CONTROL AND OPTIMIZATION IN CYBERPHYSICAL SYSTEMS: FROM SENSOR NETWORKS TO "SMART PARKING" APPS. C. G. Cassandras
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1 CONTROL AND OPTIMIZATION IN CYBERPHYSICAL SYSTEMS: FROM SENSOR NETWORKS TO "SMART PARKING" APPS C. G. Cassandras Dvson of Systems Engneerng and Dept. of Electrcal and Computer Engneerng and Center for Informaton and Systems Engneerng Boston Unversty Chrstos G. Cassandras CODES Lab. - Boston Unversty
2 CYBER-PHYSICAL SYSTEMS INTERNET CYBER Data collecton: relatvely easy PHYSICAL Control: a challenge Chrstos G. Cassandras CISE - CODES Lab. - Boston Unversty
3 SENSOR NETWORK AS A CONTROL SYSTEM What s the functon of a SENSOR NETWORK? 1. See and detect Data Sources or Targets 2. Once a Data Source s detected, collect data from t, trac t f moble???????????????? 3. Contnue to see data sources whle collectng data from detected sources Chrstos G. Cassandras CODES Lab. - Boston Unversty
4 OUTLINE Sensor Networs as Control Systems No nowledge of msson space: Coverage control, Persstent Montorng Full nowledge of msson space: Data Collecton, Data Harvestng, Reward Maxmzaton Dstrbuted Optmzaton Framewor Informaton exchange among nodes: Event-drven communcaton Sensor + Actuaton Networs: Smart Parng system Chrstos G. Cassandras CODES Lab. - Boston Unversty
5 SENSOR NETWORK AS A CONTROL SYSTEM Know nothng - must deploy resources how many? where? - Cooperate but operate autonomously - Manage Communcaton, Energy Data fuson, buld prob. map of target locatons statc or traectores dynamc Know everythng - must deploy resources to maxmze beneft from nteractng wth data sources targets: trac, get data - Manage Communcaton, Energy COVERAGE Poston/Move to optmze detecton prob. Update event densty nformaton TARGET DETECTION Localze targets Poston/Move to optmze data collecton qualty DATA COLLECTION COVERAGE: persstently loo for new targets spread nodes out and search Model for optmzaton TRADEOFF: Control node locaton to optmze COVERAGE + DATA COLLECTION DATA COLLECTION: optmze data qualty congregate nodes around nown targets Chrstos G. Cassandras CODES Lab. - Boston Unversty
6 COVERAGE
7 MOTIVATIONAL PROBLEM: COVERAGE CONTROL Deploy sensors to maxmze event detecton probablty unnown event locatons event sources may be moble sensors may be moble Rx Hz/m ???????? 2 0? Meguerdchan et al, IEEE INFOCOM, 2001 Cortes et al, IEEE Trans. on Robotcs and Automaton, 2004 Cassandras and L, Eur. J. of Control, 2005 Gangul et al, Amercan Control Conf., 2006 Hussen and Stpanovc, Amercan Control Conf., 2007 Hoayem et al, Amercan Control Conf., 2007 Perceved event densty data sources over gven regon msson space Chrstos G. Cassandras CODES Lab. - Boston Unversty
8 OPTIMAL COVERAGE IN A MAZE Chrstos G. Cassandras Zhong Zhong and and Cassandras, Cassandras, CODES Lab. - Boston Unversty
9 COVERAGE: PROBLEM FORMULATION N moble sensors, each located at s R 2 Data source at x emts sgnal wth energy E Sgnal observed by sensor node at s SENSING MODEL: p x, s P[Detected by A x, s ] Ax = data source emts at x Sensng attenuaton: p x, s monotoncally decreasng n d x x - s Rx Hz/ 50 m ??????? 4 2?? Chrstos G. Cassandras CODES Lab. - Boston Unversty
10 COVERAGE: PROBLEM FORMULATION Jont detecton prob. assumng sensor ndependence s = [s 1,,s N ] : node locatons P x, s 1 N 1 p x, s 1 Event sensng probablty OBJECTIVE: Determne locatons s = [s 1,,s N ] to maxmze total Detecton Probablty: max s R x P x, s dx Perceved event densty Chrstos G. Cassandras CODES Lab. - Boston Unversty
