the consensus for discrete time linear multi agent systems under directed switching networks the existing results on the leaderless and leader following consensus problems for discrete time linear multi agent systems subject to jointly connected switching networks are limited to undirected networks this note will first study the stability property for a class of discrete time linear switched systems this stability result will then be applied to the two consensus problems for discrete time linear multi agent systems subject to directed jointly connected switching networks it is shown that in some interesting cases the two problems are solvable by the distributed state feedback control law even if the switching networks are directed and every time disconnected

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

robust consensus tracking control for multiagent systems with initial state shifts disturbances and switching topologies this paper deals with the consensus tracking control issues of multiagent systems and aims to solve them as accurately as possible over a finite time interval through an iterative learning approach based on the iterative rule distributed algorithms are proposed for every agent using its nearest neighbor knowledge for which the robustness problem is addressed against initial state shifts disturbances and switching topologies these uncertainties are dynamically changing not only along the time axis but also the iteration axis it is shown that the matrix norm conditions can be developed to achieve the convergence of the considered consensus tracking objectives for which necessary and sufficient conditions are presented in terms of linear matrix inequalities to guarantee their feasibility in the sense of the spectral norm furthermore simulation examples are given to illustrate the effectiveness and robustness of the obtained consensus tracking results

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

distributed robust consensus control of multi agent systems with heterogeneous matching uncertainties this paper considers the distributed consensus problem of linear multi agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input due to the existence of nonidentical uncertainties the multi agent systems discussed in this paper are essentially heterogeneous for the case where the communication graph is undirected and connected based on the local state information of neighboring agents a fully distributed continuous adaptive consensus protocol is designed under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set for the case where there exists a leader whose control input is unknown and bounded a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error a sufficient condition for the existence of the proposed protocols is that each agent is stabilizable

adaptive consensus of multi agents in networks with jointly connected topologies in this paper the consensus problem of multi agent following a leader is studied an adaptive design method is presented for multi agent systems with non identical unknown nonlinear dynamics and for a leader to be followed that is also nonlinear and unknown by parameterizations of unknown nonlinear dynamics of all agents a decentralized adaptive consensus algorithm is proposed in networks with jointly connected topologies by incorporating local consensus errors in addition to relative position feedback analysis of stability and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and lyapunov theory finally examples are provided to validate the theoretical results

covering problems with hard capacities we consider the classical vertex cover and set cover problems with hard capacity constraints this means that a set vertex can cover only a limited number of its elements adjacent edges and the number of available copies of each set vertex is bounded this is a natural generalization of the classical problems which also captures resource limitations in practical scenarios we obtain the following results for the unweighted vertex cover problem with hard capacities we give a 3 approximation algorithm that is based on randomized rounding with alterations we prove that the weighted version is at least as hard as the set cover problem yielding an interesting separation between the approximability of weighted and unweighted versions of a natural graph problem a logarithmic approximation factor for both the set cover and the weighted vertex cover problem with hard capacities follows from the work of wolsey combinatorica 2 1982 pp 385 393 on submodular set cover we provide here a simple and intuitive proof for this bound

tight approximation for partial vertex cover with hard capacities abstract we consider the partial vertex cover problem with hard capacity constraints partial vc hc on hypergraphs in this problem we are given a hypergraph g v e with a maximum edge size f and a covering requirement r each edge is associated with a demand and each vertex is associated with a capacity and an integral available multiplicity the objective is to compute a minimum vertex multiset such that at least r units of demand from the edges are covered by the capacities of the vertices in the multiset and the multiplicity of each vertex does not exceed its available multiplicity in this paper we present an f approximation for this problem improving over a previous result of 2 f 2 1 by cheung et al to the tight extent possible our new ingredient of this work is a generalized analysis on the extreme points of the natural lp developed from previous works and a strengthened lp lower bound obtained for the optimal solutions

an extension of the georgiou smith example boundedness and attractivity in the presence of unmodelled dynamics via nonlinear pi control abstract in this paper a nonlinear extension of the georgiou smith system is considered and robustness results are proved for a nonlinear pi controller with respect to fast parasitic first order dynamics more specifically for a perturbed nonlinear system with sector bounded nonlinearity and unknown control direction sufficient conditions for global boundedness and attractivity have been derived it is shown that the closed loop system is globally bounded and attractive if i the unmodelled dynamics are sufficiently fast and ii the pi control gain has the nussbaum function property for the case of nominally unstable systems the nussbaum property of the control gain appears to be crucial a simulation study confirms the theoretical results

adaptive coordinated tracking of multi agent systems with quantized information abstract in this paper we study the adaptive coordinated tracking problem for continuous time first order integrator systems with quantized information under switching undirected and fixed directed communication graphs respectively the combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated both the logarithmic quantizers and uniform quantizers are considered it is shown that when logarithmic quantizers are used exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter simulation examples are provided to illustrate the results

