Controls Primer
Fall 2001
Objectives
y Provide familiarity of the basic concepts in feedback control
y Survey tools in Lyapunov and optimization-based control
Proposed Schedule
4 Sep
Overview of feedback control
11 Sep
Introduction to state space control and feedback
18 Sep
Lyapunov stability and control
25 Sep
Lyapunov, continued
Richard
Raff
Lars
Lars
Tue
10 am
PDT
2 Oct
9 Oct
16 Oct
12 Oct
Reza
Reza
Bill
Bill
TBD
Optimal control theory
Optimal, continued
Model predictive control
MPC, continued
http://www.cds.caltech.edu/~murray/courses/primer-fa01
Lecture #1
Overview of Feedback Control
Goals
y Provide engineering context for “active control technology”, through examples
y Survey some of the standard approaches and tools for feedback control
y Describe some of the future directions for the field
Lecture Outline
1. What is Control?
2. Basic Concepts in Feedback Control
3. Application Examples
y Automotive Control
y Flight Control
4. Future Directions
Reference: Report of the Panel
On Future Directions in Control,
Dynamics and Systems, 2001
http://www.cds.caltech.edu/
~murray/cdspanel
What is Control?
Controls Primer, 4 Sep 01
Richard Murray, Caltech
3
Types of Control
Passive Control
• Make structural modifications to change the plant dynamics
• Use this technique whenever it is a viable option: cheap, robust
Open Loop Control
• Exploit knowledge of system dynamics to compute appropriate inputs
• Requires very accurate model of plant dynamics in order to work well
Active (Feedback) Control
• Use sensors and actuators connected by a computer to modify dynamics
• Allows uncertainty and noise to be taken into account
Controls Primer, 4 Sep 01
Richard Murray, Caltech
4
Early Uses of Feedback
Pre-1700
• Water clock (~300 BC, Alexandria), float valves
• Egg incubator (Drebbel, 1620) - control temperature
Watt Governor (1788)
• Regulate speed of steam engine
• Reduce effects of variations in load
(disturbance rejection)
Balls fly out as speed
increases, closing valve
Feedback Amplifiers (1920s)
• Laid mathematical foundations for
classical control
• Use feedback to reduce uncertainty
(robustness)
Controls Primer, 4 Sep 01
Richard Murray, Caltech
5
Modern Application Areas
Flight Control Systems
y Modern commercial and military
aircraft are “fly by wire”
y Autoland systems, unmanned aerial
vehicles (UAVs) are already in
place
Robotics
y High accuracy positioning for
flexible manufacturing
y Remote environments: space, sea,
non-invasive surgery, etc.
Chemical Process Control
y Regulation of flow rates,
temperature, concentrations, etc.
y Long time scales, but only crude
models of process
Heating Ventilation and Air
Conditioning (HVAC)
y Basic thermostatic controls to
building level systems
y Very distributed system with many
local control loops
Automotive
y Engine control, transmission control
, cruise control, climate control, etc
y Luxury sedans: 12 control
instruments in 1976, 42 in 1988, 67
in 1991
AND MANY MORE...
Controls Primer, 4 Sep 01
Richard Murray, Caltech
6
Emerging Application Areas
Materials Processing
y Rapid thermal processing for
increased throughput
y Control of vapor deposition for
special purpose materials (e.g.
YPCO thin films)
Noise and Vibration Control
y Active mounts and speaker systems
for noise and vibration reduction
y Variety of applications: cars, planes,
HVAC
Intelligent Vehicle Highway Systems
y Platooning of cars for high speed,
high density travel on freeways
y PATH project in California is
already in test near San Diego
Controls Primer, 4 Sep 01
Smart Engines
y Compression systems: stall, surge,
flutter control for increased
operability
y Combustion systems: operation at
leaner air/fuel ratios for low
emissions
Unsteady
Pressure
Sensing
System
Stall Precursor, ...
