Time-varying State Delays Research Articles

Output feedback based robust iterative learning control via a heuristic approach for batch processes with time-varying state delays and uncertainties

This paper proposes an output feedback (OF) based PD-type robust iterative learning control (ILC) scheme for a class of discrete batch processes with time-varying delays and uncertainties in the absence of accurate state measurements, which is convenient for practical applications. Based on a repetitive process model and Lyapunov–Krasovskii theory, sufficient conditions are established in terms of linear matrix inequalities (LMIs) to ensure the robust stability along the trial for all admissible uncertainties. A two-stage heuristic approach is developed to iteratively calculate the feasible ILC gains based on a pre-designed state feedback (SF) controller, which circumvents the non-convex stability conditions expressed in bilinear matrix inequalities caused by OF. In addition, the conditions can be extended to the case of non-repetitive uncertainties in the system and meet the prescribed H∞ performance level. Finally, a simulation of injection molding process is given to demonstrate the effectiveness of the proposed method.

Adaptive tracking control for a class of stochastic nonlinearly parameterized systems with time-varying input delay using fuzzy logic systems

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.

H∞ controller design for singular Markov jump systems with time-delays

In this article, the [Formula: see text] control problem of a class of singular Markov jump systems with time-varying inputs and state delays is investigated. Based on the Lyapunov stability theory, by constructing a different Lyapunov–Krasovskii functional, the sufficient conditions of being stochastic stable and having H∞ performance index are given. Then, the design method of state feedback controller is given to ensure the closed-loop system is stochastic stable and has [Formula: see text] performance index. Finally, simulation examples are given to verify the effectiveness of the proposed methods.

Finite-time H∞ synchronization control for coronary artery chaos system with input and state time-varying delays.

This is the first time for studying the issue of finite-time H∞ synchronization control for the coronary artery chaos system (CACS) with input and state time-varying delays. Feedback control is planned for finite-time of synchronization CACS. By constructing the Lyapunov-Krasovskii functional (LKF) is derived for finite-time stability criteria of CACS with interval and continuous differential time-varying delays. We use Wirtinger-based integral inequality to evaluate the upper bound of the time derivative of the LKF. We apply the single integral form and the double integral form of the integral inequality, according to Wirtinger-based integral inequality, to ensure that the feedback controller for synchronization has good performance with disturbance and time-varying delay. The new sufficient finite-time stability conditions have appeared in the form of linear matrix inequalities (LMIs). Numerical checks can be performed using the LMI toolbox in MATLAB. A numerical example is presented to demonstrate the success of the proposed methods. This resultant is less conservative than the resultants available in the previous works.

Dynamic anti-windup design for linear systems with time-varying state delay and input saturations

This paper considers the dynamic anti-windup design problem for linear systems with time-varying state delay, input saturations and external disturbances. A dynamic anti-windup compensator is first designed that is dependent on the upper bound of the time-varying delay. Then, using an augmented Lyapunov–Krasovskii functional, a distributed-delay-dependent sector condition, some advanced inequalities and some congruence transformations, sufficient conditions are established under which the state trajectories of the closed-loop systems are bounded and meanwhile, the performance can be guaranteed. The anti-windup compensator gain can be explicitly solved by means of linear matrix inequalities. For the case of constant delay, the corresponding result is also presented. Finally, two numerical examples illustrate the effectiveness and advantages of the proposed results.

Observer-Based Control Design for Nonlinear Systems With Unknown Delays

In this brief, we study the problem of designing observer-based controller for nonlinear system subject to unknown time-varying state delay. The unknown delay is assumed to be upper bounded, but nevertheless the bound is not required to be known. In order to tackle this interesting problem, we utilize a Halanay-inequality-based criterion which can guarantee exponential stability of the closed-loop system as well as the estimation error system. This exponential stability criterion allows us to design observer-based controller for the nonlinear time-delay system without invoking differentiability assumption on the unknown delay. A robotic system is considered to illustrate the efficiency of the new results.

Position Tracking Control of Robotic System with Time-varying Delay and Dead-zone

This paper studies the position tracking control problem of nonlinear robotic system subject to time-varying state delay and input dead-zone. The input dead-zone and unknown external disturbance are regarded as the lumped disturbance and a sliding mode disturbance observer is designed. In order to ensure the stability of the robotic system with time-varying state delay, a position tracking controller based on auxiliary position tracking error functions is designed. Considering the estimated error of the sliding mode disturbance observer, a gain adaptive law is designed to further improve the position tracking accuracy of the system. The stability of the proposed controller is theoretically proved by Lyapunov-Krasovskii function method, and the effectiveness of the controller is verified by comparative simulations. The proposed control method can achieve stable and accurate position tracking of the robotic system with simultaneous time-varying state delay and input dead-zone.

Robust Fault Estimation Based on Proportional Differential (PD) Learning Observer for Linear Continuous-time Systems with State Timevarying Delay

Robust Fault Estimation Based on Proportional Differential (PD) Learning Observer for Linear Continuous-time Systems with State Timevarying Delay

Further results on finite-time stability of neutral nonlinear multi-term fractional order time-varying delay systems

In this paper, the finite-time stability for nonlinear neutral multi-term fractional order systems with time-varying input and state delays is investigated. By use of the generalized Gronwall inequality and extended form of the generalized Gronwall inequality, new sufficient conditions for finite-time stability of such systems are obtained. Finally, numerical examples are given to illustrate the effectiveness and applicability of the proposed theoretical results.