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

stability of a class of linear switching systems with applications to two consensus problems in this paper we first establish a stability result for a class of linear switched systems involving kronecker product the problem is interesting in that the system matrix does not have to be hurwitz at any time instant this class of linear switched systems arises in the control of multi agent systems under switching network topology as applications of this stability result we give the solvability conditions for both the leaderless consensus problem and the leader following consensus problem for general marginally stable linear multi agent systems under switching network topology in contrast with some existing results our results only assume that the dynamic graph is uniformly connected

continuous global stabilisation of high order time delay nonlinear systems this paper studies the global stabilisation problem for a class of high order nonlinear systems with multiple time delays a distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval by introducing the sign functions and using the generalised method of adding a power integrator this paper successfully designs a continuous global state feedback controller independent of time delays moreover a novel lyapunov krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed loop system

a descriptor approach to robust leader following output consensus of uncertain multi agent systems with delay in this technical note a descriptor approach to leader following output consensus of multi agent systems with both stationary and dynamic leaders is given in the presence of transmission delay and model uncertainty the proposed method can deal with stable and unstable agents described by general linear models to this end a new proportional derivative integral pid consensus protocol for the closed loop multi agent system is proposed under a directed graph applying this consensus protocol to the multi agent system leads to a time delay closed loop equation of neutral type to deal with the resulting neutral system a descriptor model transformation is used to derive delay dependent sufficient conditions for the existence of the consensus protocol in terms of certain linear matrix inequalities lmi the application of the proposed method is illustrated in a teleoperation system simulation results are given to show the effectiveness of the proposed approach

approximation algorithms for the partition vertex cover problem we consider a natural generalization of the partial vertex cover problem here an instance consists of a graph g v e a cost function c v z a partition p 1 p r of the edge set e and a parameter k i for each partition p i the objective is to find a minimum cost set of vertices which cover at least k i edges from the partition p i we call this the partition vc problem in this paper we give matching upper and lower bound on the approximability of this problem our algorithm is based on a novel lp relaxation for this problem this lp relaxation is obtained by adding knapsack cover inequalities to a natural lp relaxation of the problem we show that this lp has integrality gap of o log r where r is the number of sets in the partition of the edge set we also extend our result to more general settings for example we consider a problem where additionally edges have profits and we would like to pick a minimum cost set of vertices which cover edges of total profit at least i for each partition p i we call this the knapsack partition vertex cover problem we give an o log r approximation algorithm for this problem as well

locality in distributed graph algorithms this paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion the computational model is such that each node of the graph is occupied by a processor which has its own id processors are restricted to collecting data from others which are at a distance at most t away from them in t time units but are otherwise computationally unbounded this model focuses on the issue of locality in distributed processing namely to what extent a global solution to a computational problem can be obtained from locally available data three results are proved within this model a 3 coloring of an n cycle requires time omega log n this bound is tight by previous work of cole and vishkin any algorithm for coloring the d regular tree of radius r which runs for time at most 2r 3 requires at least omega sqrt d colors in an n vertex graph of largest degree delta an o delta 2 coloring may be found in time o log n

an extension of lasalle s invariance principle and its application to multi agent consensus in the paper an extension of lasalle s invariance principle to a class of switched linear systems is studied one of the motivations is the consensus problem in multi agent systems unlike most existing results in which each switching mode in the system needs to be asymptotically stable this paper allows that the switching modes are only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability is obtained then it is used to solve the consensus reaching problem of certain multi agent systems in which each agent is modeled by a double integrator and the associated interaction graph is switching and is assumed to be only jointly connected

verifying time complexity of turing machines it is undecidable whether a multi tape tm runs in time t n iff t n n 1 for t n o n log n t n n 1 it is undecidable whether a one tape tm runs in time t n for nice t n o n log n it is decidable whether a one tape tm runs in time t n we show that for all reasonable functions t n o n log n we can algorithmically verify whether a given one tape turing machine runs in time at most t n this is a tight bound on the order of growth for the function t because we prove that for t n n 1 and t n n log n there exists no algorithm that would verify whether a given one tape turing machine runs in time at most t n as opposed to one tape turing machines we show that we can verify whether a given multi tape turing machine runs in time at most t n iff t n 0 n 0 1 for some n 0 n we also prove a very general undecidability result stating that for any class of functions f that contains arbitrary large constants we cannot verify whether a given turing machine runs in time t n for some t f this is an extension of the following folkloric results we cannot verify whether a turing machine runs in constant linear or polynomial time

theory of one tape linear time turing machines a theory of one tape two way one head off line linear time turing machines is essentially different from its polynomial time counterpart since these machines are closely related to finite state automata this paper discusses structural complexity issues of one tape turing machines of various types deterministic nondeterministic reversible alternating probabilistic counting and quantum turing machines that halt in linear time where the running time of a machine is defined as the length of any longest computation path we explore structural properties of one tape linear time turing machines and clarify how the machines resources affect their computational patterns and power

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

consensus in networks of agents with unknown high frequency gain signs and switching topology the agreement control problem of single and double integrator agents with unknown and nonidentical control directions is addressed in this note under switching network topology distributed nonlinear pi control laws are proposed which ensure asymptotic consensus among the agents based on a new boundedness lemma and a generalized version of barbalat s lemma for uniformly piecewise right continuous functions theoretical results are verified by simulation studies

an np complete language accepted in linear time by a one tape turing machine we consider one tape nondeterministic turing machines i e with a unique worktape on which the input is written it is known that there are nonregular languages accepted by such machines in time o n log log n and an np complete language accepted in time o n log n we exhibit nonregular languages accepted by such machines in time n o nlogn or n o log2 n and an np complete language accepted in time n o nlogn by using a tight padding method

sampled data consensus of general linear multi agent systems under switching topologies averaging method abstractthis paper investigates sampled data consensus problems of general linear multi agent systems under switching topologies to perform the consensus analysis by the averaging method the multi agent system in the sampled data setting is first converted into the continuous time system with the input delay then the approximate relationship between the states of this input delay system and the states of its averaged system is established by using the tool from non standard analysis subsequently a sufficient condition ensuring the sampled data consensus is obtained by linear matrix inequalities it is shown that the sampled data consensus of general linear multi agent systems including exponential unstable agents can be achieved if the speed of topology switching is fast enough and the sampled data consensus under the averaging topology can be achieved finally numerical simulations are provided to demonstrate the effectiveness of theoretical analyses

nonlinear pi control of uncertain systems an alternative to parameter adaptation a novel approach to stabilization and trajectory tracking for nonlinear systems with unknown parameters and uncertain disturbances is developed we take a drastic departure from the classical adaptive control approach consisting of a parameterized feedback law and an identifier which tries to minimize a tracking or prediction error instead we propose a simple nonlinear pi structure that generates a stable error equation with a perturbation function that exhibits at least one root trajectories are forced to converge to this root by suitably adjusting the nonlinear pi gains we consider the two basic problems of i matched uncertainties when the uncertain terms are in the image of the input matrix and ii unknown control directions when the control signal is multiplied by a gain of unknown sign we show that without knowing the system parameters and with only basic information on the uncertainties we can achieve global asymptotic stability and global tracking without injecting high gains into the loop interestingly we prove that we can take as our nonlinear pi structure an activation function reminiscent of that used in neural networks although most of the results are derived assuming full state measurement we also present an observer based solution for a chain of integrators with unknown control direction the procedure is shown to provide simple solutions to the classical problems of neural network function approximation as well as eccentricity control and friction compensation of mechanical systems