Control
Algorithm
PW4000
Engine
Richard Murray, Caltech
Dynamic
Bleed
Actuation
System
7
Technology Trends Affecting Active Control
Computation/microprocessors
y Early controllers used analog
computation Þ only simple algorithms
were possible
y Development of microprocessor in
1970s opened the door to control
applications
y Virtually all modern active control
loops use microprocessors ⇒ rapid
progress
Sensors and Actuators
y Sensors are getting cheaper, faster,
smaller
y Macro-scale actuation evolves slowly;
power electronics getting cheaper
y Micro-scale actuation is changing
rapidly
Communications and Networking
y Increased use of sensing and actuation
across networks
y Examples: IVHS, ATC, UAVs
8
Basic Concepts in Feedback Control
Controls Primer, 4 Sep 01
Richard Murray, Caltech
9
Active Control = Sensing + Computation + Actuation
Actuate
Sense
Gas Pedal
Vehicle Speed
Compute
Control Action
Goals: Stability, Performance, Robustness
Controls Primer, 4 Sep 01
Richard Murray, Caltech
10
Benefits of Feedback:
Disturbance Rejection & Robustness
disturbance
+
reference
mv = −bv + uengine + uwind
uengine = k(vdes − v)
velocity
vdes
k
1
vss =
vdes +
uwind
b+ k
b+ k
→ 1 as
k →∞
→ 0 as
k →∞
time
Controls Primer, 4 Sep 01
-
Control
+
System
Stability/performance
y Steady state velocity approaches
desired velocity as k → ∞
y Smooth response; no overshoot or
oscillations
Disturbance rejection
y Effect of disturbances (wind)
approaches zero as k → ∞
Robustness
y None of these results depend on the
specific values of b, m, or k for k
sufficiently large
Richard Murray, Caltech
11
Modern Control System Components
noise
noise
external disturbances
Actuators
System
Output
Sensors
Plant
D/A
Computer
A/D
Controller
Operator input
Plant
Controller
Feedback
Controls Primer, 4 Sep 01
Physical system, actuation, sensing
Microprocessor plus conversion hardware (single chip)
Interconnection between plant output, controller input
Richard Murray, Caltech
12
Active Control Methodologies
Black box methods
Model-based methods
y Basic idea: Learn by
observation or training
y Examples:
- Auto-tuning
regulators
- Adaptive neural nets
- Fuzzy logic
y Use a detailed model
(PDEs, ODEs) for
analysis/design
y Examples:
- Optimal regulators
- H∞ control
- Feedback linearization
Advantages:
y No need for complex modeling or
detailed understanding of physics
y Works well for controllers replacing
human experts
Disadvantages:
y No formal tools for investigating
robustness and performance
y Don’t work well for high performance
systems with complicated dynamics
Controls Primer, 4 Sep 01
Advantages:
y Works well for highly coupled,
multivariable systems
y Rigorous tools for investigating robustness
and performance (using models)
Disadvantages:
y Tools available only for restricted class of
systems (e.g., linear, time-invariant)
y Requires control-oriented physical models;
these are not always easy to obtain
Richard Murray, Caltech
13
Control Using Fuzzy Logic
Fuzzy logic allows:
Basic idea: write control actions
as fuzzy logic rules:
Standard logic:
If T < 68º then
turn heater on
Fuzzification
NL NS ZR PS PL
Fuzzy logic:
If very cold then
more heat
Inference
Engine
• Easy specification of
control actions as rules
• Partially conflicting rules
• Smoothing of control
actions
Defuzzification
ZR PS
Sensor
Actuator
Rules
Controller
Controls Primer, 4 Sep 01
Richard Murray, Caltech
14
Example: Fuzzy Control of an Inverted Pendulum
y Basic control structure unchanged:
sense, compute, actuate
y Use simple (and overlapping) rules
to specify control action
y Gives satisfactory performance with
very simple control specification
Source: Yamakawa, Fuzzy Sets and Systems, 1989
Controls Primer, 4 Sep 01
Richard Murray, Caltech
15
Additional Applications of Fuzzy Logic
Pilotless, voice-controlled helicopter (Sugeno)
y System in operation since 1992
y Responds to “hover”, “forward”, “left”, etc
y Motivated by automated crop dusting
Elevator scheduling (Kim et al)
y Simulated 3 car system; multiple scenarios
y Improvement over “conventional” algorithm
à 9% decrease in avg waiting time
à 20% decrease in long waiting periods
à 4% decrease in power consumption
Controls Primer, 4 Sep 01
Other applications
y Sendai railway systems (1987)
y Autofocus cameras (Panasonic)
y Air conditioning (Mitsubishi)
Common features that fuzzy exploits
y Feedback able to improve performance
y Lack of high-fidelity, control oriented
models
y Good human expertise available
y Relatively low performance requirements
(non-catastrophic failure modes)
Richard Murray, Caltech
16
Control using Artificial Neural Networks
Basic idea: encode controller logic
using neural network architecture
• Train weights based on learning,
inputs
gradient search ,etc
• Controller “figures out” proper inputs
to get desired response
Σ
summing
junction
output
sigmoid
weights
Sensor
Actuator
Sensor
Controls Primer, 4 Sep 01
Controller
Advantages:
• Does not require explicit model of
plant; learns from observing
• Structure allows complex,
nonlinear control actions
Disadvantages:
• Can require long training periods
• Applications appear limited
compared to other methods
Richard Murray, Caltech
17
Model-Based Control
Classical control
1940
y Frequency domain based tools; stability via gain and phase margins
y Mainly useful for single-input, single output (SISO) systems
y Still one of the main tools for the practicing engineer
Modern control
1960
y “State space” approach to linear control theory
y Works for SISO and multi-input, multi-output (MIMO) systems
y Performance and robustness measures are often not made explicit
1970
Optimal control
y Find the input that minimizes some objective function (e.g., fuel, time)
y Can be used for open loop or closed loop control (min-time, LQG)
Robust control
1980
y Generalizes ideas in classical control to MIMO context
y Uses operator theory at its core, but can be easily interpreted in
frequency domain
Nonlinear control, adaptive control, hybrid control ...
