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 toThanks 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)

OutlineOutline Autonomous collaborating vehicles

A stochastic approach based on MRF Analysis

Convergence study of a simple case Convergence speed analysis

Simulation results A hybrid scheme to improve the performance

Distributed trust in MANET Trust (and Mistrust) spreading and dynamics Effects of topology on convergence Spin glasses and cooperative games Collaboration via trust schemes

Conclusions and future work

Mission Autonomous, distributed maneuvering of a vehicle group to reach

and cover a target area

Constraints Desired inter-vehicle distance Obstacles avoidance Threats (stationary or moving) avoidance

Requirement Using only local or static information

A Battlefield ScenarioA Battlefield Scenario

Review of Deterministic Review of Deterministic Gradient-Flow ApproachGradient-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:

Target (attraction) potential Jg

Neighbor (avoidance) potential Jn

Obstacle potential Jo Potential Js due to stationary threats Potential Jm due to moving threats

, ,( ) ( ) ( ) ( ) ( ) ( ) g n o s mi t i g i n i t i o i s i m t iJ q J q J q J q J q J q

Gradient flow:

, ( )( )

i t i

ii

J qq t

q

Being Trapped by Local MinimaBeing Trapped by Local Minima

Different initial conditions may cause vehicles to be trapped by local minimum

Markov Random FieldsMarkov Random Fields

Markov Random Fields (MRF) A collection of random variables X={Xs}, s S∈ with discrete values i

n phase space s

A neighborhood system on S is a family N = {Ns}, s S, ∈ where Ns S,⊂ and r N∈ s ↔ s N∈ r

The marginal probability depends only on neighbor’s phase value

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

)|()|( )()(\\ sNsNsssSsSss xXxXPxXxXP

Cc

c xxU )()(

Gibbs Sampler and Gibbs Gibbs Sampler and Gibbs DistributionDistribution

Gibbs distribution (global description) The marginal probability is function of local potentials

Gibbs distribution is function of global potentials

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 glo

bal minimum with probability 1

sCc

sNc

sCcsNc

sS

sSs

Txx

Txx

TxU

TxxU

sNsNss

e

e

e

exXxXP

/),(

/),(

/),(

/),(

)()()(

)(

\

\

)|(

Z

exXP

TxU /)(

)(

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 mo

ve, which defines the phase space s Gibbs potential is designed to reflect glob

al objective

Obstacle

Agents

target

Modeling a Swarm as a GFModeling a Swarm as a GF 2D mission space on discrete lattice cells

Difficulties in applying classical results Non-stationary neighborhood system Time-varying and state-dependent phase space

( )

( ) ( ),

( ) ( , )s

cc C

s c s N sc C

g o ng s o s n s

U x x

x x x

J J J

Gibbs Sampler Based AlgorithmGibbs Sampler Based Algorithm

Algorithm for single vehicle Step1. Pick a cooling schedule T(n) and the total number N of a

nnealing steps Step2. At each annealing step n, conduct a location update for th

e vehicle by performing the following: Determine the set L of candidate locations for the next move For each l L∈ , evaluate

Update location by sampling above distribution Step 3. Let n = n+1. If n = N, stop; otherwise go to step 2

}:{ mRxllL

Ll

nT

l

nT

l

e

exnXlnXp

'

)(

)(

)(

)'()(|)1(

Convergence StudyConvergence Study

Single vehicle with limited sensing and moving range Fixed temperature

Assume accessible area is connected Unique stationary distribution

where

From any distribution v,

Simulated annealing

Cooling schedule

Let Qn = (PT(n))τ where

m

U x U z

T T

z x R

TT

e e

xZ

Xx Rxz

T

zU

T

xU

T

m

eeZ

))}((min)(:{ zUxUxMXz

n

nTln

Tn

Tn

vP

lim

Mxif

MxifMQvQ n

n 0

1

...lim 1

Convergence rate of a single vehicle case For the single-vehicle case, the convergence rate is characterized by

where Using convergence rate bound as a design indicator

Design λg*

to maximize the convergence rate

Potential function

Empirical distributiondistance

Convergence Rate StudyConvergence Rate Study

m

m

n nOQvQ ~2

~2

1...

myUmmxy

min~

K

kok

s

os

gs

gs

ppJppJ

1

1 ,

100121

wN

Parallel SamplingParallel 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.

Parallel stochastic path exploration based on MRF can get around the local minima

Stochastic Path Planning SimulationStochastic Path Planning Simulation

Potential function

Target (attraction) potential Jg

Neighbor (avoidance) potential Jn

Obstacle potential Jo

nsn

oso

gsgs JJJx

Simulation : GatheringSimulation : Gathering

Potential function

The first term attracts nodes close to z0

The second term tends to cluster nodes

0 ,

0 ,1

}':{,ˆ

' '

2

01

'

k

k

Nk kkk

kkkk

Nif

Nif

xxzx

Nkxx

k

Simulation: GatheringSimulation: Gathering

200 nodes on 50 by 50 grid ； 1= 0.05 , 2 =1, =103

Rm=22, Rs=62 ； T(n)=1/(4log(400+n))

specified center Z0=(25,25) unspecified center

Simulation: Line FormationSimulation: Line Formation

Potential function

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 encour

ages the formation of long lines

0 ,

0 sin1

}':{,ˆ

'

2

',',

'

k

Nk kkks

kk

k

kkkk

mif

mifR

d

m

Nkxx

k

Simulation: Line FormationSimulation: Line Formation

200 nodes on 50 by 50 grid =10 , =5 Rm=2 2 Rs=102, 62, 42 T(n)=1/(4log(400+n))

One line

Two lines

Three lines

A Hybrid Control SchemeA Hybrid Control Scheme

Deterministic potential approach Pro: Save traveling time Con: May be get trapped by some obstacles

Stochastic approach based on MRF 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 AlgorithmHybrid 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 MemoryImpact 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

s

s

s

Lz

sz

nT

z

sl

nT

l

s

Re

RelxP

)(

)(

Impact of Memory (cont.)Impact of Memory (cont.)

Hybrid scheme with memory

Autonomic Wireless Autonomic Wireless NetworksNetworks

● 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 exchan

ges

● 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 GamesCooperation 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 comp

osed 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 A Simple Distributed Trust Trust Computation PolicyComputation Policy Based on simple voting methods

Voters: Nodes that qualified as legitimate voters by certificates signed by offli

ne servers (have trust evidence about node i) Assume uniformly distributed in the network

Policy: decision based on threshold

is the total number of votes node i received (signed sum) is the decision threshold is the number of i’s neighbors

iV

| |iN

trusted, if Node is

neutral, if

i i

i i

V Ni

V N

Simple Voting SchemeSimple Voting Scheme

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”

Trusted nodes

Neutral nodes

Positive votes

Negative votes

Trust DynamicsTrust Dynamics

Initial “islands” of trusts

Trust spreads

Trust-connected network

• Trust spreading

● 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 GraphTrust 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}

secure

T TN (N -1)/2sp

NPP

Trust metric Psp: percentage of trusted pairs that are connected by one or more secure paths, which are composed of trusted nodes

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 ModelRandom 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 t

o be trusted Psp is dominated by the edge p

resent 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 truste

d nodes Increasing critical values Smaller Psp

Small-world NetworksSmall-world Networks

Psp vs. η after one iteration 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 t

he formation of secure paths The effects of topology are obvious, so any distributed trust computation model s

hould take into account the topology properties

Psp vs. η in steady states

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?

Trust RevocationTrust 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

Trust

Revoke

A

Phase Transition of Phase Transition of RevocationRevocation

Revocation is launched from a randomly chosen node in an Erdös-Rényi 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 WorkPrevious Work Decentralized path-inference protocols

Combination of trust along and across paths (Beth,1994) Probability of finding a trust path from source to target (Maurer, 1996)

Local interaction 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 SchemeVoting Scheme Voting rule:

is the trust value of node i is the voting value of node j about node i Local voting rule

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

where is the threshold, which is a constant

trusted, if Node is

neutral, if i

i

ti

t

it

jiv

( , , , 0)i ji j i jt f v t j N t

Simple Voting RuleSimple Voting Rule We use the weighted average as the voting rule, where

weights are trust values of voters

is the degree of node i n represents discrete time Assume 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

where D = diag[d1 ,d2 ,…, dN], T is a vector representing trust values of all nodes and V is the matrix for votes

0

1( ) ( 1) ( )

i

j

i j jij Nit

t n t n v nd

| |i id N

jiv

1( ) ( 1),T n D VT n

Convergence of Simple Convergence of Simple Voting RuleVoting 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.

then

If , all nodes are trusted, and none is trusted otherwise.

The initial trust values are very crucial. Voting with uncertainty

vij ≤ 1, D-1A is a semi-stochastic matrix. We proved , so T0. Trust cannot be

established at all!!!