improved approximation algorithms for the vertex cover problem in graphs and hypergraphs we obtain improved algorithms for finding small vertex covers in bounded degree graphs and hypergraphs we use semidefinite programming to relax the problems and introduce new rounding techniques for these relaxations on graphs with maximum degree at most delta the algorithm achieves a performance ratio of 2 1 o 1 frac 2 ln ln delta ln delta for large delta which improves the previously known ratio of 2 frac log delta o 1 delta obtained by halld orsson and radhakrishnan using similar techniques we also present improved approximations for the vertex cover problem in hypergraphs for k uniform hypergraphs with n vertices we achieve a ratio of k 1 o 1 frac k ln ln n ln n for large n and for k uniform hypergraphs with maximum degree at most delta the algorithm achieves a ratio of k 1 o 1 frac k k 1 ln ln delta ln delta for large delta these results considerably improve the previous best ratio of k 1 c delta frac 1 k 1 for bounded degree k uniform hypergraphs and k 1 c n frac k 1 k for general k uniform hypergraphs both obtained by krivelevich using similar techniques we also obtain an approximation algorithm for the weighted independent set problem matching a recent result of halldorsson

a unified time varying feedback approach and its applications in adaptive stabilization of high order uncertain nonlinear systems we are concerned with two key problems of adaptive control design one is to find the feasible conditions and the valid boundary of the time varying feedback scheme another one lies in the improved generalization of the homogeneous idea in the global adaptive stabilization of high order uncertain nonlinear systems the distinguished feature of the system to be investigated is the serious coexistence between unknown time varying parameters and unknown time varying control coefficients design procedures of the continuous controller are provided based on the sign function technique and the delicate search of the time varying function and a lyapunov function finally the control of uncertain single link robotic manipulator demonstrates the application of design scheme

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

distributed adaptive consensus for multiple mechanical systems with switching topologies and time varying delay abstract this paper studies the adaptive consensus problem of networked mechanical systems with time varying delay and jointly connected topologies two different consensus protocols are proposed first we present an adaptive consensus protocol for the connected switching topologies based on graph theory lyapunov stability theory and switching control theory the stability of the proposed algorithm is demonstrated then we investigate the problem under the more general jointly connected topologies and with concurrent time varying communication delay the proposed consensus protocol consists of two parts one is for the connected agents which contains the current states disagreement among them and the other is designed for the isolated agents which contains the states difference between the current and past a distinctive feature of this work is to address the consensus control problem of mechanical systems with unknown parameters time varying delay and switching topologies in a unified theoretical framework numerical simulation is provided to demonstrate the effectiveness of the obtained results

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

on the structure of one tape nondeterministic turing machine time hierarchy abstract we show that if the number of available states is fixed and is sufficiently large then one tape nondeterministic turing machines can accept more sets within time bound a 2 n than within a 1 n for 0 a 1 a 2 here n is any function of the form n b 0 log n b 1 log 2 n b 2 log h n b h b 0 b h are rational numbers with order n log n and n 2 crossing sequences and kolmogorov complexity are used to prove it

approximation algorithms for data placement problems we develop approximation algorithms for the problem of placing replicated data in arbitrary networks where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data access cost we introduce the data placement problem to model this problem we have a set of caches mathcal f a set of clients mathcal d and a set of data objects mathcal o each cache i can store at most u i data objects each client j in mathcal d has demand d j for a specific data object o j in mathcal o and has to be assigned to a cache that stores that object storing an object o in cache i incurs a storage cost of f i o and assigning client j to cache i incurs an access cost of d jc ij the goal is to find a placement of the data objects to caches respecting the capacity constraints and an assignment of clients to caches so as to minimize the total storage and client access costs we present a 10 approximation algorithm for this problem our algorithm is based on rounding an optimal solution to a natural linear programming relaxation of the problem one of the main technical challenges encountered during rounding is to preserve the cache capacities while incurring only a constant factor increase in the solution cost we also introduce the connected data placement problem to capture settings where write requests are also issued for data objects so that one requires a mechanism to maintain consistency of data we model this by requiring that all caches containing a given object be connected by a steiner tree to a root for that object which issues a multicast message upon a write to any copy of that object the total cost now includes the cost of these steiner trees we devise a 14 approximation algorithm for this problem we show that our algorithms can be adapted to handle two variants of the problem a a k median variant where there is a specified bound on the number of caches that may contain a given object and b a generalization where objects have lengths and the total length of the objects stored in any cache must not exceed its capacity

hermitian normalized laplacian matrix for directed networks abstract in this paper we extend and generalize the spectral theory of undirected networks towards directed networks by introducing the hermitian normalized laplacian matrix for directed networks in order to start we discuss the courant fischer theorem for the eigenvalues of hermitian normalized laplacian matrix based on the courant fischer theorem we obtain a similar result towards the normalized laplacian matrix of undirected networks for each i 1 2 n any eigenvalue of hermitian normalized laplacian matrix i 0 2 moreover we prove some special conditions if 0 or 2 is an eigenvalue of the hermitian normalized laplacian matrix l x on top of that we investigate the symmetry of the eigenvalues of l x and the edge version for the eigenvalue interlacing result finally we present two expressions for the coefficients of the characteristic polynomial of the hermitian normalized laplacian matrix as an outlook we sketch some novel and intriguing problems to which our apparatus could generally be applied

a ptas for the cardinality constrained covering with unit balls in this paper we address the cardinality constrained covering with unit balls problem given a positive integer l and a set of n points in r d partition them into a minimum number of parts such that each part contains at most l points and it can be covered by a unit ball of the given p metric developing a constant factor approximation algorithm for this problem is an old open problem by proving a structural property in the problem and applying the shifting strategy and dynamic programming we derive the first email protected d approximation n o 1 e d time algorithm for this problem when d is a fixed constant

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

output tracking control for generalised high order nonlinear system with serious uncertainties abstractthis paper focuses on the problem of output tracking control for a class of generalised high order uncertain nonlinear systems serious uncertainties are composed of unknown high order terms unknown nonlinear functions and the signal to be tracked the new feedback scheme guarantees that the tracking error belongs to a prescribed small neighbourhood of the origin in finite time design procedures are presented by combining improved adding a power integrator method with the recursive construction as an application the control methodology is used in the tracking control of the mass spring mechanical system

leader following consensus problem with a varying velocity leader and time varying delays abstract in this paper we study a leader following consensus problem for a multi agent system with a varying velocity leader and time varying delays here the interaction graph among the followers is switching and balanced at first we propose a neighbor based rule for every agent to track a leader whose states may not be measured in addition we consider the convergence analysis of this multi agent system under two different conditions the connection between the followers and the leader is time invariant and time varying for the first case a novel decomposition method is introduced to facilitate the convergence analysis by utilizing a lyapunov krasovskii functional we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors finally two simulations are also presented to illustrate our theoretical results

distributed adaptive control for time varying formation tracking of a class of networked nonlinear systems abstractthis paper considers the time varying formation problem of tracking a reference for a class of networked systems consisting of multiple nonlinear subsystems with unknown parameters and non identical nonlinear dynamics the communication status among the subsystems is represented by a directed graph a portion of subsystems have no access to the information of reference distributed adaptive controllers are proposed by employing backstepping technique it is proved that with the proposed scheme all the closed loop signals are globally bounded and all the subsystems can track the reference while building and keeping the prescribed time varying formation shape simulation results are given to illustrate the effectiveness of the proposed scheme

global stabilisation of high order nonlinear systems with multiple time delays this paper focuses on the stabilisation for a class of high order nonlinear systems with multiple time delays growth restriction on system nonlinearities is further relaxed design procedures of a continuous controller are provided by the method of adding a power integrator and the stability of the resulting closed loop system is rigorously proven with the help of the elegant choice of a lyapunov krasovskii functional finally a simulation example is provided to demonstrate the validness of the proposed approach

existence properties and trajectory specification of generalised multi agent flocking a class of flocking algorithms for second order multi agent networks with single virtual leaders are developed by including more weighting and navigating matrices in this paper flocking existence

almost decouplability of any directed weighted network topology abstract this paper introduces a conception that any weighted directed network topology is almost decouplable which can help to transform the topology into a similar form composed of uncoupled vertices and thus reduce the complexity of analysis for networked dynamical systems as an example of its application the consensus problem of linear multi agent systems with time varying network topologies is addressed as a result a necessary and sufficient condition for uniform consensus is proposed

primal dual schema for capacitated covering problems primal dual algorithms have played an integral role in recent developments in approximation algorithms and yet there has been little work on these algorithms in the context of lp relaxations that have been strengthened by the addition of more sophisticated valid inequalities we introduce primal dual schema based on the lp relaxations devised by carr et al for the minimum knapsack problem as well as for the single demand capacitated facility location problem our primal dual algorithms achieve the same performance guarantees as the lp rounding algorithms of carr et al which rely on applying the ellipsoid algorithm to an exponentially sized lp furthermore we introduce new flow cover inequalities to strengthen the lp relaxation of the more general capacitated single item lot sizing problem using just these inequalities as the lp relaxation we obtain a primal dual algorithm that achieves a performance guarantee of 2 computational experiments demonstrate the effectiveness of this algorithm on generated problem instances