11 CONTINUED DISTRIBUTED COOPERATIVE SCHEME Set dx x p x R s s H N N ,, Chrstos G. Cassandras CODES Lab. - Boston Unversty Maxmze Hs 1,,s N by forcng nodes to move usng gradent nformaton: dx x d x s x d x p x p x R s H N 1 1, s H s s 1 Desred dsplacement = V t Cassandras and L, 2005 Zhong and Cassandras, 2011 Cassandras and L, 2005 Zhong and Cassandras, 2011
12 PERSISTENT MONITORING PERSISTENT SEARCH, SURVEILLANCE
13 COVERAGE CONTROL v PERSISTENT MONITORING PERSISTENT MONITORING: envronment cannot be fully covered by statonary team of nodes all areas of msson space must be vsted nfntely often mnmze some measure of overall uncertanty????????? Chrstos G. Cassandras CODES Lab. - Boston Unversty
14 PERSISTENT SEARCH IN 2D MISSION SPACE Dar brown: HIGH uncertanty Whte: NO uncertanty Agents play a cooperatve PACMAN game aganst uncertanty whch contnuously regenerates Chrstos G. Cassandras JAVA mult agent smulator desgned to nteractvely test varous controllers. Polygonal obstacles may be added to the envronment. CODES Lab. - Boston Unversty
15 PERSISTENT MONITORING PROBLEM SENSING MODEL: px,s Probablty agent at s senses pont x x st UNCERTAINTY MODEL: Assocate to x Uncertanty Functon Rx,t such that 0 f R x, t 0, A x Bp x, s t R x, t A x Bp x, s t otherwse Chrstos G. Cassandras CODES Lab. - Boston Unversty
16 PERSISTENT MONITORING PROBLEM Partton msson space = [0,L] nto M ntervals: 1 M For each nterval = 1,,M defne Uncertanty Functon R t: 0 R t A BP s t f R t 0, A otherwse BP s t P s 1 N 1 p s 1 p s p, s where P s = ont prob. s sensed by agents located at s = [s 1,,s N ] Chrstos G. Cassandras CODES Lab. - Boston Unversty
17 Chrstos G. Cassandras CODES Lab. - Boston Unversty OPTIMAL CONTROL PROBLEM s.t. 1 mn 0 1,, 1 T M u u dt t R T J N L t s t u u s n n n n 0 1,, otherwse 0, f 0 t BP A t BP A t R t R s s Determne u 1 t,,u N t such that Uncertanty measure Agent dynamcs Uncertanty dynamcs r s x r s x r s x s x p f 0 f 1, Sensng model
18 OPTIMAL CONTROL SOLUTION Optmal traectory s fully characterzed by parameter vectors: such that agent swtches, 1, N 1 S, * * from u t 1 to t 1 at s =, f s odd u * * from u t 1 to t 1 at s =, f s even u Chrstos G. Cassandras Cassandras, Cassandras, Ln, Ln, Dng, Dng, CODES Lab. - Boston Unversty
19 DATA COLLECTION
20 COVERAGE + DATA COLLECTION Recall tradeoff: COVERAGE: persstently loo for new targets spread nodes out TRADEOFF: Control node locaton to optmze COVERAGE + DATA COLLECTION DATA COLLECTION: optmze data qualty congregate nodes around nown targets MODIFIED DISTRIBUTED OPTIMIZATION OBJECTIVE: collect nfo from detected data sources targets whle mantanng a good coverage to detect future events Su : data source value Hs, t RxPx, sdx u Dt SuFu, s D t : set of data sources, estmated based on sensor observatons Fu,s : ont data collecton qualty at u e.g., covarance Chrstos G. Cassandras CODES Lab. - Boston Unversty
21 DEMO: REACTING TO EVENT DETECTION Important to note: There s no external control causng ths behavor. Algorthm ncludes tracng functonalty automatcally Chrstos G. Cassandras CODES Lab. - Boston Unversty
22 DEMO: REACTING TO EVENT DETECTION Important to note: There s no external control causng ths behavor. Algorthm ncludes tracng functonalty automatcally Chrstos G. Cassandras CODES Lab. - Boston Unversty
23 DATA COLLECTION: REWARD MAXIMIZATION, DATA HARVESTING
