Time-delay Case Research Articles

Output Synchronization on Strongly Connected Graphs

In this technical note, we study output synchronization of networked multiagent systems. The agents, modeled as nonlinear systems with relative degree one, exchange information over a network described by an interagent communication graph. Inspired by the results of Igarashi , we extend our earlier results on output synchronization to include the case of strongly connected graphs. We first demonstrate output synchronization for input-output passive systems communicating over strongly connected graphs and include the practical case of constant time delays in communication. It is well known (Byrnes ) that weakly minimum phase systems with relative degree one are feedback equivalent to a passive system with a positive definite storage function. We exploit this feedback equivalence to develop control laws for output synchronization of such systems, exchanging outputs on strongly connected graphs, and in the presence of communication delays. A numerical example is also presented to illustrate the proposed results.

An executable modelling and simulation framework for NP-complete complexity problems and different forms of uncertainties

With rapid globalisation and increasing complexity of processes in service systems, there is need for a new and executable modelling framework that can be used to model, simulate and analyse the complex processes. The target processes often belong to the class of problems that are NP-complete. Existing frameworks for modelling NP-complete problems have certain limitations. A new Petri Net-based framework, Fuzzy Coloured Petri Net with stochastic time delay and NP-complete cases (FCPN-std/NPC), is presented in this paper that allows modelling, simulation and analysis of processes that have an underlying NP-complete complexity problem. The framework has the ability to characterise two types of uncertainties, variance type uncertainty and ambiguity type uncertainty. A new set of process-semantics-based nodes and mapping functions are defined for the FCPN-std/NPC framework that allows modelling of a class of NP-complete problems. A small supply chain example is used to illustrate the operational characteristics of the framework.

새로운 구간 분해 방법을 이용한 구간 시변지연을 갖는 선형시스템의 안정성

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

Further results on H∞ filtering for discrete‐time systems with state delay

AbstractThis article studies the problem of H∞ filtering for linear discrete‐time systems with state delay. Via delay partitioning idea, two new H∞ filter design methods are proposed with much less conservatism than most existing results. The improvement lies in constructing two new Lyapunov–Krasovskii functionals by partitioning the known constant lower bound of delay into several segments equally. Using free‐weighting matrix and Jensen inequality methods, two new delay‐dependent bound real lemmas (BRLs) are obtained, which depend on both the delay and the partitioning number. Based on the obtained BRLs, new H∞ filter design approaches are proposed in terms of linear matrix inequalities. The results are immediately extended to multiple time delay case and polytopic uncertain case, respectively. Three numerical examples are presented to illustrate the effectiveness and advantage of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.

A new mathematical model for car drivers with spatial preview

AbstractA mathematical driver model is given in the spatial equation form, which takes into account the previewed information of the path. An optimal control method is considered for the ideal no time-delay case and a Lyapunov-Krasovskii functional approach is applied to deal with drivers’ reaction time-delay. For both cases, exponential stability is guaranteed for the closed-loop system.

The L2-LInfinite Control for Leader-following Coordination with Switching Topology and Time-delay

In this paper, we investigate the L_2 - L_\infinity leader-following coordination problems with undirected switching topologies and external disturbance in two cases of the time delay and non-delayed networks. The agent dynamics is expressed in the form of a second-order model and the control laws are neighbor-based feedback laws. We first establish LMI sufficient conditions to guarantee that all following agents can track the leader agent with zero and nonzero communication delays respectively. Furthermore, we get a explicit estimation expression of L_2 - L_\infinity disturbance attenuation by constructing a parameter-dependent common Lyapunov function in case that there is no delay time. Finally, numerical examples are provided to illustrate the effectiveness of our results.

A delay decomposition approach to fuzzy Markovian jumping genetic regulatory networks with time-varying delays

In this paper, we investigated the asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach. The genetic regulatory networks are composed of s modes and the network switches from one mode to another according to a Markovian chain with known transition probabilities. Purpose of this work is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov–Krasovskii functional (LKF) is constructed by nonuniformly dividing the whole delay intervals into multiple segments. Choosing proper functionals with different weighting matrices corresponding to different segments in the LKFs. Employing these new LKFs for the case of constant time delays and time-varying delays, some new delay-dependent stability criteria are established with Markovian jumping parameters by T–S fuzzy model. Maximum admissible upper bounds (MAUBs) for the time-varying delays are determined. All the conditions presented here are in the form of linear matrix inequalities (LMI) which are efficiently solved by the LMI toolbox in Matlab. Numerical examples are given to show the effectiveness of the proposed method.

Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction

This paper aims at investigating the fuzzy adaptive control design for uncertain multivariable systems with unknown actuator nonlinearities and unknown control direction that possibly exhibit time-delay. The actuator nonlinearities involve dead-zone or backlash-like hysteresis, while the control direction is closely related to the sign of the control gain matrix. Two fuzzy adaptive controllers are proposed to deal with such an issue. The design of the first controller is mainly carried out in the free time-delay case, while the second control design is performed assuming that the system exhibits time-varying delays. Of practical interest, the adaptive compensation of the effects of the actuator nonlinearities requires neither the knowledge of their parameters nor the construction of their inverse. Furthermore, the lack of knowledge of the control direction is handled by incorporating in the control law a Nussbaum-type function. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.

Global stability in “delay” systems with cross-diffusions dominated by self-diffusions

In this paper, applying a method of energy estimation similar to that of Seong-A. Shim [Seong-A. Shim, Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions, Nonlinear Anal. RWA 4 (2003) 65–86], which used Gagliardo–Nirenberg-type inequalities in the estimates of solutions in order to establish W 2 1 -bounds uniform in time, we extend the result to the case of time delays, and establish conditions for the uniform boundedness of solutions and global asymptotic stability for the constant steady state of a quasilinear parabolic “delay” system with cross-diffusions dominated by self-diffusions and large diffusion coefficients in population dynamics.

Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies

This article studies a consensus problem for a group of high-order dynamic agents with fixed and switching topologies. Two linear consensus protocols, which only depend on the agent's own information and its neighbours' partial information, are proposed, respectively, for the group with and without communication time-delays. For the case of fixed topology and zero communication time-delay, a necessary and sufficient condition for the consensus is established. The parameter design of the protocol is also discussed. Under switching topology, the consensus is investigated for two cases: the case of zero communication time-delay and the case of nonuniform communication time-delays. For each case, a sufficient condition for the consensus is provided. Moreover, for a group of double/triple-integrator agents with fixed topology and uniform constant time-delay, some necessary and sufficient conditions for the consensus are given. Finally, numerical simulations are worked out to illustrate the effectiveness of the theoretical results.

On the Effects of Network Delays on an Energy-based Controller

In this paper, the design of an energy-based controller for a platoon of nonholonomic vehicles is presented and its performance is analysed for the case of random time delays in the network. The nonholonomic constraints of the models are taken into account during the design process by considering them in the goal virtual Lagrange function. The introductory section gives an overview of the energy methods for the case of mass point vehicles. Subsequently, the strategy is extended to apply to the case of nonholonomic vehicles. The controller is analysed by means of simulation tools in order to evaluate the effects of random Rayleigh distributed delays on the network.

When classical nonlinear time-delay state-space systems admit an input-output equation of neutral type

This paper deals with nonlinear retarded time-delay systems that surprisingly admit an input-output representation of neutral type. It is shown that such an unexpected behaviour represents a strictly nonlinear phenomenon, for it cannot happen in the linear time-delay case where retarded systems always admit an input-output representation of retarded type. A necessary and sufficient condition under which the nonlinear systems admit a neutral input-output representation is given and strategies for finding an inputoutput representation of retarded type are briefly outlined. Some open problems that arise, like minimality and system transformations, are discussed as well.

Control under limited information: Special issue (part II)

Control under limited information: Special issue (part II)

Synthesis and analysis of robust dynamic linear protocols for dynamic average consensus estimators

The dynamic average consensus problem in multi-agent networks is considered. Each agent residing on the network establishes a dynamic average consensus estimator whose output tracks the average of time-varying inputs to all the agents in the network. The authors propose a systematic methodology to construct any dynamic linear protocol for the dynamic average consensus having desired stability and performance properties. Our aim is to reduce the design problem of the dynamic average consensus protocols to the design problem of a simple system constructed of a simple integrator with a disturbance rejection controller as a feedback control. The authors rigorously analyse the input-to-state stability and some important performance properties of the dynamic linear protocol. The important case of switching topology is precisely analysed and therefore sufficient conditions for the uniform-input-to-state stability of the switched dynamic average consensus estimators are identified. Also the cases of initialisation errors and uniform time delays are well addressed. The case of addition/deletion of the agents is also pointed out. A design example of the dynamic linear protocol and its simulation results is presented demonstrating the efficiency of the proposed method.

