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

Networked ControlHardware

Diagnostics+Monitoring

Software Engineering

Security

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*

[Thermostat]

[Raibert’s Hopper]

[Bouncing Ball]

___________________* M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.

Adding Control: CHDS*

[Tiptronic Transmission]

• An HDS plus controlled switching and jumps

___________________* 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• Packet Loss

Plant

Controller

h(t)

Plant

Controller

h

DelayDelay

Plant

Controller

r

Plant

Plant

Controller

Controller

.

.

.N

etw

ork

h1(t)

hN(t)

___________________* 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*

• Control-theoretic characterization of stability and performance (bounds on transmission rate)

• Transmission scheduling satisfying network bandwidth constraints

Simultaneous optimization ofboth of these = Co-Design

Plant

Plant

Controller

Controller

.

.

.

Net

wor

k

h1(t)

hN(t)

___________________* M.S. Branicky, S.M. Phillips and W. Zhang. Scheduling and feedback co-design for networked control systems. Proc. CDC, 2002.

Co-Simulation*

Simulation languages

Bandwidthmonitoring

VisualizationNetwork dynamics

Plant output dynamics

Packet queueing and forwarding

Co-simulation of systems and networks

Plant agent(actuator, sensor, …)

Router

Controlleragent(SBC, PLC, …)

___________________* 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.

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

Co-Simulation Components (2):Plant and Controller Dynamics

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-basedhierarachical, 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