24 REWARD MAXIMIZATION MISSION X X X X? X TARGETS WITH DIFFERENT REWARDS AND DEADLINES X UNKNOWN TARGETS?? MISSION Node 4 repelled OBJECTIVE: by Node MAXIMIZE 3 TOTAL REWARD COLLECTED BY VISITING Search tas TARGETS performed BEFORE THEIR DEADLINES EXPIRE Chrstos G. Cassandras CODES Lab. - Boston Unversty
25 REWARD MAXIMIZATION MISSION CONTINUED Ths s le the notorous TRAVELING SALESMAN problem, except that there are multple cooperatng salesmen there are deadlnes + tme-varyng rewards envronment s stochastc nodes may fal, threats damage nodes, etc. Chrstos G. Cassandras CODES Lab. - Boston Unversty
26 COOPERATIVE RECEDING HORIZON CRH CONTROL: MAIN IDEA Do not attempt to assgn nodes to targets Cooperatvely steer nodes towards PLANNING hgh expected reward regons HORIZON, H Repeat process perodcally/on-event Worry about fnal node-target assgnment at the last possble nstant ACTION HORIZON, h u 1 Turns out nodes converge to targets on ther own! Solve optmzaton problem by selectng all u to maxmze total expected rewards over H u 2 u 3 Chrstos G. Cassandras CODES Lab. - Boston Unversty
27 REWARD MAXIMIZATION DEMO Chrstos G. Cassandras CODES Lab. - Boston Unversty
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29 BOSTON UNIVERSITY TEST BEDS Chrstos G. Cassandras SMARTS Kcoff Meetng CISE - CODES Lab. - Boston Unversty
30 THE BIGGER PICTURE: DISTRIBUTED OPTIMIZATION
31 DISTRIBUTED COOPERATIVE OPTIMIZATION N system components processors, agents, vehcles, nodes, one common obectve: s mn H s1,, s 1,, s s. t. N N constrants on each s mn H s s 1 s. t. 1,, s N constrants on s 1 mn H s s N, s N s. t. constrants on, 1 s N Chrstos G. Cassandras CODES Lab. - Boston Unversty
32 DISTRIBUTED COOPERATIVE OPTIMIZATION Controllable state s, = 1,,n s 1 s d s Step Sze mn H s s, s Chrstos G. Cassandras N s. t. constrants on, 1 s Update Drecton, usually d s H s requres nowledge of all s 1,,s N Inter-node communcaton CODES Lab. - Boston Unversty
33 HOW MUCH COMMUNICATION FOR OPTIMAL COOPERATION?
34 SYNCHRONIZED TIME-DRIVEN COOPERATION 1 COMMUNICATE + UPDATE 2 3 Drawbacs: Excessve communcaton crtcal n wreless settngs! Faster nodes have to wat for slower ones Cloc synchronzaton nfeasble Bandwdth lmtatons Securty rss Chrstos G. Cassandras CODES Lab. - Boston Unversty
35 ASYNCHRONOUS COOPERATION Nodes not synchronzed, delayed nformaton used Update frequency for each node s bounded + techncal condtons Chrstos G. Cassandras s 1 s d s converges Bertseas Bertseas and and Tstsls, Tstsls, CODES Lab. - Boston Unversty
36 ASYNCHRONOUS EVENT-DRIVEN COOPERATION UPDATE COMMUNICATE UPDATE at : locally determned, arbtrary possbly perodc COMMUNICATE from : only when absolutely necessary Chrstos G. Cassandras CODES Lab. - Boston Unversty
37 WHEN SHOULD A NODE COMMUNICATE? Node state at any tme t : x t s = x t Node state at t : s AT UPDATE TIME t : s : node state estmated by node Estmate examples: s x Most recent value t s t x d x Lnear predcton Chrstos G. Cassandras CODES Lab. - Boston Unversty
38 WHEN SHOULD A NODE COMMUNICATE? AT ANY TIME t : x t : node state estmated by node If node nows how estmates ts state, then t can evaluate x t Node uses ts own true state, x t the estmate that uses, x t and evaluates an ERROR FUNCTION g x t, x t Error Functon examples: x t x t, x t x t 1 2 Chrstos G. Cassandras CODES Lab. - Boston Unversty
