Swarm Collaborative Intelligence:
From Networked Control to Trust in MANET
John S. Baras
Institute for Systems Research
Department of Electrical and Computer Engineering
And Department of Computer Science
University of Maryland, College Park, MD 20742
Workshop on Swarming in Natural and Engineered Systems
Napa Valley, California
August 3-4, 2005
Thanks to

Collaborators:
Tao Jiang, George Theodorakopoulos, Xiaobo Tan, Wei
Xi, Pedram Hovareshti

Funding sources:
ARL (CTA on C&N), ARO, ARO CIP URI (Wireless
Network Security), ARO MURI (Networked Control
Systems), DARPA (Dynamic Coalitions)
Outline

Autonomous collaborating vehicles


A stochastic approach based on MRF
Analysis





Simulation results
A hybrid scheme to improve the performance
Distributed trust in MANET





Convergence study of a simple case
Convergence speed analysis
Trust (and Mistrust) spreading and dynamics
Effects of topology on convergence
Spin glasses and cooperative games
Collaboration via trust schemes
Conclusions and future work
A Battlefield Scenario

Mission


Constraints




Autonomous, distributed maneuvering of a vehicle group to reach
and cover a target area
Desired inter-vehicle distance
Obstacles avoidance
Threats (stationary or moving) avoidance
Requirement

Using only local or static information
Review of Deterministic
Gradient-Flow Approach

Dilemma of the Deterministic gradient-flow approach



Potentials-based approach can accommodate multiple objectives
and constraints in a distributed and computationally effective way
The system dynamics could be trapped by the local minima
Weighted sum of potential functions:
Ji ,t (qi )  g J g (qi )  n Ji ,t n (qi )  o J o (qi )  s J s (qi )  m Jt m (qi )





Target (attraction) potential Jg
Neighbor (avoidance) potential Jn
Obstacle potential Jo
Potential Js due to stationary threats
Potential Jm due to moving threats

Gradient flow:
qi (t )  
J i ,t (qi )
qi
Being Trapped by Local Minima
Different initial conditions may cause vehicles to be trapped by local minimum
Markov Random Fields

Markov Random Fields (MRF)



A collection of random variables X={Xs}, s∈ S with discrete values
in phase space s
A neighborhood system on S is a family N = {Ns}, s∈ S, where Ns ⊂ S,
and r ∈ Ns ↔ s ∈ Nr
The marginal probability depends only on neighbor’s phase value
P ( X s  xs | X S \ s  xS \ s )  P ( X s  xs | X N ( s )  x N ( s ) )

Gibbs Field (GF)


A clique is a subset c ⊂ S, such at for all s,r ∈ c, r ∈ Ns
The potential energy of a configuration x={xs} is defined as a sum of
all clique potentials
U ( x )   c ( x )
cC
Gibbs Sampler and Gibbs Distribution

Gibbs distribution (global description)

The marginal probability is function of local potentials
  c ( x , x N ( s ) ) / T
U ( xs , xS \ s ) / T
e
e cCs
P ( X s  xs | X N ( s )  x N ( s ) ) 

U (  , xS \ s ) / T
  c ( x , x N ( s ) ) / T
e

 e cCs

Gibbs distribution is function of global potentials
e U ( x ) / T
P( X  x ) 
Z
Hammersley-Clifford theorem: A MRF on a graph is equivalent to a GF


Gibbs sampler



Gibbs sampler (MCMC method)defines a Markov chain on a Gibbs Field
The stationary distribution of the MC is the Gibbs distribution
Using simulated annealing algorithm, final configuration converges to
global minimum with probability 1
Modeling a Swarm as a GF
2D mission space on discrete lattice cells




Agent s can communicate with
neighboring agents in Ns which stay
within the interaction range Rs
An agent can go at most Rm within one
move, which defines the phase space s
Gibbs potential is designed to reflect
global objective
Obstacle
U ( x)    c ( x),
cC
 s ( x) 
  (x , x
cCs
c
s
N (s)
)
 g J sg  o J so  n J sn
Difficulties in applying classical results



