cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time varying actuator faults in this paper the cooperative adaptive fault tolerant fuzzy tracking control caftftc problem of networked high order multiagent with time varying actuator faults is studied and a novel caftftc scheme is proposed to guarantee that all follower nodes asymptotically synchronize a leader node with tracking errors converging to a small adjustable neighborhood of the origin in spite of actuator faults the leader node is modeled as a higher order nonautonomous nonlinear system it acts as a command generator giving commands only to a small portion of the networked group each follower is assumed to have nonidentical unknown nonlinear dynamics and the communication network is also assumed to be a weighted directed graph with a fixed topology a distributed robust adaptive fuzzy controller is designed for each follower node such that the tracking errors are cooperative uniform ultimate boundedness cuub moreover these controllers are distributed in the sense that the controller designed for each follower node only requires relative state information between itself and its neighbors the adaptive compensation term of the optimal approximation errors and external disturbances is adopted to reduce the effects of the errors and disturbances which removes the assumption that the upper bounds of unknown function approximation errors and disturbances should be known analysis of stability and parameter convergence of the proposed algorithm are conducted that are based on algebraic graph theory and lyapunov theory comparing with results in the literature the caftftc scheme can minimize the time delay between fault occurrence and accommodation and reduce its adverse effect on system performance in addition the ftc scheme requires no additional fault isolation model which is necessary in the traditional active ftc scheme finally an example is provided to validate the theoretical results

adaptive neural asymptotic control for uncertain nonlinear multiagent systems with a fuzzy dead zone constraint abstract a consensus control scheme is developed for a class of leader follower multiagent systems with a fuzzy dead zone constraint differently from previous work the method developed implements a predefined convergence of tracking errors for multiagent systems especially the dynamic model for each follower has a fuzzy dead zone input to solve the problem not only a set of smooth functions are used within the control design to increase the stability of the systems but also the unfuzziness and center of gravity method are used to analyze and process the actuator constraint model where each slope of the dead zone is uncertain and fuzzy it is verified that the method developed effectively guarantees that the tracking errors of multiagent systems can converge to a predefined interval that is the problem of better asymptotic consensus performance for nonlinear multiagent systems is solved simulation illustrates the results obtained

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse abstract a number of applications require the computation of the trace of a matrix that is implicitly available through a function a common example of a function is the inverse of a large sparse matrix which is the focus of this paper when the evaluation of the function is expensive the task is computationally challenging because the standard approach is based on a monte carlo method which converges slowly we present a different approach that exploits the pattern correlation if present between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively we leverage various sampling and fitting techniques to fit the diagonal of the approximation to the diagonal of the inverse depending on the quality of the approximate inverse our method may serve as a standalone kernel for providing a fast trace estimate with a small number of samples furthermore the method can be used as a variance reduction method for monte carlo in some cases this is decided dynamically by our algorithm an extensive set of experiments with various technique combinations on several matrices from some real applications demonstrate the potential of our method

multi agent consensus with relative state dependent measurement noises in this note the distributed consensus corrupted by relative state dependent measurement noises is considered each agent can mea sure or receive its neighbors state information with random noises whose intensity is a vector function of agents relative states by investigating the structure of this interaction and the tools of stochastic differential equa tions we develop several small consensus gain theorems to give sufficient conditions in terms of the control gain the number of agents and the noise intensity function to ensure mean square m s and almost sure a s consensus and quantify the convergence rate and the steady state error especially for the case with homogeneous communication and control channels a necessary and sufficient condition to ensure m s consensus on the control gain is given and it is shown that the control gain is independent of the specific network topology but only depends on the number of nodes and the noise coefficient constant for symmetric measurement models the almost sure convergence rate is estimated by the iterated logarithm law of brownian motions index terms distributed consensus distributed coordination fading channel measurement noises multi agent system

the residue of the global η function at the origin where i dvol x l denotes the riemannian measure on m using the calculus of pseudo differential operators depending upon a complex parameter which was developed by seeley 9 one can show that both q s x p and r s p can be meromorphically extended to the complex plane with simple poles at s m n u for n 0 the residues of l s x p at the poles for n 0 m are given by local formulas in the jets of the total symbol of p we define

consensus for multi agent systems with inherent nonlinear dynamics under directed topologies abstract this paper considers the consensus problem for multi agent systems with inherent nonlinear dynamics under directed topologies a variable transformation method is used to convert the consensus problem to a partial stability problem both first order and second order systems are investigated under fixed and switching topologies respectively it is assumed that the inherent nonlinear terms satisfy the lipshitz condition sufficient conditions on the feedback gains are given based on a lyapunov function method for first order systems under a fixed topology the consensus is achieved if the feedback gain related to the agents positions is large enough for first order systems under switching topologies the effect of the minimum dwell time for the switching signal on the consensus achievement is considered for second order systems under a fixed topology the consensus is achieved if the feedback gains related to the agents positions and velocities respectively are both large enough for second order systems under switching topologies a switching variable transformation is given then the consensus problem is investigated when all the digraphs are strongly connected and weighted balanced with a common weighted vector finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

