CYBER-PHY CYBER PHYSICAL SY SICAL SYSTEMS: STEMS: MOTIV MO TIVATION TION AND AND CHALLENGES CHALLENGES C. G . G. Cassand . Cassandras as Division of Systems Engineering Center for Information and Systems Engineering Boston University CODES Lab. - Boston University Christos G. Cassandras
CYBER-PHYSICAL SYSTEMS INTERNET Data collection: relatively easy… CYBER PHYSICAL Control: a challenge… THE “INTERNET OF THINGS” Christos G. Cassandras CISE SE - CODES Lab. - Boston University
“SMART CITY” AS A CYBER-PHYSICAL SYSTEM SENSO NSOR NETWO TWORKS RKS Security Privacy Data collection Control and Information Optimization Processing Actions BIG BI DAT ATA Decision Making Safety Energy Management Christos G. Cassandras CISE SE - CODES Lab. - Boston University
“SMART CITY” AS A CYBER-PHYSICAL SYSTEM PHYSICAL Data collection CYBER CYBER Model Control and Information x ( t ) Optimization Processing Actions Model Decision Making x ( t ) x f ( x , u , t ) t PHYSICAL Christos G. Cassandras CISE SE - CODES Lab. - Boston University
WHAT IS REALLY “SMART” ? INFO COLLECTING DATA IS NOT “ SMART ” - JUST A NECESSARY STEP TO BEING “ SMART ” INFO ACTION PROCESSING DATA TO MAKE GOOD DECISIONS IS “ SMART ” Christos G. Cassandras CISE SE - CODES Lab. - Boston University
MODELING: MODELING: TIMED TIMED-DRIVEN DRIVEN vs vs EVENT EVENT-DRIVEN DRIVEN
TIME-DRIVEN v EVENT-DRIVEN SYSTEMS STATE SPACE: STATES TIME -DRIVEN x ( t ) X SYSTEM DYNAMICS: x f x t , t TIME STATE SPACE: STATES EVENT -DRIVEN s 4 X s s s s , , , SYSTEM 1 2 3 4 s 3 x ( t ) s 2 DYNAMICS: ' x f x , e s 1 t TIME t 1 t 2 t 3 t 4 t 5 EVENTS e 1 e 2 e 3 e 4 e 5 Christos G. Cassandras CODES Lab. - Boston University
TIME-DRIVEN v EVENT-DRIVEN CONTROL REFERENCE + ERROR INPUT OUTPUT CONTROLLER PLANT - MEASURED OUTPUT SENSOR EVENT-DRIVEN CONTROL: Act only when needed (or on TIMEOUT) - not based on a clock REFERENCE + ERROR INPUT OUTPUT CONTROLLER PLANT - MEASURED OUTPUT EVENT: SENSOR g ( STATE ) ≤ 0 Christos G. Cassandras CODES Lab. - Boston University
SELECTED REFERENCES - EVENT-DRIVEN CONTROL - Astrom, K.J., and B. M. Bernhardsson, “Comparison of Riemann and Lebesgue sampling for first order stochastic systems,” Proc. 41st Conf. Decision and Control , pp. 2011 – 2016, 2002. - T. Shima, S. Rasmussen, and P. Chandler, “UAV Team Decision and Control using Efficient Collaborative Estimation,” ASME J. of Dynamic Systems, Measurement, and Control , vol. 129, no. 5, pp. 609 – 619, 2007. - Heemels, W. P. M. H., J. H. Sandee, and P. P. J. van den Bosch, “Analysis of event-driven controllers for linear systems,” Intl. J. Control , 81, pp. 571 – 590, 2008. - P. Tabuada, “ Event-triggered real- time scheduling of stabilizing control tasks,” IEEE Trans. Autom. Control , vol. 52, pp. 1680 – 1685, 2007. - J. H. Sandee, W. P. M. H. Heemels, S. B. F. Hulsenboom, and P. P. J. van den Bosch, “Analysis and experimental validation of a sensor-based event-driven controller,” Proc. American Control Conf. , pp. 2867 – 2874, 2007. - J. Lunze and D. Lehmann, “A state -feedback approach to event-based control,” Automatica , 46, pp. 211 – 215, 2010. - P. Wan and M. D. Lemmon, “ Event triggered distributed optimization in sensor networks,” Proc. of 8th ACM/IEEE Intl. Conf. on Information Processing in Sensor Networks , 2009. - Zhong, M., and Cassandras, C.G., “Asynchronous Distributed Optimization with Event-Driven Communication”, IEEE Trans. on Automatic Control , AC-55, 12, pp. 2735-2750, 2010. Christos G. Cassandras CODES Lab. - Boston University
REASONS FOR EVENT-DRIVEN MODELS, CONTROL, OPTIMIZATION Many systems are naturally Discrete Event Systems (DES) (e.g., Internet) → all state transitions are event-driven Most of the rest are Hybrid Systems (HS) → some state transitions are event-driven Many systems are distributed → components interact asynchronously (through events) Many systems are wirelessly networked → energy constrained → time-driven communication consumes significant energy Christos G. Cassandras CODES Lab. - Boston University