Non-stationary neighborhood system
Time-varying and state-dependent phase space
Agents
target
Gibbs Sampler Based Algorithm

Algorithm for single vehicle


Step1. Pick a cooling schedule T(n) and the total number N of
annealing steps
Step2. At each annealing step n, conduct a location update for
the vehicle by performing the following:

Determine the set L of candidate locations for the next move
L  {l : l  x  Rm }

For each l ∈ L, evaluate

p  X ( n  1)  l | X ( n )  x  
e

(l )
T (n)
l 'L



e
 ( l ')
T (n)
Update location by sampling above distribution
Step 3. Let n = n+1. If n = N, stop; otherwise go to step 2
Convergence Study

Single vehicle with limited sensing and moving range

Fixed temperature


Assume accessible area is connected
Unique stationary distribution
e
T  x  



U  x
T

e
z  x  Rm

U  z
T
where Z T 
ZT
From any distribution v, lim vPT n  T
e
xX

U x 
T
e

U z 
T
z  x  Rm
n 
Simulated annealing

Cooling schedule T n   
ln n

Let Qn = (PT(n))τ
 1
if x  M

lim vQ1...Qn   M
n 
 0
if x  M
where
M  {x : U ( x )  min (U ( z ))}
zX
Convergence Rate Study

Convergence rate of a single vehicle case

For the single-vehicle case, the convergence rate is characterized by
~
vQ1...Qn   
where

  2 m~2m 

 O n


~  min U  y   m
m
y  xm
Using convergence rate bound as a design indicator


Design λg* to maximize
the convergence rate
Potential function
J  ps  p
g
s

K
g
,J 
o
s
k 1
1
ps  pok
Empirical distribution
distance

 N   1  2 1  w
100

Parallel Sampling

Problems with sequential sampling



Global indexing is difficult in practice
Long time for one sweep
Parallel sampling



Agents update locations in parallel by sampling local
characteristics
Conflicts could be solved by coin-toss.
Simulation showed the MAS achieve global objective with only
local strategies.
Stochastic Path Planning Simulation

Parallel stochastic path exploration based on MRF can
get around the local minima

Potential function
 s x   g J sg  o J so  n J sn
Target (attraction) potential Jg
 Neighbor (avoidance) potential
Jn


Obstacle potential Jo
Simulation : Gathering

Potential function
ˆ  x , {x : k ' N }

k
k
k'
k


2

, if N k  0

1
 1 xk  z0   
x  xk '
 k 'N k k

, if N k  0

The first term attracts nodes close to z0
The second term tends to cluster nodes
Simulation: Gathering
specified center Z0=(25,25)


unspecified center
200 nodes on 50 by 50 grid；1= 0.05 , 2 =1,  =103
Rm=22, Rs=62 ； T(n)=1/(4log(400+n))
Simulation: Line Formation

Potential function
ˆ k  xk , {xk ' : k ' N k }



  mk







k 'N k


d k ,k '
2
1  sin  k ,k '  if mk  0
Rs

, if mk  0
 is scaling factor
 is a penalization for node with no neighbor
mk is the number of neighboring nodes of node k
k,k’ is the desired angle of the line segment
dk,k’ /Rs puts more weight on farther neighbors, which
encourages the formation of long lines
Simulation: Line Formation
One line
Three lines




Two lines

200 nodes on 50 by 50 grid
=10 , =5
Rm=2 2
Rs=102, 62, 42
T(n)=1/(4log(400+n))
A Hybrid Control Scheme

Deterministic potential approach



Stochastic approach based on MRF



Pro: Save traveling time
Con: May be get trapped by some obstacles
Pro: Trouble free. Converge to global minimum for sure.
Con: Waste time for path exploration
Hybrid control scheme combines both advantages and
may strike the right balance
Hybrid Scheme Algorithm

Step 1. Each vehicle (node) starts
with the deterministic gradient-flow
method and goes to Step2

Step 2. If a vehicle stops moving for
d consecutive time instants and its
location is not within the target area,
then it switches to the simulated
annealing method with a
predetermined cooling schedule

Step 3. After performing simulated
annealing for N time instants, the
vehicle switches to the gradient
method and goes to Step 2
Impact of Memory

Hybrid scheme with memory


Experience can help vehicle to learn the complex environments
better and thus change its behavior to achieve better performance.
Implementation: when a vehicle determines it is trapped , it
increases the risk level R of that spot, and does local sampling as
follows
P  xs  l  
e
 s l 

T (n)
e
zLs
Rls
s z 

T (n)
Rzs
Impact of Memory (cont.)