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

global regulation for a class of stochastic high order nonlinear systems with multiple unknown control directions this paper concerns the global regulation for a class of stochastic high order nonlinear systems which admit more general system form than the existing works for details except for the serious sy

a distributed 2 e approximation for vertex cover in o log δ e log log δ rounds we present a simple deterministic distributed 2 e approximation algorithm for minimum weight vertex cover which completes in o log elog log rounds where is the maximum degree in the graph for any e 0 that is at most o 1 for a constant e this implies a constant approximation in o log log log rounds which contradicts the lower bound of kmw10

immunity and pseudorandomness of context free languages we discuss the computational complexity of context free languages concentrating on two well known structural properties immunity and pseudorandomness an infinite language is reg immune resp cfl immune if it contains no infinite subset that is a regular resp context free language we prove that i there is a context free reg immune language outside reg n and ii there is a reg bi immune language that can be computed deterministically using logarithmic space we also show that iii there is a cfl simple set where a cfl simple language is an infinite context free language whose complement is cfl immune similar to the reg immunity a reg primeimmune language has no polynomially dense subsets that are also regular we further prove that iv there is a context free language that is reg n bi primeimmune concerning pseudorandomness of context free languages we show that v cfl contains reg n pseudorandom languages finally we prove that vi against reg n there exists an almost 1 1 pseudorandom generator computable in nondeterministic pushdown automata equipped with a write only output tape and vii against reg there is no almost 1 1 weakly pseudorandom generator computable deterministically in linear time by a single tape turing machine

global practical tracking for high order uncertain nonlinear systems with unknown control directions this paper addresses the global practical tracking problem for a class of high order uncertain nonlinear systems with unknown control directions under fairly weak conditions although the stabilization problem has been studied for the systems the tracking problem remains unsolved up to now mainly because of the essential differences between stabilization and tracking problems when control directions are unknown in this paper by introducing a novel coordinate transformation and new updating laws an approach is presented for the first time to design a continuous adaptive controller to make the tracking error prescribed arbitrarily small after a finite time and simultaneously to keep all the closed loop states bounded it is worth emphasizing that the proposed adaptive tracking control design scheme is motivated by the recent tracking works inspired by the ideas of universal control and dead zone and obtained by the approaches of nussbaum gain and adding a power integrator most importantly this paper removes the basic assumption that the control directions are precisely known in the related tracking works without additional conditions imposed on the systems and the reference signal

a primal dual bicriteria distributed algorithm for capacitated vertex cover in this paper we consider the capacitated vertex cover problem which is the variant of vertex cover where each node is allowed to cover a limited number of edges we present an efficient deterministic distributed approximation algorithm for the problem our algorithm computes a 2 epsilon approximate solution which violates the capacity constraints by a factor of 4 epsilon in a polylogarithmic number of communication rounds on the other hand we also show that every efficient distributed approximation algorithm for this problem must violate the capacity constraints our result is achieved in two steps we first develop a 2 approximate sequential primal dual algorithm that violates the capacity constraints by a factor of 2 subsequently we present a distributed version of this algorithm we demonstrate that the sequential algorithm has an inherent need for synchronization which forces any naive distributed implementation to use a linear number of communication rounds the challenge in this step is therefore to achieve a reduction of the communication complexity to a polylogarithmic number of rounds without worsening the approximation guarantee

space efficient deterministic simulation of probabilistic automata given a description of a probabilistic automaton one head probabilistic finite state automaton or probabilistic turing machine and an input string x of length n we ask how much space does a deterministic turing machine need in order to decide the acceptance of the input string by that automaton the question is interesting even in the case of one head one way probabilistic finite state automata 1pfa s we call rational stochastic languages ss rat the class of languages recognized by 1pfa s whose transition probabilities and cutpoints i e recognition thresholds are rational numbers the class ss rat contains context sensitive languages that are not context free but on the other hand there are context free languages not included in ss rat our main results are as follows begin itemize item the proper inclusion of ss rat in zlo which is optimal i e ss rat not subset dspace o log n the previous upper bounds were dspace n obtained by p d dieu in 1972 and linebreak 4 dspace log n log log n obtained by h jung in 1984 item probabilistic turing machines with space bound f n in o log n can be deterministically simulated in space o min c f n log n log n f n log log n where c is a constant depending on the simulated probabilistic turing machine the best previously known simulation uses o log n f n log log n space obtained by h jung in 1984 end itemize to obtain these results we develop and use two space efficient but also parallel time efficient techniques which are of independent interest begin itemize item a technique to compare deterministically using only o log n space large numbers given in terms of their values modulo a sequence of primes p1 p2 cdots pn in o na where a is some arbitrary constant item a technique to compare deterministically a threshold with entries of the inverse of a given banded matrix end itemize

