Consensus Tracking Control of Uncertain Multiagent Systems With Sampled Data and Time-Varying Delay.

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

This paper establishes a framework for stability analysis and memoryless state-feedback control synthesis of linear discrete-time systems with time varying state delay. The underlying idea is converting the considered system into an equivalent constrained switched system, leading to sufficient and necessary condition for stability analysis. Based on this switched system modeling, available information about the time-varying delay such as known bounds of variation rate can be incorporated into the analysis in a natural way. Moreover, sufficient conditions for memoryless state-feedback control design are obtained in a similar style. The analysis and synthesis conditions are given in terms of solvability of a set of linear matrix inequalities (LMIs). Numerical examples are included for illustration.

This article addresses the finite-time consensus tracking control problem for nonlinear multiagent systems (MASs), in which state variables are unmeasured and nonlinear functions are totally unknown. An observer is designed to estimate state variables and fuzzy-logic systems are employed to approximate nonlinearities. Then, an observer-based adaptive fuzzy consensus tracking controller is developed by using the backstepping technique and constructing a novel barrier Lyapunov function with the consideration of the characteristics of MASs. The proposed control protocol can guarantee that: 1) all signals in the closed-loop system keep bounded and 2) the consensus tracking error converges to a prespecified region of the origin in the prescribed finite time. Compared with the existing observer-based finite/fixed-time control protocols, the settling time and the convergence region in our work can be both preassigned by the designer and not affected by the unknown positive constant, which lies in the Lyapunov derivative inequality. Finally, two comparison simulation examples, including a numerical example and a practical example, check the availability of the designed control scheme.

In this paper, we propose a new adaptive cooperative tracking control algorithm for a class of uncertain nonlinear multiagent systems with unknown control coefficients. It is assumed that there exist parametric uncertainties and unknown dynamics with the informed agent as well, and only a limited number of agents have the access to the state value of the informed agent. The proposed adaptive cooperative tracking control solves the problem of making all agents asymptotically track the desired trajectory specified by an informed agent based on the use of neural network parameterization of unknown dynamics of agents. The unknown bounds of neural network approximation errors are also estimated online. Using Lyapunov stability theorem, it is rigorously proved that asymptotically cooperative tracking can be achieved under the assumption that the sensing/communication topology among agents is undirected and connected. A simulation example is given to illustrate the effectiveness of the proposed control design.

Adaptive event-triggered tracking control for strict-feedback nonlinear ODE cascaded n+1 coupled hyperbolic PDE systems.

Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

Neural network-based adaptive finite-time tracking control of switched nonlinear systems with time-varying delay

This paper concerns the problem of adaptive compensation tracking control for a class of time-varying delay nonlinear systems with unknown structures and unknown actuator dead zones where time-varying delays are unknown. First, a variable separation approach is used to overcome the difficulty in dealing with a nonstrict-feedback structure, and multilayer neural networks are used to approximate the unknown nonlinear structures with time-varying delays. On this basis, we designed an adaptive multilayer neural-network compensation controller to reduce the error of multilayer neural networks. Furthermore, for unknown actuator dead zones, this paper separates the controller and adopts multilayer neural networks to deal with unknown actuator dead zones. In order to reduce the error of the dead-zone controller, wer designed an adaptive compensation controller for the dead zones. Lastly, this paper proves the stability of the systems with the Lyapunov method, and simulation results demonstrate the effectiveness of the scheme.

The robust passivity synthesis problem is addressed for a class of uncertain delayed systems with time-varying delays in both state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all the matrices of the model. The problem aims at designing an observer-based dynamic controller that renders the closed-loop systems strongly robustly stable with strictly passive for all admissible uncertainties, dependently of the maximum of delay derivative. By converting the problem at present into a class of strongly stable with strictly passive control problem for some parameterized systems equivalently, the explicit solution is established and expressed in terms of a linear matrix inequality.

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario. Copyright © 2016 John Wiley & Sons, Ltd.