Hybrid scheme with memory
Autonomic Wireless Networks
● Wireless networks, such as mobile ad hoc networks
(MANET) and sensor networks:





No trusted centralized authority
Resource (power, bandwidth, computation etc.) constraints
Rapidly and dynamically changing topology and connectivity
Uncertainty & incompleteness of trust evidence: trust values in [-1, 1]
Distributed trust computation and locality of trust information
exchanges
● Unique properties
 Each node is its own authority and it is selfish
 Networking functions (route discovery, packet forwarding and etc. )
rely on cooperation between nodes
 Cooperation utilizes local information and local interactions (between
neighbors)
Cooperation and Games
● In distributed wireless networks




Cooperation is restricted to only local interactions
Decision is made by each node individually
Nodes are self-interested
Explain and analyze emergent properties
● Game theoretic methods




Provide a framework for modeling individual interactions
Understand complex global structures and dynamics of a system
composed of a large number of agents with simple local interactions
Guide for analytical approach
Examples: Ising model, prisoner’s dilemma
● Goal: how to encourage nodes to collaborate in games?

Incentive: trust systems to promote cooperation and circumvent
misbehaving nodes.
A Simple Distributed Trust
Computation Policy


Based on simple voting methods
Voters:



Nodes that qualified as legitimate voters by certificates signed by
offline servers (have trust evidence about node i)
Assume uniformly distributed in the network
Policy: decision based on threshold

 trusted, if Vi   Ni
Node i is 

neutral, if Vi   Ni



Vi is the total number of votes node i received (signed sum)
 is the decision threshold
| Ni | is the number of i’s neighbors
Simple Voting Scheme
Trusted nodes
Neutral nodes
Positive votes
Negative votes




Number of positive votes on node i: Vp,i = 3
Number of negative votes on node i: Vn,i = 1
Effective votes: Vi = Vp,i - Vn,i= 2
Given η = 0.3, Vi > η|Ni| = 1.8, node i is designated “trusted”
Trust Dynamics
• Trust spreading
Initial “islands” of trusts
Trust spreads
Trust-connected network
● Trust revocation:
 Changes in topology, membership, secure paths
 Referees of a node may change, trust evidence for a node may change
 Votes timeout or negative votes
Trust Graph

Trust graph: GT(VT, ET)




Induced subgraph of G(V, E) by VT
VT is the set of nodes which are
designated “trusted” by the trust
computation algorithm
ET = {e | e in E and both ends of e are
in VT}
Trust metric Psp: percentage of trusted pairs that are
connected by one or more secure paths, which are
composed of trusted nodes
NP
Psp 


secure
N T (N T -1)/2
NPsecure is the number of trusted pairs that are connected by one
or more secure paths.
It is dependent of the cluster size and connectivity of GT
Random Graph Model
Erdos and Renyi random graphs (ER model)


Simulation results of Psp as
function of decision threshold η
When η is small
 Most of nodes are considered
to be trusted
 Psp is dominated by the edge
present probability p in ER
random graphs
 Zero-one law in random graph
theory is present
Increasing the threshold η
results in
 Reducing the number of
trusted nodes
 Increasing critical values
 Smaller Psp
Small-world Networks
Psp vs. η after one iteration


Psp vs. η in steady states
Number of trusted paths increases as trust spreads with each iteration
Different curves are with different rewiring probability Prw
Prw= 0 represents a regular lattice

Prw = 1 converges to a random graph
Observe the transition from lattices to random graphs

With a relative small portion of shortcuts, small-world networks
facilitate the formation of secure paths



The effects of topology are obvious, so any distributed trust computation model
should take into account the topology properties
Trust Revocation