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

adaptive periodic event triggered consensus for multi agent systems subject to input saturation abstractthis paper investigates the distributed adaptive event triggered consensus control for a class of nonlinear agents each agent is subject to input saturation two kinds of distributed event triggered control scheme are introduced one is continuous time based event triggered scheme and the other is sampled data based event triggered scheme compared with the traditional event triggered schemes in the existing literatures the parameters of the event triggered schemes in this paper are adaptively adjusted by using some event error dependent adaptive laws the problem of simultaneously deriving the controller gain matrix and the event triggering parameter matrix and tackling the saturation nonlinearity is cast into standard linear matrix inequalities problem a convincing simulation example is given to demonstrate the theoretical results

linear time limited automata the time complexity of 1 limited automata is investigated from a descriptional complexity view point though the model recognizes regular languages only it may use quadratic time in the input length we show that with a polynomial increase in size and preserving determinism each 1 limited automaton can be transformed into an halting linear time equivalent one we also obtain polynomial transformations into related models including weight reducing hennie machines and we show exponential gaps for converse transformations in the deterministic case

robustness analysis of nonlinear feedback systems an input output approach this paper presents an approach to robustness analysis for nonlinear feedback systems we pursue a notion of model uncertainty based on the closeness of input output trajectories which is not tied to a particular uncertainty representation such as additive parametric structured etc the basic viewpoint is to regard systems as operators on signal spaces we present two versions of a global theory where stability is captured by induced norms or by gain functions we also develop local approaches over bounded signal sets and give a treatment for systems with potential for finite time escape we compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations e g small time delays we also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations the paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection

a simple parallel algorithm for the maximal independent set problem two basic design strategies are used to develop a very simple and fast parallel algorithms for the maximal independent set mis problem the first strategy consists of assigning identical copies o

a time complexity gap for two way probabilistic finite state automata it is shown that if a two way probabilistic finite state automaton 2pfa m recognizes a nonregular language l with error probability bounded below frac 1 2 then there is a positive constant b depending on m such that for infinitely many inputs x the expected running time of m on input x must exceed 2 n b where n is the length of x this complements a result of freivalds showing that 2pfa s can recognize certain nonregular languages in exponential expected time it also establishes a time complexity gap for 2pfa s since any regular language can be recognized by some 2pfa in linear time other results give roughly exponential upper and lower bounds on the worst case increase in the number of states when converting a polynomial time 2pfa to an equivalent two way nondeterministic finite state automaton or to an equivalent one way deterministic finite state automaton

dynamic programming based algorithms for set multicover and multiset multicover problems given a universe n containing n elements and a collection of multisets or sets over n the multiset multicover msmc problem or the set multicover smc problem is to cover all elements at least a number of times as specified in their coverage requirements with the minimum number of multisets or sets in this paper we give various exact algorithms for these two problems with or without constraints on the number of times a multiset or set may be chosen first we show that the msmc without multiplicity constraints problem can be solved in o b 1 n f time and polynomial space where b is the maximum coverage requirement and f denotes the total number of given multisets over n the o notation suppresses a factor polynomial in n to our knowledge this is the first known exact algorithm for the msmc without multiplicity constraints problem second by combining dynamic programming and the inclusion exclusion principle we can exactly solve the smc without multiplicity constraints problem in o b 2 n time compared with two recent results in q s hua y wang d yu f c m lau set multi covering via inclusion exclusion theoretical computer science 410 38 40 2009 3882 3892 and j nederlof inclusion exclusion for hard problems master thesis utrecht university the netherlands 2008 respectively ours is the fastest exact algorithm for the smc without multiplicity constraints problem finally by directly using dynamic programming we give the first known exact algorithm for the msmc or the smc with multiplicity constraints problem in o b 1 n f time and o b 1 n space this algorithm can also be easily adapted as a constructive algorithm for the msmc without multiplicity constraints problem

