78 07 ~~~ CG2 I J. ~ 71 ~~~~~ I.c 7 - ~~~~~~~~ ~~~~~~~~~~~~ r ~~~~ Office of Naval Research. Division of Applied Sciences

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1 ADA HARARD M CAMBRDGE MA D OF APPLED SCENCES F/G 5/ NFORMATONAL PROBLEMS N LARGE SCALE SYSTEMS (U) JA 75 Y C HO N000LU77 C0531 NL UNCLASSFED ni L

2 r Office of Naval Research uo COc 49 L477C, Ø1 53lJ NR Division of Applied Sciences Harvard University Cambridge, Massachusetts H CG2 71 c 7 J

3 * Unclassified SECURTY C LASS F CATO N OF THS PAGE (*Th,% Dab E nf t r d) REPORT DOCUMENTATON PAGE BEFORE CO% PLETN G FORM 2 GOT AC CESSON NO 3 RCCPENT S CATA LOG NUMBE R REPORT NUMBER Final Report 4 TT E (ond Sub tbt) S Final Report m iy i TYPE OF REPORT S June 30, 19 8 PEROD COERED NFORMATONAL PROBLEMS N LARGE SCALE SYSTEMS 6 PERFORMNG ORG REPORT 7 A UTsOR() Y C NuMBER S COp T RACT OR GRANT NUMPER() Ho N C053l4 *0 PROGRAM LEME NT PROJECT TAa AR EA S WOR( UNT NUMBERS S PERFORMNG ORGANZATON NAME AND ADDRESS J Division of Applied Sciences a Harvard University CambridQe MA CONTROLLNO OFFC E NAME ANDAD ORESS *2 REPORT OAT S *3 *4 MONTORNG AGENCY NAME 6 A ODRESS(1 diu,w e from Contr olin 4 Oc ) July 1978 NUMBER OF PAGES 7 *5 SECURTY CLASS (of (All rop ort) Unclassif ied S DEC LASSFCATON /CO W NGRA 3NG SCHEDULE *4 DSTRBUTON STATEMENT (of this Rpor) This document has been approved for public release and sale; its distribution is unlimited Reproduction in whole or in part is permitted by the US Government dll,,,t from Rport) 17 DSTRBUTON STATEMENT (of (A baftact nc,d n Block 20 *6 SUPPLEMENTARY NOTES S KEY WORDS (Covttffiu on v, idii ncevy ond dntily by block n&onbr) Decentralized Control Large Scale Systems nformat ion Struc tur e ndus tr ial Control and Optimization 30 ABSTRACT (Clntlnu, on r v ro aid nco,y ond idnuty bp block ombr) This is an account of the tecbnica1 wrr p,r f r med Contract ONR N000l4 7 C0351 which was used to partially support the research leave of the Principal nve sti ga tor during the academic year DO j 4l EDTON OF 1 NO OS S OPSOLT S/N * Unclassified UCUS?Y 1U?$CATON OF?$t3 PAG E N0on Dia n *d3

4 FNAL REPORT FOR, ONR N000l477C053l by Y C Ho The principal investigator spent the academic year visiting the Electronic Systems Laboratory of MT and doing research in the area of nformation in Large Systems Three specific topics are in ) vestigated 1 Decentralized Control, Signaling, and Real Tim e nformation Theory n cen tralized con trol, a decis ion maker is concerned wi th two effects of his decisions or controls: Ci) direct impact of the decision on the payof f, (ii) indirect impact of the decision on the payoff by allowing acquisition of better ijfozmation for later decisions The tradeoff between these two desires is sometimes known as dual control When there are more than one decision makers, a third possibility occur s, that of influencing other decision makers info rmation through one s action This is signaling The simplest case of signaling is captured by nformation theory under the real time constraints Ci e no arbitrary delays are permitted) The application and modification of classical informationtheoretic results to decentralized control problems and signaling problems in economic organizations represent a difficult and wide open problen area for future investigation The p incipa1 investigator was an invited plenary session ipeaker at the 1977 nternationa l nforma tion Theory Symposium, anc(* invited speaker at the Third Xingston Conference on Differential G es and )atheaatical Economics He spoke on the above topics He also act ively participated in th supervision of two PhD thesis at MT in this area

5 * 1 ; P 7T7!T 7 C) Two papers were written and published Data Base and Large nfo rmation Systems 2 / Concept ually, a data base appear s at first glance as the embodiment of simplicity n formation are stored and retrieved automatically and systematically by stra ightforward computer routines However, the sheer size of the volume of data completely destroys this simplicity Hours of computer time may be required to locate a single piece of data Thus organization and optimization questions naturally arise in data base management in addition to any hardware, sof tware, an d interface problem s inherent in any real system These logical and structural questions fall under the domai n of system theory They have been partially treated by computer scientists However, it appears that system and control theorist can al so make contributions The principal investigator spent the year mostly in understanding the issues involved in data base management theory He also interacted with the nstitute of Defense Analysis to learn about real data base systems such as the WWMCC and FORSTAT systems He initiated two re search problems in security and query optimization in DB systems The effort will culminate in his talk, A Control Theorist s iew of Data 3 Base in C at the August 1978? Workshop at M T 3 Nanaaenent of Large ndustrial Systems t has been clear for sometime that optimization and control problems xist in large industr ial systems However, it has also been clear that usual decision and control techniques of the x Ax + Bu variety are not applicable to the dynamics of such systems As vehicles for study general problems in this area, we have solved an inventory management problem in a l arg warehouse and a buffer stor age problem in a production line S 1? t r ;r,,

6 L The former involves a novel application of the ArrowHurwicz decomposition algoritist which in this case r educed an optimization problem involving one million variables to one of twentyfour variables The latter is a well known problem of long standing for which we have developed an effective successive approximation technique for solution While it is interesting to solve these specific problems, the overall objective is to discern generally applicable techniques in these systems t appears that our solution techniques can be applied to other areas of large systems, such as file allocation in distributed computer systems, buffers and queues in networks Efforts will be continued

7 a 4 References: 1 y C Ho, 14 P Kastner, and E Wong, Teams, Market Signaling and nformation Structure, EEE Transactions on Automatic Control, Special ssue on Decentralized Control, ol AC23, No 2, April 1978, pp Y C Ho and T S Chang, On Sending One Bit of nformation Over an AGWN Channel with Noiseless Feedback, Journal of Optimization Theory and Applications, ol 27, No 3, January B Sun and Y C Ho, Resource Allocation in An Automated Warehouse, to appear in the 1978 CDC Proceedings, San Diego, California (January 79, 1979) 4 T T chien, A Eyler, and Y C Ho, A Gradient Approach to Buffer Storage Design in a General Production Line, to appear 1978 CDC a Proceedings, San Diego, California (January 79, 1979) 4