Hybrid Systems and Networked Control Systems

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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

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(No Transcript)
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Hybrid Dynamical System

• A set of dynamical systems plus rules for jumping
  among them

Raiberts Hopper
___________________ M.S. Branicky.
Introduction to hybrid systems. In Handbook of
Networked and Embedded Control Systems,
Birkhauser, 2005.
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Hybrid Dynamical System Automata Viewpoint
Raiberts Hopper
Bouncing Ball
Thermostat
___________________ M.S. Branicky.
Introduction to hybrid systems. In Handbook of
Networked and Embedded Control Systems,
Birkhauser, 2005.
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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.
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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.
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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.
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Mathematical ModelNCS Architecture

• An NCS Architecture is a 3-tuple
• Agent Dynamics a set of stochastic hybrid
  systems
• dXi(t)/dt fi (Qi(t), Xi(t), QIt, YIt,
  R(t))
• Yi(t) gi (Qi(t), Xi(t), QIt, YIt,
  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.
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Fundamental Issues

• Time-Varying Transmission Period
• Network Schedulability, Routing Protocols
• Network-Induced Delays
• Packet Loss

___________________ M.S. Branicky, S.M.
Phillips, W. Zhang (various) Proc. ACC, 2000
IEEE Cont. Systs. Mag., 2001 Proc. CDC, 2002.
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Previous Work

• Nilsson Time-Stamp Packets, Gain Schedule on
  Delay
• Walsh et al. no delayMax. 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

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Control and Scheduling Co-Design

• Control-theoretic characterization of stability
  and performance (bounds on transmission rate)
• Transmission scheduling satisfying network
  bandwidth constraints
• 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.
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Co-Simulation
Co-simulation of systems and networks
___________________ M.S. Branicky, V.
Liberatore, and S.M. Phillips. Networked control
system co-simulation for co-design. Proc. ACC,
2003.
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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.
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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.
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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.
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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.
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Information Flow

• Flow
• Sensor data
• Remote controller
• Control packets
• Timely delivery
• Stability
• Safety
• Performance

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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.
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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.
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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.
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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.
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Plant Output
Open Loop
Play-Back
___________________ V. Liberatore. Integrated
play-back, sensing, and networked control. Proc.
INFOCOM, 2006.
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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
  Stankovics 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 Shas
  observability), resource management (discovery,
  start up), certificates

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Thanks

• NSF CCR-0329910 on Networked Control
• Colleague Vincenzo Liberatore, CWRU