Controls Primer, 4 Sep 01
Richard Murray, Caltech
18
Representations of Systems
Ordinary Differential Equations
x = f ( x,u)
y = h( x, u)
Block diagrams (Operators)
u(t)
y(t)
P
x
Linearization
around x0=0
x = Ax +Bu
y = Cx +Du
Laplace transform
Linearization
around x0 =0
u(s)
P(s)
y(s)
a n −1 s n −1+
+ a0
P ( s) = n
s + bn −1 s n −1 +
+ b0
Controls Primer, 4 Sep 01
Richard Murray, Caltech
19
Stability and Robustness
Stability: bounded inputs produce bounded outputs
y Necessary and sufficient condition: check for
nonzero solutions around feedback loop
y Basic problem: positive feedback (internal or
external)
Robustness: stability in the presence of unknown
dynamics
y Check for stability in presence of uncertainty
y Need to check stability for set of systems
y “Small gain theorem” gives tight conditions based on
bounds of uncertainty operator
P
K
∆
P
K
No uncertainty ⇒ No need for control
Controls Primer, 4 Sep 01
Richard Murray, Caltech
20
Modeling Uncertainty
Noise and disturbances
y Model the amount of noise by its signal strength in different frequency bands
y Can model signal strength by peak amplitude, average energy, and other
norms
y Typical example: Dryden gust models (filtered white noise)
Parametric uncertainty
y Unknown parameters or parameters that vary from plant to plant
y Typically specified as tolerances on the basic parameters that describe system
Unmodeled dynamics
y High frequency dynamics (modes, etc) can be excited by control loops
y Use bounded operators to account for effects of unmodelled modes:
Additive uncertainty
∆
P
Controls Primer, 4 Sep 01
Multiplicative uncertainty
∆
Feedback uncertainty
P
P
Richard Murray, Caltech
∆
21
Robust Performance
∆
d
W2
P
W1
z
K
d
disturbance signal
z
output signal
∆
uncertainty block
W2
performance weight
W2
uncertainty weight
Goal: guaranteed performance in presence of uncertainty
z 2 ≤ γ d 2 for all ∆ ≤ 1
y Compare energy in disturbances to energy in outputs
y Use frequency weights to change performance/uncertainty descriptions
y “Can I get X level of performance even with Y level of uncertainty?”
Controls Primer, 4 Sep 01
Richard Murray, Caltech
22
Tools for Analyzing and Synthesizing Controllers
(Post-) Modern Control Theory
y Generalizes gain/phase margin to MIMO systems
y Uses operator theory to handle uncertainty, performance
∆
y Uses state space theory to performance computations (LMIs)
Analysis Tools
P
y H gains for multi-input, multi-output systems
∞
K
y µ analysis software
à Allow structured uncertainty descriptions (fairly general)
à Computes upper and lower bounds on performance
à Wide usage in aerospace industry
Synthesis Tools
y LQR/LQG + H∞ “loop shaping”; modern tools for control engineers
y µ synthesis software; tends to generate high order controllers
y Model reduction software for reducing order of plants, controllers
Controls Primer, 4 Sep 01
Richard Murray, Caltech
23
Achilles Heel: Effects of Time Delay on Performance
Control
Control
Vehicle
Delay
Sensor
1.4
1
Second order system
ms^2 + bs = u
Lead compensation
m = 1000 kg
b = 100 N-sec/m
0.4
0.2
0 0
0.05 0.1
0.15
0.2
0.25 0.3
Amplitude
Amplitude
1.2
0.6
Sensor
Step Response
Step Response
0.8
Vehicle
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Original
1 msec delay
0
Time (sec.)