The trust revocation process is initiated:




when topology, membership or secure paths change
when referees or trust evidence for a node changes
when positive votes are timeout or new negative votes are received
Decision policy of the revocation process



Revocation on a specific node, say B,
usually starts from few nodes that have
negative observations on B;
A node A accepts the revocation on B, if it
finds that more than a threshold fraction
Φ of its neighbors revoke node B;
Question: can a revocation be accepted
by a large fraction of nodes in the
network?
A
Trust
Revoke
Phase Transition of
Revocation



Revocation is launched from a randomly chosen node in an ErdösRényi random graph with average degree set as the Y-axis.
Global cascade: area that lie inside of the contour represents the
percentage of nodes, which accept the revocation, is greater than
the value corresponding to the contour (level surfaces of histogram)
Phase transitions happen suddenly: the steep of the contours is
very sharp, which represents phase transitions
Previous Work

Decentralized path-inference protocols



Local interaction




Combination of trust along and across paths (Beth,1994)
Probability of finding a trust path from source to target (Maurer,
1996)
EigenTrust (Kamvar, 2003)
PeerTrust (Xiong, 2004)
Bayesian methods (Buchegger, 2003)
Our work is similar with EigenTrust and PeerTrust,
which provided promising results.



However, results of EigenTrust and PeerTrust are all based on
simulations.
We analyze our local interaction rule using graph theory.
We also provide a theoretical justification for network management
that facilitates trust propagation.
Voting Scheme

Voting rule:


ti is the trust value of node i

v ji is the voting value of node j about node i

Local voting rule
t i  f (v ji , t j , j  Ni , t j  0)

Function f should satisfy the following properties:
 The range of f is [-1,1].
 Votes from neighbors with higher trust value are more credible,
so they should carry larger weights.
Policy: threshold rule for trustworthiness of the target agent
trusted, if ti  
Node i is 
neutral, if ti  
where  is the threshold, which is a constant
Simple Voting Rule

We use the weighted average as the voting rule, where
weights are trust values of voters
1
t i (n ) 
di




 t (n  1)v
j Ni
t j 0
j
ji
(n )
di  | Ni | is the degree of node i
n represents discrete time
Assume v ji is a constant, i.e. it doesn’t change with time, which is
true when considering the steady state
The voting rule can be written in system equation
T (n )  D1VT (n  1),
where D = diag[d1 ,d2 ,…, dN], T is a vector representing
trust values of all nodes and V is the matrix for votes
Convergence of Simple
Voting Rule

Voting without uncertainty



For each pair (i, j) , if i and j are neighbors, then vij = 1.
V = A, where A is the adjacency matrix of graph G, and D-1A is a
stochastic matrix with the largest eigenvalue being 1.
Let  be the right eigenvector of D-1A corresponding to eigenvalue 1.
(D1A)n  [ , , , ]', as n  ,
N
then
N


If
i V , ti  lim ti (n )    T (0)    j t j (0).
n 
j 1
  t (0)   , all nodes are trusted, and none is trusted otherwise.
j 1
j j
The initial trust values are very crucial.
Voting with uncertainty


vij ≤ 1, D-1A is a semi-stochastic matrix.
We proved (D1A)n  0, as n  , so T0. Trust cannot be
established at all!!!
Voting with Headers

We have shown that using the simple voting scheme,
trust can only be established under certain strict
conditions:

All votes value are 1 and the initial configuration must satisfy
N
 t (0)  .
j 1


j j
A single vote with value less than 1 will result in failure of trust
establishment.
We introduce the notion of headers



Headers are pre-trusted agents and only vote for nodes that they
fully trust.
If node i is trusted with bi headers, it will get bi more votes with
value 1. Let B = diag[b1 , b2 ,…, bN ].
The system equation changes to


T (n )  (D  B)1 VT (n  1)  B1 .
Convergence of Voting
with Headers

Voting without uncertainty

V = A, and define
T (n )  1  T (n ). The
system equation changes to
T (n )  (D  B )1 AT (n  1).