REASONS FOR EVENT-DRIVEN MODELS, CONTROL, OPTIMIZATION Many systems are stochastic → actions needed in response to random events Event-driven methods provide significant advantages in computation and estimation quality Time- driven sampling inherently inefficient (“open loop” sampling) System performance is often more sensitive to event-driven components than to time-driven components Christos G. Cassandras CODES Lab. - Boston University
SYNCHRONOUS v ASYNCHRONOUS BEHAVIOR Indistinguishable events INCREASING TIME GRANULARITY Wasted clock ticks More wasted clock ticks … Even more wasted clock ticks Christos G. Cassandras CODES Lab. - Boston University
SYNCHRONOUS v ASYNCHRONOUS COMPUTATION x x y x + y y TIME t 1 t 2 TIME Time-driven (synchronous) implementation: - Sum repeatedly evaluated unnecessarily - When evaluation is actually needed, it is done at the wrong times ! Christos G. Cassandras CODES Lab. - Boston University
MUL MULTI TI-AGENT GENT NETW NETWORK SY ORK SYSTEMS STEMS
COOPERATIVE MULTI-AGENT SYSTEMS The multi-agent system framework consists of a team of autonomous agents cooperating to carry out complex tasks within a given environment. Applications: – Monitoring (data sources/targets) – Search and rescue – Smart buildings – Intelligent transportation – Formation flight of Unmanned Aerial Vehicles Christos G. Cassandras CODES Lab. - Boston University
MULTI-AGENT OPTIMIZATION: PROBLEM 1 Ω s i : agent state, i = 1,…, N a 1 s = [ s 1 , … , s N ] a O 1 i O j : obstacle (constraint) x R ( x ): property of point x O 2 a 3 a 2 P ( x , s ): reward function max ( s ) ( , s ) ( ) H P x R x dx s s i F , i 1 , , N GOAL: Find the best state vector s = [ s 1 , … , s N ] so that agents achieve a maximal reward from interacting with the mission space Christos G. Cassandras CODES Lab. - Boston University
MULTI-AGENT OPTIMIZATION: PROBLEM 2 Ω a 1 a O 1 i x O 2 a 3 a 2 May also have dynamics T max J P ( x , s ( u ( t ))) R ( x ) dx dt 0 u ( t ) s f ( s , u , t ), i 1 , , N s i ( t ) F , i 1 , , N i i i i GOAL: Find the best state trajectories s i ( t ) , 0 ≤ t ≤ T so that agents achieve a maximal reward from interacting with the mission space Christos G. Cassandras CODES Lab. - Boston University
PR PROBLEMS OBLEMS THA THAT FIT THIS T FIT THIS FRAMEW FRAMEWORK ORK
COVERAGE CONTROL: ACTIVE COOPERATION Deploy sensors to maximize “event” detection R ( x ) probability - unknown event locations ( Hz / 50 m 2 ) 40 30 ? 20 ? ?? ? ? ? 10 ? ? 10 0 10 8 5 6 4 2 0 0 max H ( s ) P ( x , s ) R ( x ) dx s Event density : Prior Joint event detection probability: estimate of event N occurrence frequency P ( x , s ) 1 1 p ( x , s ) i i i 1 Event sensing probability Christos G. Cassandras CODES Lab. - Boston University
COVERAGE CONTROL: VORONOI PARTITIONING N max H ( s ) f ( x s ) R ( x ) dx i V s i i 1 V x : x s x s , j i i i j f ( x s ) : sensing quality i R ( x ) : event occurrence frequency s s max H ( ) P ( x , ) R ( x ) dx N s s P ( x , ) p ( x , s ) i i i 1 f ( x s ) x V i i ( , ) p x s i i 0 x V i Christos G. Cassandras CODES Lab. - Boston University
COVERAGE CONTROL: ACTIVE COOPERATION vs PARTITIONING Voronoi patition ; Optimal obj. function = 1346.5 Gradient-based cooperative algorithm ; Optimal obj. function = 1388.1 Christos G. Cassandras CODES Lab. - Boston University
CONSENSUS Ω s ( t ) s ( t ) s ( t ) s 1 t ( ) i j i s 4 t ( ) j N i s s s 2 t ( ) s 3 t ( ) 1 N N Only x that matter max H ( s ) P ( x , s ) R ( x ) dx R ( x ) 1 ( x s ) i are agents s i 1 N 1 max H ( s ) P ( s , s ) P ( s , s ) p ( s , s ) i i i j i 2 s j N i 1 i 2 s s j N , j i p ( s , s ) j i i i j i 0 otherwise i Christos G. Cassandras CODES Lab. - Boston University
COVERAGE CONTROL v PERSISTENT MONITORING COVERAGE CONTROL: Deploy sensors to maximize “event” detection probability – unknown event locations – event sources may be mobile – sensors may be mobile R ( x ) ( Hz / m 2 ) 50 40 30 20 ? 10 ? ? ? ? ? ? ? 10 0 ? 10 8 5 6 4 2 0 0 Perceived event density (data sources) over given region (mission space) Christos G. Cassandras CODES Lab. - Boston University
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