0.05 0.1
0.15 0.2
0.25 0.3
Time (sec.)
Communications delays and uncertainty can have a major effect on high
performance systems
Controls Primer, 4 Sep 01
Richard Murray, Caltech
24
Application Examples
Smart cars and intelligent highways
Flight Control
Controls Primer, 4 Sep 01
Richard Murray, Caltech
25
Feedback Control in Automobiles
Air bags
Temperature control
EGR control
Electronic fuel injection
Electronic ignition
Active
suspension
Electric power
steering (PAS)
Electronic transmission
Cruise control
Anti-lock brakes
1950
1960
1970
1980
ABS (Bosch)
Electronic
ignition
Cruise
control
Controls Primer, 4 Sep 01
EGR
EFI
i4004
Muskie laws
1990
ABS
PAS
Air bags
Active
suspension
Richard Murray, Caltech
Navigation
systems
2000
Traction control
Heads-up displays
4W steering
Obstacle avoidance
26
Engine Control
Reliance on active control is increasing
y Increasingly strict emissions and fuel
efficiency requirements
y Continued Improvements in sensing,
actuation, electronics, microprocessors
y Main bottlenecks are uncertainty,
complexity, and sensing capability
y Integration of control functions
becoming more difficult due to
increased reliance on outside suppliers
Engine control electronics
50
40
Functions
30
20
Actuators
10
Sensors
0
1980
1983
1986
1989
1992
1995
1998
Year
Source: Barron & Powers, IEEE/ASME T. Mechatronics, Mar 96
Controls Primer, 4 Sep 01
Richard Murray, Caltech
27
Trends and Lessons in Automotive Control
Advances often driven by gov’t
regulations
y Muskie laws (1970) for emissions
y Restraint laws in 1980s → air bags
y CAFE → electric power steering
systems
Electronics + control provided solution
y Feedback was needed to get reliable
performance in multiple operating
conditions, with variations in parts
Strict reliability and cost requirements
y Control solutions must show
demonstrated benefit and have low cost
y Reliability has improved steadily in
past 20 years
These issues are common to many
emerging applications areas that
make use of active control technology
Additional benefits
y Increasing use of controls for nonregulated functions
à Anti-lock brakes
à Active suspension
y Increased sensing allows improved
diagnostics and prognostics (not
used?)
Emerging Trends
y Networking: car is no longer an
isolated
à Security systems: lo-jack, etc
à GPS-based navigation
à Diagnostics? IVHS?
y Distributed control
à Increased reliance on suppliers
for (smart) components
à Presents integration challenges
29
Intelligent Vehicle Highway Systems (IVHS)
Weigh-in-Motion
Inductive Loop
Detector
Vehicle -- Platoon leader
Vehicle -- Platoon Member
Electronic
Toll Collection
Vehicle -- Free Agent
Roadside
Beacon
Variable
Message Signs
Ramp
Meetering
Video Camera
Traffic Management
Center (TMC)
Arterial
Roadway Control
AHS
Entry Screening
Highway
Advisory Radio
Use Feedback Control to Regulate and Optimize Traffic Control
Controls Primer, 4 Sep 01
Richard Murray, Caltech
30
High Confidence, Reconfigurable,
Distributed Control
(Hickey, Murray, Chandy, Doyle)
Optimization-Based Control
• Real-time model predictive
control for online control
customization: theory +
software
• Online implementation on
Caltech Ducted Fan
Software Environments
• Logical programming
environments for embedded
control systems design
• “On-the-fly”, correct by
construction techniques
Multi-Vehicle Testbed
• Implementation on multivehicle, wireless testbed
using Open Control Platform
• Bluetooth-based point to
point communications with
ad-hoc networking
Output: Framework and Prototype Environment