If there is at least one node i such that bi > 0, (D+B)-1A goes to 0.
Therefore T(n)  1 and all nodes are trusted.
Voting with uncertainty



Using the same technique as above, let T (n )  ξ  T (n ) . We are
able to find the condition such that T (n )  ξ.
If we let ξ   1 , then all nodes are trusted.
Theorem: Given the threshold is η , the number of headers for each

node must satisfy
B1 
(D  V )1.
1 

This theorem proves, as well as provides, a network design method to
establish a fully trusted network by introducing headers
Spreading Speed and Topology


The time for updating rule to reach the steady state, i.e.,
how fast the trust values converge.
Perron-Frobenius Theorem in algebraic graph theory:
For a stochastic matrix A
n
m2 1
n
n
T
A  1 v1u1  O(n
2 ).
1 is the largest eigenvalue of A, which is 1 and

is2the



second largest eigenvalue of A.
n
The convergence rate of An is of order 2 .
Normalized adjacency matrices are stochastic matrices,
therefore those with smaller 2 converge faster.
What kind of networks or which network topology has
smaller second largest eigenvalue 2 n ?
Spreading Speed and
Topology (cont’)

We consider the small-world model proposed by Watts
and Strogatz in 1998



High clustering coefficient and small average graphical distance
between any pair.
We use Φ-model, which is modeled by adding small number of
new edges into a regular lattice.
Adding just 1% more edges, spreading finishes in 10 times less rounds.
Ising and Spin Glass Models
● Statistical Physics models for magnetization



Orientation of each particle’s spin
depends on its neighbors
Ising Model: behavior of simple magnets
Spin Glass Model: complex materials
● Math interpretation:
 s = {s1, s2,…, sn} is a configuration of n
particle spins, where sj = 1 or -1 , spin j
is up or down
 Hamiltonian, or Energy for configuration s
H (s)  
1
mH
J
s
s

 ij i j T
T iV
– Ising Model: Jij = J for all i, j
jNi
– Spin Glass Model: Jij depend on i,j and can be random processes
s
i
i
Ising/SG Models and Games
●
Ising and Spin Glass models can be interpreted as dynamic (repeated)
games: each particle selects its own spin to maximize its own payoff
 i  (  J ij si s j ) / T
jNi


●

High T, conservative agents, not willing to change, small payoffs

Low T, aggressive agents, larger payoffs
Collection of local decisions reduces the total energy of the interacting particles
Statistical Mechanics primary object of interest


●
Ising model (Jij = J) : align its spin with the majority of neighbors spin
P( s)  (e (1/ T ) H ) / Z
Recent excitement: computation of ground state, partition function Z, NP - complete,
Replica Method
[log Z ]  lim  ([ Z n ]  1) / n
n
Application to: turbocodes, image restoration, neural networks, learning, associative
memory, SAT, knapsack, SA, number parttioning, graph partitioning, CDMA, MIMO, …
Inspires an approach where trust is used as an incentive for cooperation



si represents whether node i cooperates or not with neighbors
Jij can be interpreted as the worth of player j to player i
Cooperate or not based on benefit from cooperation and trust values of neighbors
Spin Glass Cooperative Game
● Spin Glass model as a cooperative game (spin glass game)
In  i  (


i , jNi
w ss ,
J ij si s j ) / T 
jNi
ij i
j
the weights wij frustrate the system
Both positive and negative local feedback (e.g. wij{-1, 1})
Interaction topology (i.e. the matrix J = [Jij] ) moderates effects pos. and neg. fback
S  N = {1, 2, …, N} is a coalition, in which all nodes cooperate
v(S) : value of characteristic function of the game , v: 2NR; maximum payoff S
can get without cooperation from other nodes N /S.