Discrete-time H∞ Full-information Control of Structural Systems with Control Delay

H ∞ full information control method for structural vibration suppression with control delay is proposed within a discrete-time framework. Firstly, the continuous-time system equation with control delay is discretized by precise computation of matrix exponentials. By introducing an appropriate extended state vector, the time-delay system is transformed into standard discrete forms without time delays. Then a controller is designed based on the discrete time H ∞ full information control theory. The controller consists of a regular feedback closed-loop and a feed-forward compensator which utilizes external excitation signals measured in real time. The feed-forward plus feedback controller has better performance than feedback only controllers. The feedback loop of the deduced controller contains linear combinations of former control inputs besides the current state feedback terms. Thus the proposed method is applicable to large time-delay cases. Considering the complexity of the transformed system, a 2 N algorithm is introduced to search the optimal attenuation level and evaluate the control law. The present algorithm can be executed parallel, which makes the design of H ∞ controllers very convenient. Finally, numerical simulations of a three-story structure control are implemented. Time-delay effects on the optimal attenuation level are given to show that it is an important factor for system stability. Simulation results demonstrate the feasibility and effectiveness of the proposed control method.

Global behavior of dynamical agents in directed network

This paper investigates the global behavior of controlled dynamical agents in directed networks. The agents are Lyapunov stable, are distributed in a line, and communicate through a directed network. The communication topology of the network is characterized by a directed graph and the control protocol is designed in simple linear decentralized feedback law. We study the different conditions under which agents will achieve aggregation, and critical and divergent trajectories, respectively. Our investigation on the dynamical agent system under network is extended to the time-delay network case. Furthermore, we study the case with two pre-specified virtual leaders in the system. Numerical simulations are given and demonstrate that our theoretical results are effective.

Unified framework for developing testing effort dependent software reliability growth models

Several software reliability growth models (SRGMs) have been presented in the literature in the last three decades. These SRGMs take into account different testing environment depending on size and efficiency of testing team, type of components and faults, design of test cases, software architecture etc. The plethora of models makes the model selection an uphill task. Recently, some authors have tried to develop a unifying approach so as to capture different growth curves, thus easing the model selection process. The work in this area done so far relates the fault removal process to the testing/execution time and does not consider the consumption pattern of testing resources such as CPU time, manpower and number of executed test cases. More realistic modeling techniques can result if the reliability growth process is studied with respect to the amount of expended testing efforts. In this paper, we propose a unified framework for testing effort dependent software reliability growth models incorporating imperfect debugging and error generation. The proposed framework represents the realistic case of time delays between the different stages of fault removal process i.e Failure Observation/Fault Detection and Fault Removal/Correction processes. The Convolution of probability distribution functions have been used to characterize time differentiation between these two processes. Several existing and new effort dependent models have been derived by using different types of distribution functions. We have also provided data analysis based on the actual software failure data sets for some of the models discussed and proposed in the paper.

Rate limited stabilization: Sub‐optimal encoder–decoder schemes

AbstractWe extend in this paper results from packet‐based control theory and present sufficient conditions on the rate of a packet network to guarantee asymptotic stabilizability of unstable discrete LTI systems with less inputs than states. We use a truncation‐based encoder/decoder scheme and two types of network control systems are considered in the absence of communication delays, then for one of the two types, the case of a constant time delay is discussed. For one of the network types, we also propose a zoom‐in‐type dynamic quantizer scheme with lower data rate but a more complex encoding scheme than the truncation‐based one. The new dynamic quantizer requires a lower data rate to achieve stabilization, and while it does not achieve the minimum data rate given by the Data Rate Theorem, it uses an encoding algorithm that is simpler than others reported in the literature. Copyright © 2009 John Wiley & Sons, Ltd.

Delay-Dependent Stability Analysis of Neutral Systems Using Positive Polynomials Optimization

The main goal of this paper is to investigate the stability of neutral systems, by using some features of the method introduced by Zhang et al. (2003) for the standard time-delay case. The central idea consists in replacing the delay by some appropriate Pade approximation, obtaining a (sufficient) delay-dependent stability condition for the neutral system. Such a condition can be rewritten as a positivity constraint on a two-variable matrix polynomial, leading to an effective computation of the delay margin by using sum-of-squares representations of multivariable positive matrix polynomials.

New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type

This paper deals with the problem of the delay-dependent asymptotic stability analysis for bidirectional associative memory (BAM) neural networks of neutral type. Two cases of time delays in which whether the neutral delays are equal to the state delays or not are involved. The activation functions are supposed to be bounded and globally Lipschitz continuous, which are more general than the usual bounded monotonically increasing ones such as the activation functions of the sigmoidal type. By introducing some new integral inequalities and resorting to the Lyapunov–Krasovskii functional approach, one novel delay-dependent condition is established checking the asymptotic stability for a given BAM neural system. All the conditions are presented in terms of linear matrix inequalities (LMIs), which can be easily checked by using recently developed algorithms in solving LMIs. Two numerical examples are provided to show the reduced conservatism of the main results.