Results 1  10
of
60
Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
, 2002
"... In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the a ..."
Abstract

Cited by 604 (44 self)
 Add to MetaCart
In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its \neighbors." In their paper, Vicsek et. al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models.
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
Abstract

Cited by 435 (13 self)
 Add to MetaCart
In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader determination) for groups of discretetime agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing averageconsensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
Abstract

Cited by 116 (21 self)
 Add to MetaCart
The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
Control Using LogicBased Switching
 Trends in Control: A European Perspective
, 1998
"... this paper is to give a brief tutorial review of four different classes of hybrid systems of this type  each consists of a continuoustime process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic. Three of the logics, called prerouted switching, ..."
Abstract

Cited by 67 (19 self)
 Add to MetaCart
this paper is to give a brief tutorial review of four different classes of hybrid systems of this type  each consists of a continuoustime process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic. Three of the logics, called prerouted switching, hysteresis switching and dwelltime switching respectively, are simple strategies capable of determining in real time which candidate controller should be put in feedback with a process in order to achieve desired closedloop performance. The fourth, called cyclic switching, has been devised to solve the longstanding stabilizability problem which arises in the synthesis of identifierbased adaptive controllers because of the existence of points in parameter space where the estimated model upon which certainty equivalence synthesis is based, loses stabilizability
The Lyapunov exponent and joint spectral radius of pairs of matrices are hard  when not impossible  to compute and to approximate
, 1997
"... We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities  the lower spectral radius and th ..."
Abstract

Cited by 61 (18 self)
 Add to MetaCart
We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities  the lower spectral radius and the largest Lyapunov exponent  are not algorithmically approximable.
The Boundedness of All Products of a Pair of Matrices is Undecidable
, 2000
"... We show that the boundedness of the set of all products of a given pair Sigma of rational matrices is undecidable. Furthermore, we show that the joint (or generalized) spectral radius #(#) is not computable because testing whether #(#)61 is an undecidable problem. As a consequence, the robust stabil ..."
Abstract

Cited by 48 (15 self)
 Add to MetaCart
We show that the boundedness of the set of all products of a given pair Sigma of rational matrices is undecidable. Furthermore, we show that the joint (or generalized) spectral radius #(#) is not computable because testing whether #(#)61 is an undecidable problem. As a consequence, the robust stability of linear systems under timevarying perturbations is undecidable, and the same is true for the stability of a simple class of hybrid systems. We also discuss some connections with the socalled "finiteness conjecture". Our results are based on a simple reduction from the emptiness problem for probabilistic finite automata, which is known to be undecidable.
Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
 J. of the American Mathematical Society
, 2001
"... A topical map is a map from Rn into itself verifying some conditions (see §1.2) and which, roughly speaking, behaves like a translation along some line, the amount of which is measured by a real number, called the average height (or average displacement) of the map. Then we look at a topical Iterate ..."
Abstract

Cited by 36 (3 self)
 Add to MetaCart
A topical map is a map from Rn into itself verifying some conditions (see §1.2) and which, roughly speaking, behaves like a translation along some line, the amount of which is measured by a real number, called the average height (or average displacement) of the map. Then we look at a topical Iterated Function System (IFS),
Complexity of Stability and Controllability of Elementary Hybrid Systems
, 1997
"... this paper, weconsider simple classes of nonlinear systems and provethatbasic questions related to their stabilityandcontrollabilityare either undecidable or computationally intractable (NPhard). As a special case, weconsider a class of hybrid systems in which the state space is partitioned into tw ..."
Abstract

Cited by 34 (10 self)
 Add to MetaCart
this paper, weconsider simple classes of nonlinear systems and provethatbasic questions related to their stabilityandcontrollabilityare either undecidable or computationally intractable (NPhard). As a special case, weconsider a class of hybrid systems in which the state space is partitioned into two halfspaces, and the dynamics in eachhalfspace correspond to a differentlinear system
An Elementary Counterexample to the Finiteness Conjecture
 SIAM JOURNAL ON MATRIX ANALYSIS
, 2001
"... ..."
On Codes That Avoid Specified Differences
 IEEE Transactions on Information Theory
, 2001
"... Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spec ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.