39 WHEN SHOULD A NODE COMMUNICATE? Compare ERROR FUNCTION g x t, x t to THRESHOLD Node communcates ts state to node only when t detects that ts true state x t devates from estmate of t so that g x t, x t x t x t Event-Drven Control Chrstos G. Cassandras CODES Lab. - Boston Unversty
40 CONVERGENCE Asynchronous dstrbuted state update process at each : s 1 s d s Estmates of other nodes, K d s 1 f evaluated by node THEOREM: Under certan condtons, there exst postve constants α and K δ such that lm H s 0 sends otherwse update INTERPRETATION: Event-drven cooperaton achevable wth mnmal communcaton requrements energy savngs Chrstos G. Cassandras Zhong Zhong and and Cassandras, Cassandras, IEEE IEEE TAC, TAC, CODES Lab. - Boston Unversty
41 COONVERGENCE WHEN DELAYS ARE PRESENT g x, x Error functon traectory wth NO DELAY t Red curve: Blac curve: g x, x g x, x ~ DELAY Chrstos G. Cassandras CODES Lab. - Boston Unversty t
42 COONVERGENCE WHEN DELAYS ARE PRESENT Add a boundedness assumpton: ASSUMPTION: There exsts a non-negatve nteger D such that f a message s sent before t -D from node to node, t wll be receved before t. INTERPRETATION: at most D state update events can occur between a node sendng a message and all destnaton nodes recevng ths message. THEOREM: Under certan condtons, there exst postve constants α and K δ such that lm H s 0 NOTE: The requrements on α and K δ depend on D and they are tghter. Zhong Zhong and and Cassandras, Cassandras, IEEE IEEE TAC, TAC, Chrstos G. Cassandras CODES Lab. - Boston Unversty
43 SYNCHRONOUS v ASYNCHRONOUS OPTIMAL COVERAGE PERFORMANCE Energy savngs + Extended lfetme SYNCHRONOUS v ASYNCHRONOUS: No. of communcaton events for a deployment problem wth obstacles Chrstos G. Cassandras SYNCHRONOUS v ASYNCHRONOUS: Achevng optmalty n a problem wth obstacles CODES Lab. - Boston Unversty
44 DEMO: OPTIMAL DISTRIBUTED DEPLOYMENT WITH OBSTACLES SIMULATED AND REAL Chrstos G. Cassandras CODES Lab. - Boston Unversty
45 SENSOR + ACTUATION NETWORK INTERNET CYBER Data collecton: relatvely easy PHYSICAL Control: a challenge Chrstos G. Cassandras CISE - CODES Lab. - Boston Unversty
46 SENSOR + ACTUATION: A SMART PARKING SYSTEM
47 SMART PARKING - MOTIVATION 30% of vehcles on the road n the downtowns of maor ctes are crusng for a parng spot. It taes the average drver 7.8 mnutes to fnd a parng spot n the downtown core of a maor cty. R. Arnott, T.Rave, R.Schob, Allevatng Urban Traffc Congeston Over one year n a small Los Angeles busness dstrct, cars crusng for parng created the equvalent of 38 trps around the world, burnng 47,000 gallons of gasolne and producng 730 tons of carbon doxde. Donald Shoup, The Hgh Cost of Free Parng Chrstos G. Cassandras CISE - CODES Lab. - Boston Unversty
48 SMART PARKING - CONCEPT OPTIMAL PARKING SPOT Fnd optmal parng spot for DESTINATION A Mnmze a functon of COST and DISTANCE from A
49 SMART PARKING - CONCEPT DESTINATION OPTIMAL PARKING SPOT
50 GUIDANCE-BASED PARKING DRAWBACKS Drvers: May not fnd a vacant space May mss better space Processng nfo whle drvng Cty: Imbalanced parng utlzaton May create ADDED CONGESTION as multple drvers converge to where a space exsts Searchng for parng Competng for parng
51 SMART PARKING NEW FEATURES System fnds BEST parng space for drver based on PROXIMITY to destnaton + parng COST Space RESERVED guaranteed parng space System contnuously IMPROVES assgned parng space System ensures FAIRNESS n parng space allocaton Parng space UTILIZATION INCREASES Drver maes decsons System maes optmal decsons for drver
52 GUIDANCE-BASED PARKING v SMART PARKING COLLECTING DATA IS NOT SMART, JUST A NECESSARY STEP TO BEING SMART INFO PROCESSING DATA TO MAKE GOOD DECISIONS IS SMART ACTION INFO
53 SMART PARKING IMPLEMENTATION Parng space avalablty detecton Standard sensors e.g., magnetc, cameras Wreless sensor networng Vehcle localzaton GPS System-Drver communcaton Smartphone Vehcle navgaton system Parng reservaton Foldng/Retreatng barrer Red/Green/Yellow lght system
54 PROBLEM FORMULATION Request WAIT Allocaton Fal Allocaton RESERVE 1 2. Departure Allocaton Succeed N
55 OBJECTIVE FUNCTION Obectve functon at th decson pont: J mn x X W R J Decson varables: 0 x 1 f f user user s s NOT assgned to resource assgned to resource User cost functon: J M 1 M D D cost upper bound max proxmty to dest. weght
56 , {0 1},,,, s.t. 1 mn 1 R W x W m t t m m x x R J J x R x W x x x J x m m m n n q R W W R W, Reservaton Guarantee MIXED INTEGER LINEAR PROBLEM MILP Reservaton Upgrade Farness Satsfed User Cost Unsatsfed User Cost
57 SMART PARKING TEST BED Chrstos G. Cassandras CODES Lab. - Boston Unversty
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59 SIMULATION CASE STUDY On-street parng spaces Off-street parng spaces Ponts of nterest
60 CASE STUDY RESULTS Traffc Traffc Traffc Traffc SP: BU Smart Parng system G: Parng usng gudance-based systems NG: No gudance status quo
61 KEY CONCLUSIONS % hgher parng utlzaton HIGHER REVENUE, LOWER CONGESTION 2. % drvers searchng for parng wanderng < 2% HIGHER REVENUE, LOWER CONGESTION 3. 50% reducton n parng tme under heavy traffc LOWER CONGESTION, LESS FUEL, DRIVER COMFORT
62 IMPLEMENTATION Smart Parng proof-of-concept study mplemented n a small 27 space garage at Boston Unversty durng summer 2011: - Parng request through Phone app. - Smart Parng Allocaton Center SPAC: Server located n CODES Lab SPAC determnes optmal allocaton for request f one exsts and notfes drver through Phone app showng the dentty of reserved spot - Garage gateway: Laptop computer located n garage -Sensor and lght system devce: Custom-bult devce affxed on celng over each parng spot.
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64 PROJECT TEAM, RECOGNITION TEAM: Yanfeng Geng PhD student, Ted Grunberg Undergrad. Student, Andy Ochs, Mhal Gurevch, Greg Berman BU SOM students 2011 IBM/IEEE Smarter Planet Challenge competton, team won 2nd place prze Best Student Paper Award, Fnalst, 2011 IEEE Mult-Conference on Systems and Control Thrd prze poster on Smart Parng, INFORMS 2011 Northeastern Conference Ongong mplementaton under BU OTD Ignton Award Worng wth Cty of Boston under IBM Award for Combatng Clmate Change Through Smarter Urban Transportaton Polces Geng, Y., and Cassandras, C.G., Dynamc Resource Allocaton n Urban Settngs: A Smart Parng Approach, Proc. of 2011 IEEE Mult-Conference on Systems and Control, Oct Geng, Y., and Cassandras, C.G., A New Smart Parng System Based on Optmal Resource Allocaton and Reservatons, Proc. of 14th IEEE Intellgent Transportaton Systems Conf., pp , Nov
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66 SMART CITY AS A CYBER-PHYSICAL SYSTEM Prvacy Data collecton Securty TRAFFIC LIGHT CONTROL Geng, Y., and Cassandras, C.G., Traffc Lght Control Usng Infntesmal Perturbaton Analyss, subm. to 51st IEEE Conf. Decson and Control, 2012 Control and Optmzaton Actons Informaton Processng SENSOR NETWORKS Safety Decson Mang Energy Management SMART PARKING Chrstos G. Cassandras CISE - CODES Lab. - Boston Unversty
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