Γ =(N, v)
J21
2
6
v( S ) 
J
i , jS
ij


iS , jS
J ij
J12
5
3
1
J34
J14
J41

4
J43
Subset S={1,2,3,4}
v(S)=J12+J21+J14+J41+J43+J34 -J36 -J15
Model can be used to find what form or policy for Jij can induce all (or most)
nodes to cooperate: maximize the coalition
Cooperative Games and
Dynamic Coalitions
● Have a number of players, some can be coalitions themselves
● How do they negotiate an “acceptable” DC security policies set?
● What are the properties of the final result: “the negotiated policy set”?
● Is there an efficient scheme that gets us there?
● Cooperative games allow us to set up different types of games between
the players, examine different concepts of solutions and values
● Can prove mathematically properties of the solution and value: e.g.
minimizes maximum dissatisfaction, is anonymous, is stable
● Can get iterative methods to get to solution (negotiation schema), can
use all kinds of constraints, invariance to aV + b scaling (preferences)
● Working on extensions to partial information, learning, robustness
to uncertainties
Spin Glass Cooperative
Game Properties
● Spin Glass game is a convex and superadditive game iff (net pos. effects)
i, j , J ij  J ji  0
● Shapley value :
 (v ) i 

N
in the core
J ij
j
● Not well understood in the regime of both negative and positive net effects
● Effects of interaction matrix structure (sparsity, neighborhood structure,
range of interactions, strength of interactions) not well understood;
Topology effects in network analog
● Oriented Spin Glass Game Γ(N,v) where v now depends on both an
interaction matrix J and a preference vector L ; a pair of char. fcns
v ( S ) 
J
i , jS
ij


iS , jS
J ij   Li
iS
● Replica method can be used to analyze various problems under various
models and constraints on J and L
Cooperative Games
with Negotiation
● Consider Γ = (N, v), N as before but with
v (S ) 
S x
i , j
● Γ = (N, v) convex, superadditive, if i, j , xij  x ji  0
● Theorem : Γ = (N, v) has a nonempty core. The payoff
ij
allocation to node i , xˆi   jN xˆij ( xˆij  0 and xˆ ji  0)
i
is in the core. Compute ( xˆij , xˆ ji ) as follows
 xij ,
if xij  0, x ji  0

ˆxij   xij  ij x ji , if xij  0, x ji  0
(1   ) x , if x  0, x  0
ij
ij
ij
ji

with 0  ij = ji  1


This payoff allocation indicates a way to encourage cooperation
Players with positive gain can negotiate with their neighbors by
sacrificing certain gain (offering their partial gain ijxji )
Trust as Mechanism to
Induce Collaboration
● Trust is an incentive for collaboration
 Nodes who refrain from cooperation get lower trust values
 They will be eventually penalized because other nodes tend to only
cooperate with highly trusted ones.
● Assume, for node i, that the loss for not cooperating with
node j is a nondecreasing function of xji as f (xji), and the new
characteristic function is
v(S ) 
S x
i , j
● Theorem : if
xi   jN xij
i

ij


S
S
i , j
f ( xij )
 i, j, xij  f ( x ji )  0 , the core is nonempty and
is a feasible payoff allocation in the core.
By introducing a trust mechanism, all nodes are induced to collaborate
without any negotiation
Dynamics of Cooperation
● System model
Two linked dynamics
• Trust propagation
• Game evolution
● The network is modeled as a discrete-time system
j all neighbors of i
vij trust value node i
votes for node j
Game Evolution
● Strategy of node i:  ij {0,1}, j  Ni
 γij= 1 (= 0) represents that i cooperates (does not cooperate) with
its neighbor j
● Payoff for node i when interacting with j: xij = Jij γij γji
 xij > 0 (< 0) positive link (negative link)
 Node selfishness  cooperate with neighbors on positive links
● Strategy updates: node i chooses γij= 1 only if all of the
following are satisfied:



Neighbor j has not been revoked
Neighbor j is cooperative
xij > 0, or the cumulative payoff of i is less than the case when it
unconditionally conducts γij= 1.
● Trust propagation:
 The threshold is chosen to ensure global revocation propagation
 Reestablishing period τ : once a node is revoked, in order to reestablish
trust the revocation has to be nullified for τ consecutive time steps
Results of Game Evolution
● Theorem:
i  N i and xi   jN xij , there exists τ0, such that for
a reestablishing period τ > τ0


i
The iterated game converges to Nash equilibrium;
In the Nash equilibrium, all nodes cooperate with all their neighbors.
● Comparison of games with (without) trust mechanism, strategy update:
Percentage of cooperating pairs vs negative links
Average payoffs vs negative links
Conclusions and Future Research