1( ) [ , , , ] ', as ,nD A n

1

, lim ( ) (0) (0).N

i i j jnj

i V t t n T t

1

(0)N

j jj

t

1( ) 0, asnD A n

Voting with HeadersVoting 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

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

1

(0) .N

j jj

t

1( ) ( ) ( 1) .T n D B VT n B 1

Convergence of Voting Convergence of Voting with Headerswith Headers

Voting without uncertainty V = A, and define . The system equation changes to

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 . We are

able to find the condition such that If we let , then all nodes are trusted. Theorem: Given the threshold is η , the number of headers for each

node must satisfy

This theorem proves, as well as provides, a network design method to establish a fully trusted network by introducing headers

( ) ( )T n T n 1

1( ) ( ) ( 1).T n D B AT n

( ) ( )T n T n ξ

( ) .T n ξ

ξ 1

( ) .1

B D V

1 1

Spreading Speed and Spreading Speed and TopologyTopology

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

is the largest eigenvalue of A, which is 1 and is the second largest eigenvalue of A.

The convergence rate of An is of order Normalized adjacency matrices are stochastic matrices,

therefore those with smaller converge faster. What kind of networks or which network topology has

smaller second largest eigenvalue

2

1

11 1 2( ).

nmn n TA v u O n

1

2 .n

2

2

2 ?n

Spreading Speed and Spreading Speed and Topology (cont’)Topology (cont’)

Adding just 1% more edges, spreading finishes in 10 times less rounds.

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.

Ising and Spin Glass Ising and Spin Glass ModelsModels

● 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 parti

cle spins, where sj = 1 or -1 , spin j is up or down

Hamiltonian, or Energy for configuration s

1( )

i

ij i j ii V ij N

mHH J s s s

T T

s– Ising Model: Jij = J for all i, j

– Spin Glass Model: Jij depend on i,j and can be random processes

Ising/SG Models and GamesIsing/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

Ising model (Jij = J) : align its spin with the majority of neighbors spin 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 Recent excitement: computation of ground state, partition function Z, NP - complete, Re

plica Method Application to: turbocodes, image restoration, neural networks, learning, associative me

mory, 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

(1/ )( ) ( ) /T HP e Zs

( ) /i

i ij i jj N

J s s T

[log ] lim ([ ] 1) /n

nZ Z n

Spin Glass Cooperative Spin Glass Cooperative GameGame

● Spin Glass model as a cooperative game (spin glass game) In , 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: 2NR; maximum payoff S

can get without cooperation from other nodes N /S.

Model can be used to find what form or policy for Jij can induce all (or most) nodes to cooperate: maximize the coalition

,

( ) /i i

i ij i j ij i ji j N j N

J s s T w s s

Subset S={1,2,3,4}

v(S)=J12+J21+J14+J41+J43+J34 -J36 -J154

6

5 1

2

3J12

J21

J14

J41

J34

J43

Γ =(N, v)

, ,

( ) ij iji j S i S j S

v S J J

Cooperative Games Cooperative Games and and Dynamic CoalitionsDynamic 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 Spin Glass Cooperative Game PropertiesGame Properties

● Spin Glass game is a convex and superadditive game iff (net pos. effects)

● Shapley value : in the core

● 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

● Replica method can be used to analyze various problems under various models and constraints on J and L

( )i ijj

v J

N

, , 0 ij jii j J J

, ,

( ) ij ij ii j S i S j S i S

v S J J L

Cooperative Games Cooperative Games with Negotiationwith Negotiation

● Consider Γ = (N, v), N as before but with ● Γ = (N, v) convex, superadditive, if ● Theorem : Γ = (N, v) has a nonempty core. The payoff

allocation to node i , is in the core. Compute as follows

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 )

,

( ) iji j

v x

S

S

, , 0ij jii j x x

ˆ ˆi

i ijj Nx x

, if 0, 0

ˆ , if 0, 0

(1 ) , if 0, 0

0 = 1

ij ij ji

ij ij ij ji ij ji

ij ij ij ji

ij ji

x x x

x x x x x

x x x

with

ˆ ˆ( 0 and 0)ij jix x ˆ ˆ( , )ij jix x

Trust as Trust as Mechanism to Mechanism to Induce Induce CollaborationCollaboration● 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

● Theorem : if , 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

, ,

( ) ( )S S S

S ij iji j i j

v x f x

, , ( ) 0ij jii j x f x

ii ijj N

x x

Dynamics of CooperationDynamics of Cooperation

● The network is modeled as a discrete-time system

● System model

Two linked dynamics

• Trust propagation

• Game evolution

j all neighbors of i

vij trust value node i

votes for node j

Game EvolutionGame Evolution● Strategy of node i:

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

{0,1},ij ij N

Results of Game EvolutionResults of Game Evolution

● Theorem: , there exists τ0, such that for a reestablishing period τ > τ0

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:

and i

i i ijj Ni N x x

Percentage of cooperating pairs vs negative links Average payoffs vs negative links

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 ResearchConclusions and Future Research

Conclusions and Future Conclusions and Future ResearchResearch

● 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

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)

PublicationsPublications

PublicationsPublications

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.