR Tme (UT) Fg. 9. Open loop and FTR closed loop evoluton of x (t) = P (t)- P. 8 The FTR control law H q for the actve subsystem wth q=5 s gven by H = [ ]. It s consdered the system evoluton startng from the nonzero ntal state x n = [ ] T. 88 Buletnul AGIR Suplment 2 / 25

10 COMPUTING SYSTEMS MULTI-OBJECTIVE OPTIMIZATION USING DOMAIN-KNOWLEDGE In Fgure 8., the evoluton of the FTR control nput s presented. To the controlled process, a pecewse constant nput (black) s appled. It s obtaned from the calculated feed-back varable (drawn n red), through a zero order holder of perod T. Fgure 9. llustrates the evoluton of prce P () t,n varaton wth respect to ts steady state value P, n open loop (drawn n red) and wth FTR closed loop (drawn n black), startng from the same nonzero ntal state. All three next fgures Fg.., Fg.., Fg.2., llustrate evolutons of the x (), t 2: 4, representng P (), t 2: 4 n varatons wth respect to ther steady state values P, 2: 4, () () x t P t P, 2 : 4, n open loop (drawn n red) and wth FTR closed loop (drawn n black), startng from the same nonzero ntal state Economcal process wth 4 agents Evoluton of the agent P 2 (t) P 2 (t)- P 2 (t) P 2 (t)- P 2 (t) wth FTR wthout FTR Tme (UT) Fg.. Open loop and FTR closed loop evoluton of x 2 (t)=p 2 (t)-p 2. Economcal process wth 4 agents Evoluton of the agent P 4 (t) Economcal process wth 4 agents.6 Evoluton of the agent P 3 (t) P 3 (t)- P 3 (t) P 3 (t)- P 3 (t) wth FTR wthout FTR Tme (UT) Fg.. Open loop and FTR closed loop evoluton of x 3 (t)=p 3 (t)-p 3. Economcal process wth 4 agents Evoluton of the output y(t) P 4 (t)- P 4 (t) P 4 (t)- P 4 (t) wth FTR wthout FTR.5..5 y(t)- y(t) y(t)- y(t) wth FTR wthout FTR. Tme (UT) Tme (UT) Fg. 2. Open loop and FTR closed loop evoluton of x 4 (t) = P 4 (t)-p 4. Fg. 3. Open loop and FTR closed loop evoluton of y(t) = Y(t)-Y. As the above fgures, Fg. 3., llustrates evolutons of the varable y() t representng the economcal process output varable Y() t, wth C [ ]; D n varaton wth respect to ts steady state value Y, yt () Yt () Y, n open loop (drawn n red) and wth FTR closed loop (drawn n black), startng from the same nonzero ntal state. ACKNOWLEDGMENT Ths work was supported by the Natonal Unversty Research Councl CNCS-UEFISCDI, Romana, Project Number PI , Contract 66C/.7.24 Contract 2/24. Buletnul AGIR Suplment 2 / 25 89

11 DEZVOLTAREA DURABILĂ FAVORABILĂ INCLUZIUNII REFERENCES [] Halanay A., Samuel J., Dfferental Equatons, Dscrete Systems, and Control: Economc Models, Kluwer Academc Publshers, 997. [2] Swan Trevor W., Economc Growth and Captal Accumulaton, John Wley & Sons, 956, [3] Marn C., Selşteanu D., Şendrescu D., Fnte tme response control of state blockng systems, 9th Internatonal Conference on Control Systems and Computer Scence, CSCS9, May 29-3,23, Bucharest, Romana, pp. -7. [4] Mosa A., The Influence of Monetary and Fscal Polces on Socal Welfare, Academy of Economc Studes Press, Bucharest, 26. [5] Kalath Th., Lnear systems, Prentce Hall Englewood Clfs, New Jersey, 98. [6] Marn C., Identfcaton and control of varable causalty systems (n Romanan), SITECH, Craova, 2. [7] Marn, C., 22, System Identfcaton Based on Dstrbuton Theory, Proceedngs of the IASTED Internatonal Conference Appled Smulaton and Modellng (ASM 22), Crete, June, 22. [8] Maror A. Sstem de conducere ş coordonare a actvtǎţlor economce ş ntelectuale, Teza de doctorat, Unverstatea dn Craova, Iule 22. [9] Barkley Rosser J., On the Complextes Fall of Complex Economc Dynamcs, Journal of Economc Perspectves, 999, vol. 3, no. 4, pp [] Cagan P., The Monetary Dynamcs of Hypernflaton, Studes n the Quantty Theory of Money, Ed. by Mlton Fredman, Chcago: Unversty of Chcago Press, 956, pp [] Marn, C., Selşteanu, D., Sendrescu D., State Blockng Systems: Modelng and Behavor, 4th Internatonal Carpathan Control Conference, Kraków-Rytro, POLAND, May , ISBN , pp [2] Marn, C., Popescu, D., Petre, E., Ionete, C., Selşteanu, D., System Theory (n Romanan), Unverstara, Craova, 24. [3] Marn C., Dgtal systems wth fnte transent regme, SITECH, Craova, 28. CONDUCEREA ŞI COORDONAREA ACTIVITĂŢILOR ECONOMICE ŞI INTELECTUALE PRIN STRUCTURI COMPLEXE INTEGRATE Constantn MARIN,2 Membru corespondent al Academe de Ştnțe Tehnce dn Româna, 2 Unverstatea dn Craova Rezumat: Lucrarea se înscre în categora cercetărlor pentru dezvoltarea ş mplementarea unor structur heterogene în care se aplcă ncluzunea favorablă a factorulu uman pentru conducerea ş coordonarea unor actvtăţ complexe dn cele ma dverse domen: economc, ntelectual, bologc, mltar, etc. Se poate consdera ca fnd o nouă drecţe de dezvoltare ş aplcare a conceptulu modern CPS (Cyber Physcal Systems) în care actvtăţle dn domenle menţonate ma sus sunt asmlate proceselor fzce specfce CPS. Structura propusă evdenţază nteracţunea dntre factorul uman de conducere ş procesele fzce reprezentate prn echpamentele numerce de conducere ş prn procesele conduse. În această structură în crcut închs, nformaţa este reprezentată în tre forme:. Numere în echpamentele numerce; 2. Semnale fzce în procesele conduse (economce sau ntelectuale); 3. Documente, pentru factor uman care fac parte dn structura de conducere. Organsmele consttute dn factor uman (comtet, conslu, brou, drector, etc.) nteracţonează atât între ele cât ş cu celelate componente ale sstemulu heterogen, prn schmb de nformaţ care au ca ş suport fzc documentul. Pentru crearea, transmterea ş operarea documentelor, ca ş suport purtător de nformaţe, se folosesc nstrumente specfce: fluxur de actvtăţ, platforma de dezvoltare.net. procedur de vrtualzare, medul Sharepont. O problemă partculară pentru conducerea actvtăţlor economce o consttue exstenta pauzelor, defnte ca ş peroade de tmp de nacvtvtate când toate sau numna anumte componente ale stăr sunt menţnute constante astfel că modelele clasce nu ma sunt în general valable. Acestea sunt nterpretate ca ş o categore specfcă de ssteme ş anume Ssteme cu Blocare a Stăr (SBS). Sunt prezentate exemple de conducere a unu proces economc bazat pe legea cerer ş oferte care modelează evoluţa preţurlor ş un proces ntelectual de coordonare a poltc monetare. Rezultatele obţnute prn smulare numercă evdenţază avantajele aceste abordăr. 9 Buletnul AGIR Suplment 2 / 25