for Robust, Software Enabled Control Systems
Overview: Optimization-Based Control
Nonlinear design
• global nonlinearities
• input saturation
• state space constraints
ref
Trajectory
Generation
Op Maps
Local design
∆
ud
Plant
P
noise
xd
δu
NTG
output
Local
Control
MPC+CLF
y Use real-time trajectory generation to construct (suboptimal) feasible trajectories
y Use model predictive control for reconfigurable tracking & robust performance
y Extension to multi-vehicle systems performing cooperative tasks (ongoing)
Controls Primer, 4 Sep 01
Richard Murray, Caltech
33
Overview: Optimization-Based Control
T
∆T
u[t ,t +∆T ] = arg min ∫
t +T
t
L( x(τ ), u (τ )) dτ + V ( x(t + T ))
x0 = x(t ) x f = xd (t + T )
x = f ( x, u ) g ( x, u ) ≤ 0
Online control customization
y System: f(x,u)
y Constraints/environment: g(x,u)
y Misssion: L(x,u)
Controls Primer, 4 Sep 01
Update in real-time to achieve
reconfigurable operation
Richard Murray, Caltech
34
Theory: MPC + CLF Approach
T
J T* ( x0 ) = min ∫ q ( x(τ ), u (τ )) dτ + V ( x(T ))
u (⋅)
0
Finite horizon
CLF
≈ “cost to go”
inf (V + q)(x,u) ≤ 0
u
Basic Idea
y Use online models to compute receding horizon optimal control
y CLF-based terminal cost gives stability + short time horizons
Properties
y Can prove stability (in absence of constraints)
y Incremental improvement property ⇒ finite iterations OK
y Increased horizon ⇒ larger region of attraction
Controls Primer, 4 Sep 01
Richard Murray, Caltech
35
Real-Time Trajectory Generation / Optimization
x = f ( x, u )
Ducted Fan Terrain Avoidance
Collocation
( x, u ) = ∑ α iψ i (t )
x(ti ) = f ( x(ti ), u (ti ))
Flatness
z = z ( x, u , u , … , u ( p ) )
x = x( z , z ,…, z ( q ) )
u = u ( z, z,…, z ( q ) )
z = ∑ α iψ i (t )
Quasi-collocation
y = h( x )
( x, u ) = Γ ( y , y , … , y ( q ) )
0 = Φ ( y, y,…, y ( p ) )
Controls Primer, 4 Sep 01
Richard Murray, Caltech
36
Experimental Results: Caltech Ducted Fan
NTG +
MPC +
CLF
Pitch
Control
dSPACE
RTOS
Controls Primer, 4 Sep 01
Richard Murray, Caltech
37
Multi-Vehicle Optimization-Based Control
Assume we have real-time, finite horizon optimal control as a primitive
u[t ,t +∆T ] = arg min ∫
t +T
t
L( x, u )dt + V ( x(t + T ))
Choose f, g, L to represent the
coupling between the various
subsystems
x0 = x(t ) x f = xd (t + T )
x = f ( x, u ) g ( x, u ) ≤ 0
Cooperation depends on how we model “rest of the world”
q1 = 0
u1 ≤ L
u2,[t ,t +∆T ] = arg min ∫
t +T
t
L(q1, x2 , q3 , u2 )dt + V
x2 = f ( x2 , u2 ) g ( x2 , u2 ) ≤ 0
q3 = 0
u3 ≤ L
Reconfigurable based on condition, mission, environment
Controls Primer, 4 Sep 01
Richard Murray, Caltech
38
Simulation Example: Formation Flight
Global MPC + CLF
Local MPC + CLF
• Assume neighbors follow
straight lines
Task:
y Maintain equal
spacing of vehicles
around circle
y Follow desired
trajectory for
center of mass
Parameters:
y Horizon: 2 sec
y Update: 0.5 sec
y High damping
Controls Primer, 4 Sep 01
Richard Murray, Caltech
39
Multi-Vehicle Wireless Testbed for Integrated Control,
Communications and Computation
(Hickey, Low, Murray, Doyle, Effros + 8 undergrads)
Hub
Comms
Computing
Propulsion
Testbed features
y Distributed computation on individual vehicles + command
and control console
y Point to point, ad-hoc networking (bluetooth) + local area
networking (802.11)
y Cooperative control in dynamic, uncertain, and adversarial
environments
Controls Primer, 4 Sep 01
Richard Murray, Caltech
40
RoboCup Video (Raff D’Andrea [Cornell], CIT `96)
Controls Primer, 4 Sep 01
Richard Murray, Caltech
41
Summary
Actuate
Sense
Compute