A stochastic potential based approach guarantees global objective can be
achieved by simple local strategies
The parallel sampling algorithm saves running time compared with the
sequential sampling algorithm
Emergent behaviors of self-organized swarms are observed in simulations
A hybrid scheme is proposed to achieve better performance by combining
deterministic gradient-flow approach and stochastic potential based
approach
Convergence study of the distributed parallel algorithm
Tighter convergence rate bound estimation and parameters estimation of
the hybrid scheme
Cooperative learning to further improve the performance of the hybrid
scheme
Convergence analysis when only partially observed potential functions
available due to imperfect sensors
Schedule of measurements due to sensor power constraints
Conclusions and Future Research
● Analyzed and evaluated fundamental methods to induce collaboration
●
●
●
●
●
●
●
in wireless networks with mobile nodes
Focused on distributed schemes using only local interactions
Developed and analyzed a cooperative game framework and showed
that negotiation between agents can induce collaboration
We developed a distributed trust establishment, propagation and
maintenance scheme for such networks and showed that it can also
induce collaboration
Showed that trust propagation displays phase transitions
Investigated the linked dynamics of trust propagation and game
evolution and showed the benefits in inducing collaboration
Methods inspired from statistical physics of spin glasses
Future directions include analysis of networks with dynamic
topologies, robustness of these collaboration inducing mechanisms,
identification of parameters (including topology types) that influence
the dynamics and qualities of collaborative behavior
Publications
 Tao Jiang and John S. Baras, “Ant-based Adaptive Trust Evidence Distribution in MANET”,
Proceedings of 2nd International Workshop on Mobile Distributed Computing, in conjunction
with the Intern. Conference on Distributed Computing Systems, Tokyo, Japan, March 2004.
 John S. Baras and Tao Jiang, “Dynamic and Distributed Trust for Mobile Ad-Hoc
Networks”, Proceedings of 24th Army Science Conference, Orlando, Florida, December 2004.
 John S. Baras and Tao Jiang, “Cooperative Games, Phase Transitions on Graphs and
Distributed Trust In MANET”, invited paper, Proceedings 2004 IEEE Conference on Decision
and Control, December 2004, Bahamas.
 John S. Baras and Tao Jiang, “Managing Trust in Self-organized Mobile Adhoc Networks”,
invited paper, Wireless and Mobile Security Workshop, Network and Distributed Systems
Security Symposium, February 2005, San Diego, USA.
 Tao Jiang and John S. Baras, “Autonomous Trust Establishment”, 2nd International Network
Optimization Conference (INOC), February 2005, Lisbon, Portugal.
 John S. Baras and Tao Jiang, “Cooperation, Trust and Games in Wireless Networks”,
invited paper, in Proceedings of Symposium on Systems, Control and Networks, honoring
Professor P. Varaiya, Birkhauser, June 2005.

Tao Jiang and John S. Baras, “Graph Algebraic Interpretation of Trust Establishment in
Autonomic Networks”, submitted to Wiley Journal of Networks (special issue)
Publications

J.S. Baras, X. Tan and P. Hovareshti, Decentralized Control of Autonomous Vehicles,” in
Proc. of 42nd IEEE Conference on Decision and Control, Hawai, Dec 2003.

W. Xi, X. Tan, and J. S. Baras, “A stochastic algorithm for self-organization of
autonomous swarms,” to appear in Proc. 44th IEEE Conference on Decision and Control.

J. S. Baras and X. Tan, “Control of autonomous swarms using Gibbs sampling,” in
Proceedings of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise
Island, Bahamas, 2004, pp. 4752–4757.

W. Xi, X. Tan, and J. S. Baras, “Gibbs sampler-based path planning for autonomous
vehicles: Convergence analysis,” in Proceedings of the 16th IFAC World Congress,
Prague, Czech Republic, 2005.

[4]W.Xi, X. Tan, and J.S. Baras, “A hybrid scheme for distributed control of autonomous
swarms,” 2005, in Proc. of 24th American Control Conference.