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Feedback Control and
Multi-Agent Systems:
Ubiquitous and Increasingly
Interdependent
Prof. Bill Dunbar
Autonomous Systems Group
Computer Engineering
What are Systems? … ANYTHING
in Engineering, usually with
Dynamics.
Some familiar examples:
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How do we describe systems?
… with math!
Math: Describing Diverse Engineering
Systems in a Common Way
Internet backbone
CA power grid
In these Examples:
San Fran ATC
Control Systems are Hidden
Engineering Systems
“A Control System is
a device in which a
sensed quantity is
used to modify the
behavior of a
system through
computation and
actuation.”
•
My (and Potentially Your)
Research
Robotics
– Exploration
– Toys
– Competition (soccer)
• Automated Freeways
• Supply Chain Management
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Eventually…A Fully
Autonomous Vehicle
Off-Road Dessert Race
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The Potential is Enormous
• Researchers at
Caltech are working
toward the math
model of the “fruit fly
system,” with the
ultimate objective of
making a micromechanical fly!
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Distributed Optimization-Based Control of
Multiagent Systems
Ass. Prof. Bill Dunbar
Autonomous Systems Group
Computer Engineering
Multiagent Systems are Everywhere
• The Internet
• Air traffic control
• The Power Grid
• Autonomous Formations
Control Problems with:
• Subsystem dynamics
• Shared resources
(constraints)
• Communications
topology
• Shared objectives
Multiagent Systems:
Inherently Distributed and Cooperative
Multiagent System:
• autonomous agents
• communication network
Distributed: local
decisions based on local
information.
Cooperative: agents agree
on roles & dynamically
coordinate.
Agent
sensor
input
Environment
output
action
A Relevant Decision Method: Receding
Horizon Control (RHC)
RHC uses optimization to find feasible/optimal plans for near future.
objective
Minimize (distance to pump & fuel)
s.t. Car model (dynamics)
Without hitting wall (constraint)
To mitigate uncertainty, plan is revised after a short time.
actual
computed
X
Mathematics of RHC is Finite Horizon
Optimal Control
objective
Minimize (distance to
pump& fuel)
s.t. Car dynamics
Without hitting wall
(constraint)
Convergence of RHC Requires
Appropriate Planning Horizon and
Terminal Penalty
Theoretical conditions sufficient & in absence of explicit uncertainty.
*[Mayne et al., 2000]
RHC Compared to Other Control
Techniques
• Gives planning &
feedback with builtin contingency
plans.
• Only technique that
handles state and
control constraints
explicitly.
• Tradeoff:
computationally
intensive.
z(t0)
state
t0
t0+
z*(;t0)
T
zk()
time
RHC Successful in Applications:
Process to Flight Control
Caltech flight control
experiment: Tracking
ramp input of 16 meters in
horizontal, step input of
1m in altitude.
RHC updates at 10 Hz,
trajectories generated by
NTG software package.
Movie
RHC Admits Cooperation
ok
follow
3
ok
2
Get 1 to pump, 2 follow
1 & 3 follow 2.
Decoupled dynamics
Avoid collision
follow
1
RHC of Multiagent Systems: What’s
Missing?
Enables autonomy of single
agent.
Amenable to cooperation for
multiple agents.
Missing?…Distributed Implementation*
Why not Centralized?…Local decision require Global
information
Parallelization**?…If you can, but sometimes not applicable.
*[Krogh et al, 2000, 2001]
**[Bertsekas & Tsitsiklis, 1997]
My Contribution: A Distributed
Implementation of RHC
Distributed: local decisions based on local information.
Decoupled subsystem dynamics/constraints, Coupled cost L
Decomposition
Solution of Sub-problems requires
Assumed Plan for Neighbors
Agent 3 
What 3 does
z3(t0)
state
What 2 assumes
t0
t0+
z3 (;t0)
*
z3 ()
k
time
Compatibility of Actual and Assumed
Plans via Constraint
Compatibility
constraint
Assumed plan
Bounds discrepancy
z3(tk)
state
tk
tk+
time
Distributed Implementation Requires
Synchrony & Common Horizon T
Conditions for Theory are General
Convergence Conditions: Same as
Centralized plus Bound on Update
Period
*[Dunbar & Murray, Accepted to Automatica, June, 2004]
Venue: Multi-Vehicle Fingertip
Formation
4
2
qref
d31
Decomposition of Coupled Cost
Simulation Parameters
4
2
: Reference signal
: Actual COM of {1,2,3}
Centralized RHC:
Benchmark for Comparison
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Centralized RHC Simulation
Distributed RHC is Comparable to
Centralized RHC
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Distributed RHC Simulation
Naïve Approach Produces Less
Desirable Performance
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Naïve Approach: Bad Overshoot
Summary of Contribution
Distributed implementation of RHC is provable
convergent, performs well, and is applicable to a
class of Multiagent Systems:
•
Distributed & cooperative structure:
●
Local decisions based on local information
●
Decomposition and incorporation of compatibility constraint
●
Coordination via sharing feasible plans
•
Applicable for:
●
Heterogeneous nonlinear dynamics
●
Generic objective function (need not be quadratic)
●
Coupling constraints
Conclusions
• Theory conservative; useful as guideline for implementation.
• Scalable: computational complexity independent of Na ;
communication complexity independent of Na but dependent
on Ni (size of neighborhood).
• Communicating trajectories: more intensive than traditional
decentralized control, but not too bad, given smoothness
properties.
• Less communication than required by parallelization.
Tradeoff: not recovering centralized solution to original
problem, but that of a modified problem.
Current and Ongoing Work
Theoretically:
● Locally synchronous and asynchronous versions
● DONE: Coupled subsystem dynamics. Potential
applications:
● Process control
● Supply chain management
● Reduced order contingency plans
● Connection with rollout algorithms in MDPs
Current and Ongoing Work
Applications:
● Coordinated UAVs
● Mobile Sensor Networks
● Robots coordinating for toxin detection
● Intelligent Transportation Systems
● Automated freeways
● Semi-automated Air Traffic Control
● Interdisciplinary examples:
● Supply chain management (Business)
● Power/Water resource management