Feedback enables performance in the presence of uncertainty
y Uncertainty management requires clever and appropriate use of feedback
y Model-based control and black box controllers can both enhance performance
Rapid improvements in sensing, computation, communication drives control
y All of these are becoming cheaper and more ubiquitous; networking will have a
large impact on control, diagnostics, prognostics, maintainence, etc
y Actuation still remains a bottleneck; control configured design is key
Controls Primer, 4 Sep 01
Richard Murray, Caltech
42
Future Directions
Controls Primer, 4 Sep 01
Richard Murray, Caltech
43
Future Directions in
Control, Dynamics,
and Systems
Panel on Future Directions in
Control, Dynamics, and
Systems
Richard M. Murray (chair)
Caltech
Outline
• Review of Panel Activities
• Overview of Panel Report
• Next Steps & Timeline
http://www.cds.caltech.edu/~murray/cdspanel
Controls Primer, 4 Sep 01
Richard Murray, Caltech
44
Motivation for the Panel
Articulate the challenges and opportunities for the field
y Present a vision that can be used to inform high level decision makers
of the importance of the field to future technological advances
y Identify possible changes in the way that research is funded and
organized that may be needed to realize new opportunities
y Provide a compelling view of the field that continues to attract the
brightest scientists, engineers, and mathematicians to the field
Respond to the changing nature of control, dynamics, and systems
research
y Many new application areas where controls tools are playing a stronger
role: biology, environment, materials, information, networks, …
y Controls engineers taking on a much broader, systems-oriented role,
while maintaining a rigorous approach and practical toolset
Controls Primer, 4 Sep 01
Richard Murray, Caltech
45
Panel Composition
Karl Astrom
Lund Institute
of Technology
Siva Banda
Air Force
Research Lab
Stephen
Boyd
Stanford
Roger
Brockett
Harvard
John Burns
Virginia Tech
Munther
Dahleh
MIT
John Doyle
Caltech
John
Guckenheimer
Cornell
Charles
Holland
DDR&E
Pramod
Khargonekar
U. Michigan
Jerrold
Marsden
Caltech
Greg
McRae
MIT
George Meyer
NASA Ames
Gunter Stein
Honeywell
Pravin
Varaiya
UC
Berkeley
P. S.
P. R. Kumar
Krishnaprasad U. Illinois,
U. Maryland
ChampagneUrbana
Richard
Murray
Caltech
Controls Primer, 4 Sep 01
William
Powers
Ford
Richard Murray, Caltech
46
Panel Activities
Panel Meeting: 16-17 June 00
y 47 attendees representing academia,
industry, government
y Subpanels in 5 application areas
y Basis for report findings
Writing Committee Meetings
y Boyd, Brockett, Burns, Dahleh,
Doyle, Laub, Murray, Stein
y Meetings in Oct 00, Mar 01
y Generated outline + drafts
Panel Presentations
y AFOSR Contractors Meeting, 8/00
y Gov’t Program Managers, 2/01
y DARPA UAV workshop, 3/01
y IFAC NOLCOS, 6/01
Controls Primer, 4 Sep 01
Announcements
y Control Systems Magazine, 6/00
y Systems and Control E-Letter, 6/00
y Systems and Control E-Letter, 9/00
Communication
y CDS Panel web site
à Draft copies of report
à Links to related activities/reports
y Mailing list (150+ people)
y Bulletin board
Linkages
y European Commission Workshop,
6/00
Richard Murray, Caltech
47
Control in an Information Rich World
Report of the Panel on Future Directions in Control, Dynamics, and Systems
(v2.0, 27 Jul 01)
1. Executive Summary (5 pages)
y What is Feedback Control?
y Why Does it Matter?
y Control Will Be Even More
Important in the Future
y …But It Won’t Be Easy
y What Needs to be Done
2. Overview (20 pages)
y What is Control?
y Control System Examples
y The Shift to Information-Based
Systems
y Opportunities and Challenges Now
Facing Us
Controls Primer, 4 Sep 01
3. Applications, Opportunities and
Challenges (30-40 pages)
y Aerospace and Transportation
y Information and Networks
y Robotics and Intelligent Machines
y Biology and Medicine*
y Materials and Processing*
y Other Applications
à Environment*
à Finance and Economics*
4. Education and Outreach* (10 pages)
5. Recommendations (5 pages)
Richard Murray, Caltech
48
Aerospace and Transportation
(DARPA Software Enabled Control Program, H. Gill)
Controls Primer, 4 Sep 01
Richard Murray, Caltech
49
Information and Networks
Pervasive, ubiquitous, convergent networking
y Heterogeneous networks merging
communications, computing, transportation,
finance, utilities, manufacturing, health,
consumer, entertainment, ...
y Robustness and reliability are the dominant
challenges
y Need “unified field theory” of
communications, computing, and control
Many applications
y Congestion control on the internet
y Power and transportation systems
y Financial and economic systems
y Quantum networks and computation
y Biological regulatory networks and evolution
y Ecosystems and global change
Controls Primer, 4 Sep 01
Richard Murray, Caltech
50
Materials and Processing
Question: can control be used to modify
surface morphology?
y Use unsteady processing conditions
and in situ diagnostics to alter growth
y Provide more structured approach
than existing techniques
y Can also be used to understand
actuation of domain walls
Controls Primer, 4 Sep 01
Challenges
y Sensing of relevant characteristics
à Nucleation events
à Grain boundary features
à Surface roughness
y Coupling between macro-scale
actuation and micro-scale physics
y Models suitable for controllability
analysis and control design
Richard Murray, Caltech
51
Biology and Medicine
“Systems Biology”
y Many molecular mechanisms for biological organisms are
characterized
y Missing piece: understanding of how network
interconnection creates robust behavior from uncertain
components in an uncertain environment
y Transition from organisms as genes, to organisms as
networks of integrated chemical, electrical, fluid, and
structural elements
Key features of biological systems
y Integrated control, communications, computing
y Reconfigurable, distributed control, built at molecular level
Design and analysis of biological systems
y Apply engineering principles to biological systems
y Systems level analysis is required
y Processing and flow information is key
Controls Primer, 4 Sep 01
Richard Murray, Caltech
52
Software Control Theory
2001 ISAT Study on Vigilant High Confidence Systems
Goal: Info systems you can bet the country on
Approach: VIGILANCE via “software control theory”
Why now?
y Network-centric systems are enablers in military and
commercial applications
y BUT, current approaches are inadequate
y Need new approach to robust info systems
Protected
Component
Sensors
Actors
Coordinators
Why will it work?
y Real-time monitoring, model checking now feasible
y New ideas in pervasive control, stream checking
y Preliminary investment: OASIS, DASADA, FTN, AT&T...
Select
Component
Model
S1
Controls Primer, 4 Sep 01
Richard Murray, Caltech
S2
S3
53
Example: Feedback Control for Distributed Sorting
Distributed sorting is a necessary
operation in many missions
y Example: target prioritization
across multiple platforms
y Current approaches: voting,
consensus, deconfliction
Question: can we use vigilance to
provide robust operation?
Controls Primer, 4 Sep 01
Richard Murray, Caltech
54
Feedback Algorithm for Target Prioritization
Approach: Interconnect individual modules to get fast, robust, distributed
sorting
y Stability: bounded computational time in each node + finite time convergence
y Robustness: algorithm converges, even if processor fails or node is hacked
y Performance: sort time is optimal with respect to stationary cycle time
distribution
y Robust performance: algorithm converges quickly even in worst case (eg,
hacked node exploiting feedback structure)
Sort1
Select
Track IDs
Sort2
Prioritized
Targets
Sort3
Feedback
Controls Primer, 4 Sep 01
Richard Murray, Caltech
55
Integrating Feedback into Algorithms
Question: how do we compute in face of uncertainty?
y Distributed algorithm with component failure, data corruption possible
y Variable CPU time available on each processor, due to other tasks
y One or more processors might be taken over by adversary
y Require high performance (fast, accurate, dynamically balanced)
cycles
Input list 1
Input list 2
Input list 3
select
source
confidence
source
eval
Controls Primer, 4 Sep 01
list
partial
iter
sort
K
∫
Answer: robustness through
feedback
output list
y Dynamic load balancing
time
by modulating iterations
remaining
in partial sort
y Robustness to software
failures and data
corruption by source
Feedback
selection and feedback
y Requires accurate sensors
Sort
i
Richard Murray, Caltech
56
Fast Select:
New Tools in Program and Stream Checking
I
Program
I1
:
Ik
O
Ok
:
O1
Checker
0100101101010110
Very
small
memory,
cycles
Processor
Memory
Controls Primer, 4 Sep 01
Program checking by comparing
input/output streams gives confidence levels
y New results give O(log(n)) check of
approximate correctness (1-ε sorting)
y Ideas fit well with control approach:
provide “sort” metric
Stream checking for rapid assessment and
selection of output
y Use to quickly determine closeness of
streams
y Provides fast computation of L1 distance
with O(log(n)) memory usage
New results provide ideas for
fast and accurate sensors that
can be used for feedback
Richard Murray, Caltech
57
Upgrade and Repair in Sort Example
Question: what happens if we insert faulty code into sort loop?