This research paper deals with a novel delay-range-dependent approach for observer design for systems with time-varying delay in the state variables and the output measurement vector. Lyapunov Karasovskii (LK) functional, Jensen's inequality and linear matrix inequality(LMI) tools are employed to derive the stability conditions ensuring the state estimation error to asymptotically converge to the origin. Further, as particular cases of proposed design methodology, delay-range-dependent design conditions are separately deduced for systems with state delays or output delays. Numerical example is simulated to validate the efficiency of the derived results.

This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinear systems with time-varying input delays, and the nonlinear functions of the systems are with not only the unknown parameters but also the unknown state time-varying delays, which is different from the previous work. In this paper, through a state transformation, the system can be easily transformed into a system without the time-varying input delay; the appropriate Lyapunov–Krasovskii functionals are used to compensate the unknown time-varying delay terms, and the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. Fuzzy logic systems (FLSs) in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is designed. The three main advantages of the developed scheme are that (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS; (ii) the number of the adjusted parameters only depend on the order of the investigated systems, which can reduce the computational burden greatly; and (iii) the existence of the time-varying input delay such that the controller design becomes much more difficult, and in this paper, it can be dealt with by using an appropriate state transformation. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded in probability, whereas the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.

This paper deals with the design of fuzzy controllers for Takagi–Sugeno (T-S) fuzzy models with state time-varying delays. New relaxed delay-dependent conditions for the stabilization purpose are proposed in terms of linear matrix inequalities (LMIs), including the knowledge of the bounds of the time-varying delay and its rate of variation. The conservatism improvement is brought through three points: (1) the choice of a convenient augmented Lyapunov–Krasovskii functional candidate, (2) the application of an extension of the Jensen’s inequality, and (3) the Finsler’s lemma. In this context, a parallel distributed compensation control law, which includes both memoryless and delayed state feedbacks, is considered. To apply such control law, it is required to assume that the time-varying delay is available online. Under this assumption, it is highlighted that the proposed LMI-based conditions are significantly relaxed for high rate of variation of the time delay. On the other hand, when this assumption cannot be guaranteed, straightforward corollaries are proposed. A numerical example is provided to illustrate the effectiveness of the proposed LMI-based conditions and their conservatism improvement regarding to previous results.

In this paper, we consider the problem of designing distributed adaptive consensus tracking controllers for multiple nonlinear systems with unknown parameters and external disturbances. The desired trajectory is time varying given by the state of a reference system, which is only available to a portion of the group of the systems. Besides, the dynamics of the reference state is bounded but unknown to all of the systems. The communication graph characterizing the interactions among the systems is assumed to have undirected, fixed and connected topology. By introducing distributed estimators for the bound of the reference dynamics, two control schemes are proposed to address the problem. In the first scheme, a sign function is employed and perfect consensus tracking can be achieved. In the second scheme, an alternative control law is developed and the chattering phenomenon caused by the sign function can be reduced. However, new challenge will be triggered which is to compensate for possible destabilizing effects of the coupling elements relating to local parameter estimation errors and the synchronization errors of the neighbors. The overall communication graph is firstly reduced to an undirected spanning tree with single system notified of the reference state. Based on this, new synchronization error for each subsystem is then defined as the weighted distance relative to only one of its neighbors. It is shown that all the synchronization errors will converge to a prescribed bound which can be made as small as desired in this case.

This brief revisits the robust H∞ filter design problem for systems with a time-varying state delay by an indirect approach. By employing a two-term approximation method, the filtering error system with a time-varying delay is reformulated into a feedback interconnection form, which contains a forward system with two constant time delays and a feedback system with uncertainties. Then, based on the scaled small gain theorem, the asymptotic stability of the filtering error system is examined, and a new delay-dependent bounded real lemma (BRL) is obtained. Based on the BRL, both the full- and reduced-order filter design approaches are proposed. Moreover, immediate extensions of the results are made to systems with polytopic uncertainties. Finally, two illustrative examples are presented to demonstrate the validity of the proposed methods.