contraction analysis of time delayed communications and group cooperation we study stability of interacting nonlinear systems with time delayed communications using contraction theory and a simplified wave variable design inspired by robotic teleoperation we show that contraction is preserved through specific time delayed feedback communications and that this property is independent of the values of the delays the approach is then applied to group cooperation with linear protocols where it is shown that synchronization can be made robust to arbitrary time delays

lyapunov based approach to multiagent systems with switching jointly connected interconnection this note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies neighbor based rules are adopted to realize local control strategies for these continuous time autonomous agents described by double integrators although the interagent connection structures vary over time and related graphs may not be connected a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed lyapunov based approach and related space decomposition technique

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

on discrete time convergence for general linear multi agent systems under dynamic topology this note aims to develop the nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which is widely used for multiple integrator agents to deal with the convergence analysis of general discrete time linear multi agent systems mass with the proposed approach it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions i e the individual uncoupled system is allowed to be strictly unstable in the discrete time sense and it is only required that the joint of the communication topologies has a spanning tree frequently enough moreover a least convergence rate as well as an upper bound for the strictly unstable mode which are independent of the switching mode of the system are specified as well

cooperative global output regulation of second order nonlinear multi agent systems with unknown control direction this technical note addresses the cooperative global output regulation problem for second order nonlinear multi agent systems without a priori knowledge of the control direction we will propose both the graph dependent and graph independent distributed controllers based on the combination of the internal model the nussbaum type dynamic gain and the adaptive control technique comparing with some existing results our novel design can handle the multi agent system with not only the arbitrary and non identical unknown control direction but also the uncertain parameter that belongs to any unknown and non compact set

a geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints we first establish a relaxed version of dines theorem associated to quadratic minimization problems with finitely many linear equality and a single nonconvex quadratic inequality constraints the case of unbounded optimal valued is also discussed then we characterize geometrically the strong duality and some relationships with the conditions employed in finsler theorem are established furthermore necessary and sufficient optimality conditions with or without the slater assumption are derived our results can be used to situations where none of the results appearing elsewhere are applicable in addition a revisited theorem due to frank and wolfe along with that due to eaves is established for asymptotically linear sets

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

maximizing a monotone submodular function subject to a matroid constraint let f 2 x rightarrow cal r be a monotone submodular set function and let x cal i be a matroid we consider the problem rm max s in cal i f s it is known that the greedy algorithm yields a 1 2 approximation m l fisher g l nemhauser and l a wolsey math programming stud no 8 1978 pp 73 87 for this problem for certain special cases e g rm max s leq k f s the greedy algorithm yields a 1 1 e approximation it is known that this is optimal both in the value oracle model where the only access to f is through a black box returning f s for a given set s g l nemhauser and l a wolsey math oper res 3 1978 pp 177 188 and for explicitly posed instances assuming p neq np u feige j acm 45 1998 pp 634 652 in this paper we provide a randomized 1 1 e approximation for any monotone submodular function and an arbitrary matroid the algorithm works in the value oracle model our main tools are a variant of the pipage rounding technique of ageev and sviridenko j combin optim 8 2004 pp 307 328 and a continuous greedy process that may be of independent interest as a special case our algorithm implies an optimal approximation for the submodular welfare problem in the value oracle model j vondrak proceedings of the 38 th acm symposium on theory of computing 2008 pp 67 74 as a second application we show that the generalized assignment problem gap is also a special case although the reduction requires x to be exponential in the original problem size we are able to achieve a 1 1 e o 1 approximation for gap simplifying previously known algorithms additionally the reduction enables us to obtain approximation algorithms for variants of gap with more general constraints

consensus analysis of switching multi agent systems with fixed topology and time delay abstract this paper investigates the average consensus problems of the discrete time markov switching linear multi agent systems lmas with fixed topology and time delay firstly we introduce a concept of the average consensus to adapt the stochastic systems secondly a time delay switching consensus protocol is proposed by developing a new signal mode the switching signal of the systems and the time delay signal of the controller can be merged into one signal thirdly by lyapunov technique two lmis criteria of average consensus are provided and they reveal that the consensus of the multi agent systems relates to the spectral radius of the laplacian matrix furthermore by our results and ccl type algorithms we can get the gain matrices finally a numerical example is given to illustrate the efficiency of our results