y
Feedback mechanisms correct (resort or reject) data
Sort1
4
Last node in
loop refines
and cleans
data stream
y
1
Sort
RotS22
Faulty node
generates
unsorted or
incorrect data
2
Select
Incoming
Track IDs
Sort3
Output from
node is
incorrect or
incomplete
3
Prioritized
Targets
Next node in
loop resorts
or rejects
faulty data
Analysis capability: use norms to bound error
• Can characterize allowable deviation of algorithm and verify stability
Controls Primer, 4 Sep 01
Richard Murray, Caltech
58
CDS Panel Recommendations
1. Substantially increase research aimed at the integration of control,
computer science, communications, and networking.
y Principles, methods and tools for control of high level, networked,
distributed systems
y Rigorous techniques for reliable, embedded, real-time software.
2. Substantially increase research in Control at higher levels of
abstraction, moving toward enterprise level systems.
y Dynamic resource allocation in the presence of uncertainty
y Learning, adaptation, and artificial intelligence for dynamic systems.
3. Explore high-risk, long-range applications of Control
y Nanotechnology, quantum mechanics, biology, and environmental
science.
y Dual investigator funding might be particularly useful mechanism in
this context.
Controls Primer, 4 Sep 01
Richard Murray, Caltech
59
Preliminary Recommendations, con’t (from draft report)
4. Maintain support for theory and interaction with mathematics,
broadly interpreted
y Dynamical systems, graph theory, combinatorics, complexity theory,
queuing theory, etc
y Strength of field relies on its close contact with rigorous mathematics;
increasingly important in the future.
5. Invest in new approaches to education and outreach for the
dissemination of basic ideas to nontraditional audiences.
y For Control to realize its potential, we must do a better job of educating
those outside Control on the principles of feedback and its use as a tool
for altering the dynamics of systems and managing uncertainty.
Controls Primer, 4 Sep 01
Richard Murray, Caltech
60
Panel Timeline
Next steps
Future Directions in
Control, Dynamics,
and Systems
• Jul ’01: updated draft available
• Post to web, distribute to m-list
• Aug ’01: finish missing sections,
collect feedback
•
•
•
•
Biology and medicine
Materials and processing
Environment, finance, etc
Education
• Sep ’01: issue final draft
• Oct ’01: release report, send to SIAM
• Nov ’01: distribute report to Congress,
funding agencies, program managers
http://www.cds.caltech.edu/~murray/cdspanel
Controls Primer, 4 Sep 01
Richard Murray, Caltech
61
Lecture #1
Overview of Feedback Control
Goals
y Provide engineering context for “active control technology”, through examples
y Survey some of the standard approaches and tools for feedback control
y Describe some of the future directions for the field
Lecture Outline
1. What is Control?
2. Basic Concepts in Feedback Control
3. Application Examples
y Automotive Control
y Flight Control
4. Future Directions
Reference: Report of the Panel
On Future Directions in Control,
Dynamics and Systems, 2001
http://www.cds.caltech.edu/
~murray/cdspanel
Controls Primer
Fall 2001
Objectives
y Provide familiarity of the basic concepts in feedback control
y Survey tools in Lyapunov and optimization-based control
Proposed Schedule
4 Sep
Overview of feedback control
11 Sep
Introduction to state space control and feedback
18 Sep
Lyapunov stability and control
25 Sep
Lyapunov, continued
Richard
Raff
Lars
Lars
Tue
10 am
PDT
2 Oct
9 Oct
16 Oct
12 Oct
Reza
Reza
Bill
Bill
TBD
Optimal control theory
Optimal, continued
Model predictive control
MPC, continued
http://www.cds.caltech.edu/~murray/courses/primer-fa01