finite frequency memory output feedback controller design for t s fuzzy dynamical systems in this paper we will investigate the problem of finite frequency memory fixed order output feedback controller design for takagi sugeno t s fuzzy affine systems it is assumed that the disturbances reside in a finite frequency range i e the low middle or high frequency range the objective is to design a memory piecewise affine pwa controller by using past output measurements to guarantee the asymptotic stability of the resulting closed loop system with a prescribed finite frequency mathscr h infty performance via the system state input augmentation a novel descriptor system approach is proposed to facilitate the controller design all the design conditions are formulated in the form of linear matrix inequalities it is also proven that the mathscr h infty performance can be improved with the memory control strategy finally simulation studies are presented to show the effectiveness of the proposed design method

consensus of a class of second order multi agent systems with time delay and jointly connected topologies this technical note investigates consensus problems of a class of second order continuous time multi agent systems with time delay and jointly connected topologies we first introduce a neighbor based linear protocol with time delay then we derive a sufficient condition in terms of linear matrix inequalities lmis for average consensus of the system furthermore we discuss the case where the time delay affects only the information that is being transmitted and show that consensus can be reached with arbitrary bounded time delay finally simulation results are provided to demonstrate the effectiveness of our theoretical results

quantized consensus of second order continuous time multi agent systems with a directed topology via sampled data abstract this paper addresses the quantized consensus problem of continuous time second order multi agent systems via sampled data where the interconnection topology has a directed spanning tree a necessary and sufficient condition on the sampling period and the design parameters is obtained to guarantee that the consensus errors converge to a neighborhood of the origin which disappears as the quantized errors tend to zero this paper also gives the final consensus values which is different from the existing works on the quantized consensus of second order multi agent systems the method is further extended to the case when the velocities of agents are unavailable two simulation examples are provided to illustrate the effectiveness of the proposed consensus protocols

how accurately should i compute implicit matrix vector products when applying the hutchinson trace estimator the hutchinson estimator defines an estimate of the trace of a matrix m based on a bilinear form with independent vectors y of zero mean unit variance uncorrelated entries this technique is particularly useful when m is only implicitly given but the matrix vector product my can be efficiently computed without m being explicitly formed well known examples in practice are m a 1 and more generally m f a we study in this paper the conditions under which the numerical error incurred in computing my is comparable with the statistical uncertainty caused by the randomness of y with these conditions we also derive the sufficient number of random vectors that guarantees a relative error bound given any desired probability for the purpose of obtaining easily computable conditions we focus on the use of random vectors consisting of normal variables a precursor technique attributed to girard by hutchinson as demonstrated in many practical scenarios normal variables are as effective a

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

fuzzy observed based adaptive consensus tracking control for second order multiagent systems with heterogeneous nonlinear dynamics in this paper the consensus tracking control problem of second order multiagent systems with unknown nonlinear dynamics immeasurable states and disturbances is investigated the nonlinear dynamics in multiagent systems do not satisfy the matched condition in this paper fuzzy logic system is introduced to approximate the unknown nonlinear dynamics and adaptive high gain observer is designed to estimate the unmeasured states based on backstepping approach and lyapunov theory a new adaptive fuzzy distributed controller is proposed for each agent only using the information of itself and its neighbors then the consensus tracking is achieved under the designed distributed controller moreover it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible finally the simulation result illustrates the effectiveness of the designed controller

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

approximating spectral sums of large scale matrices using stochastic chebyshev approximations computation of the trace of a matrix function plays an important role in many scientific computing applications including applications in machine learning computational physics e g lattice qua

adaptive consensus control for a class of nonlinear multiagent time delay systems using neural networks because of the complicity of consensus control of nonlinear multiagent systems in state time delay most of previous works focused only on linear systems with input time delay an adaptive neural network nn consensus control method for a class of nonlinear multiagent systems with state time delay is proposed in this paper the approximation property of radial basis function neural networks rbfnns is used to neutralize the uncertain nonlinear dynamics in agents an appropriate lyapunov krasovskii functional which is obtained from the derivative of an appropriate lyapunov function is used to compensate the uncertainties of unknown time delays it is proved that our proposed approach guarantees the convergence on the basis of lyapunov stability theory the simulation results of a nonlinear multiagent time delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm