Transcript Networked Cyber-physical Infrastructure

Hybrid Systems and
Networked Control Systems
Michael S. Branicky
EECS Dept.
Case Western Reserve University
NSF Planning Meeting on
Cyber-Physical Systems
27 July 2006
Hardware
Security
Networked Control
Software
Engineering
Diagnostics
+Monitoring
Hybrid Dynamical System*
• A set of dynamical
systems plus rules for
jumping among them
[Raibert’s Hopper]
___________________
* M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.
Hybrid Dynamical System:
Automata Viewpoint*
[Raibert’s Hopper]
[Thermostat]
[Bouncing Ball]
___________________
* M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.
Adding Control: CHDS*
• An HDS plus controlled
switching and jumps
[Tiptronic Transmission]
___________________
* M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.
Networked Control Systems* (1)
• Numerous distributed agents
• Physical and informational dependencies
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Networked Control Systems* (2)
• Control loops closed over heterogeneous networks
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Mathematical Model:
NCS Architecture*
An NCS Architecture is a 3-tuple:
• Agent Dynamics: a set of stochastic hybrid systems
dXi(t)/dt = fi (Qi(t), Xi(t), QI[t], YI[t], R(t))
Yi(t) = gi (Qi(t), Xi(t), QI[t], YI[t], R(t))
• Network Information Flows: a directed graph
GI = (V, EI), V = {1, 2, …, N}; e.g., e = (i, j)
• Network Topology: a colored, directed multigraph
GN = (V, C, EN), V = {1, 2, …, N}; e.g., e = (c, i, j)
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Fundamental Issues*
• Time-Varying Transmission Period
• Network Schedulability, Routing Protocols
• Network-Induced Delays
h1(t)
• Packet Loss
Plant
h
Plant
Delay
Plant
Controller
Controller
Controller
.
.
.
Network
h(t)
Delay
hN(t)
Plant
Controller
Plant
r
Controller
___________________
* M.S. Branicky, S.M. Phillips, W. Zhang (various): Proc. ACC, 2000; IEEE Cont. Systs. Mag., 2001; Proc. CDC, 2002.
Previous Work
• Nilsson: Time-Stamp Packets, Gain Schedule on Delay
• Walsh et al.: no delay+Max. Allowable Transfer Interval
• Zhang, Branicky, Phillips: hsuff
• Hassibi, Boyd: Asynchronous dynamics systems
• Elia, Mitter, others: Info theory: BW reqts. for CL stability
• Teel/Nesic: Small gain theorem, composability
Control and Scheduling Co-Design*
• Transmission scheduling
satisfying network bandwidth
constraints
h1(t)
Plant
Controller
.
.
.
Network
• Control-theoretic
characterization of stability and
performance (bounds on
transmission rate)
hN(t)
Plant
Controller
Simultaneous optimization of
both of these = Co-Design
___________________
* M.S. Branicky, S.M. Phillips and W. Zhang. Scheduling and feedback co-design for networked control systems. Proc. CDC, 2002.
Packet queueing
and forwarding
Controller
agent
(SBC, PLC, …)
Co-Simulation*
Network dynamics
Visualization
Plant agent
(actuator,
sensor, …)
Router
Bandwidth
monitoring
Plant output
dynamics
Simulation
Co-simulation of systems and networks languages
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Co-Simulation Methodology*
• Simultaneously simulate both the
dynamics of the control system and the
network activity
• Vary parameters:
–
–
–
–
–
Number of plants, controllers, sensors
Sample scheduling
Network topology, routing algorithms
Cross-traffic
Etc.
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Co-Simulation Components (1):
Network Topology, Parameters*
Capability like ns-2 to simulate network at packet level:
• state-of-art, open-source software
• follows packets over links
• queuing and de-queuing at router buffers
• GUI depicts packet flows
• can capture delays, drop rates, inter-arrival times
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Co-Simulation Components (2):
Plant and Controller Dynamics
Extensions of ns-2 release*:
• plant “agents”: sample/send output at specific intervals
• control “agents”: generate/send control back to plant
• dynamics solved numerically using Ode utility,
“in-line” (e.g., Euler), or through calls to Matlab
Also: TrueTime [Lund] (Simulink plus network modules)
Ptolemy, SHIFT [UCB] (+ other HS simu. langs.)
Need: comprehensive tools (ns-2 +SL/LV/Omola +Corba)
various HIL integrations (HW, µprocs, emulators)
___________________
* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.
Analysis and Design Tools
• Stability Regions* and Traffic Loci**
Both for an inverted pendulum on a cart (4-d), with feedback matrix
designed for nominal delay of 50ms. Queue size = 25 (left), 120 (right)
___________________
* W. Zhang, M.S. Branicky, and S.M. Phillips. Stability of networked control systems. IEEE Cont. Systs. Mag., Feb. 2001.
** J.R. Hartman, M.S. Branicky, and V. Liberatore. Time-dependent dynamics in networked sensing and control. Proc. ACC, 2005.
Information Flow
• Flow
– Sensor data
– Remote controller
– Control packets
• Timely delivery
– Stability
– Safety
– Performance
Bandwidth Allocation for Control*
• Objectives:
– Stability of control systems
– Efficiency & fairness
– Fully distributed, asynchronous, & scalable
– Dynamic & self reconfigurable
___________________
* A.T. Al-Hammouri, M.S. Branicky, V. Liberatore, and S.M. Phillips. Decentralized and
dynamic bandwidth allocation in networked control systems. Proc. WPDRTS, 2006.
Queue Control: Results*
PI
¤
P
¤
___________________
* A.T. Al-Hammouri, M.S. Branicky, V. Liberatore, and S.M. Phillips. Decentralized and
dynamic bandwidth allocation in networked control systems. Proc. WPDRTS, 2006.
Synchronization: Ideas*
• Predictable application time
– If control applied early, plant is not in the state
for which the control was meant
– If control applied for too long, plant no longer
in desired state
• Keep plant simple
– Low space requirements
• Integrate Playback, Sampling, and Control
___________________
* V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.
Synchronization: Mechanics*
• Send regular control
– Playback time
• Late playback okay
– Expiration
• Piggyback contingency control
___________________
* V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.
Plant Output*
Open Loop
Play-Back
___________________
* V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.
Cyber-Physical Systems Research
– Control theory:
(stoch.) HS, non-uniform/stochastic samp., event- vs. time-based
hierarachical, composable (cf. Omola), multi-timescale (months to ms)
– Delays, Jitter, Loss Rates, BW
• Characterization of networks (e.g., time-varying RTT, OWD delays)
• Application and end-point adaptability to unpredictable delays
– Buffers
– Control gains
– Time synchronization
– Bandwidth allocation, queuing strategies, network partitioning
• Control theoretical, blank-slate designs, Jack Stankovic’s *SP protocols
– Co-simulation, co-design
– Application-oriented, end-to-end QoS (beyond stability to performance)
– Distributed, real-time embedded middleware:
• Resource constraints vs. inter-operability and protocols
• Sensors/transducers (cf. IEEE 1451, LXI Consortium), distributed timing services
(IEEE 1588, NTP; John Eidson: Time is a first-class object), data gathering (Lui
Sha’s observability), resource management (discovery, “start up”), “certificates”
Thanks
• NSF CCR-0329910 on Networked Control
• Colleague: Vincenzo Liberatore, CWRU