Event-triggered sliding mode scaled consensus control for multi-agent systems

In this paper, the scaled consensus problem for discrete-time multi-agent systems is investigated via event-triggered sliding mode control approach subject to unknown external bounded disturbance and time-varying state delay. A new event-triggered integral sliding surface function is introduced to handle the external disturbances. Then, a distributed event-triggered control method is integrated with sliding mode control to address the energy-constrained issue in the scaled consensus problem. Subsequently, a sufficient condition is established to ensure a predefined H∞ performance can be achieved for the underlying system. Furthermore, an event-triggered sliding mode control protocol is developed to guarantee the state trajectories of all agents approach the dictated scales in the discrete-time multi-agent systems. A numerical example is given to demonstrate the effectiveness of the proposed design techniques.

PdI Regulation for Consensus: Application to Unknown Pure-Feedback Agents With State and Communication Delays

A novel proportional and delayed integral (PdI) transformation is proposed that recasts the cooperative control problem with communication delay to a simpler regulation problem. The PdI transformation enables the use of classical control techniques for solving leaderless consensus problems. Following this approach, we address for the first time the problem of leaderless consensus of heterogeneous multiagent systems in unknown pure-feedback form with state and communication time-delays and unknown disturbances. A general form of state delays is studied, which includes time-varying and distributed state delays among others. Retarded functional differential equations formalism is adopted in order to allow agent dynamics with such general state delays. The proposed algorithm guarantees that all closed-loop signals remain uniformly bounded and that the multiagent system achieves approximate consensus with prescribed steady-state error. Numerical simulations on a swarm of unmanned aerial vehicles verify the validity of the theoretical analysis.

Adaptive Fuzzy Consensus Tracking Control for Nonlinear Multiagent Systems with Time-Varying Delays and Constraints

This paper proposes an adaptive fuzzy distributed consensus tracking control scheme for a class of uncertain nonlinear dynamic multiagent systems (MASs) with state time-varying delays and state time-varying constraints. The existing controllers with Lyapunov–Krasovskii functions (LKFs) were not suitable to address time-varying delays and time-varying constraints in nonlinear MASs simultaneously. State constraints further increase the difficulty of controller design and stability analysis, especially for nonstrict feedback systems. Fuzzy logic systems (FLSs) tackle the approximation of unknown dynamics functions and parameters. Especially when the distributed consensus tracking error is infinitely close to the origin, although there is no singular value, it would lead to the rapid growth of control rate or uncontrollability. Constructing appropriate piecewise functions can effectively avoid the above occurrence and accelerate convergence. Based on Lyapunov stability theory and algebraic graph theory, the constructed tracking control can ensure states within defined time-varying constraint bounds and eliminate the influence of time delays. All signals in closed-loop systems can be guaranteed semiglobally uniformly ultimately bounded (SUUB). Finally, the validity of the theoretical method is verified by the simulation.

Design of Sliding-Mode-Based Control for Nonlinear Systems With Mixed-Delays and Packet Losses Under Uncertain Missing Probability

This paper is coped with the robust sliding-mode-based control problem for a class of discrete nonlinear systems in the presence of mixed-delays and packet losses with uncertain missing probability. Both the time-varying state delays and the infinite distributed state delays are considered. Also, the data packet losses are modeled by a Bernoulli distributed stochastic variable with uncertain missing probability and an update rule is employed to characterize the signal transmitted to controller side. A sliding function is first constructed and the desired stochastic mean-square stability of sliding motion is ensured by providing a sufficient condition based on the matrix inequality technique. Besides, a new discrete SMC strategy is designed to guarantee that the state trajectories are driven onto the bounded band of predesigned sliding surface and maintain them therein during subsequent time. Finally, the effectiveness of the developed sliding-mode control technique is verified by some simulations with comparative results.

Dynamic event-triggered output feedback control for a class of nonlinear systems with time-varying delays

This note studies the problem of dynamic event-triggered output feedback control for a class of nonlinear systems under homogeneous growth condition with unknown growth rate and time delays. Firstly, in order to deal with unknown growth rate and time-varying state delays, a double-gain dynamic scheme is introduced and a suitable Lyapunov–Krasovskii functional is selected. Secondly, a dynamic event-triggered strategy is proposed by introducing the dynamic gain to the event-triggered condition, which makes the triggering threshold be tuned dynamically. Compared with some existing works related to event-triggered strategy, the proposed strategy is more flexible for saving communication resources. Subsequently, a new output feedback control law is developed in the context of event-triggered mechanism to guarantee the boundedness of system signals while the system states globally enter a compact set around the origin. Finally, two examples are given to show the feasibility and merit of the presented scheme.

Formula omitted] filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system’s matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H∞ filtering approach are demonstrated via a practical example.

Distributed $${H_\infty }$$ State Estimation in Sensor Network Subject to State and Communication Delays

The distributed $$H_\infty $$ state estimation of delayed sensor network is dealt with in this paper. To deeply reflect the time-delay phenomenon in the process of information fusion, a model containing state time-varying delay and different communication delays is set up. Afterwards, a fresh Lyapunov–Krasovskii functional (LKF) is given, which contains different kinds of time delays, delay-dependent matrix and multiple integral terms. Meanwhile, in order to cooperate with the constructed LKF to bring down the conservatism of the result effectively, relaxed-function-based single integral inequality and convex combination are employed to estimate the functional derivative. Thus, a less conservative criterion is gained to guarantee the asymptotic stability with desirable attenuation level of the estimation error system. Several simulation examples are used to testify the validity of the proposed approach.

A New Robust Adaptive Sliding Mode Control for Discrete-Time Systems With Time-Varying State Delay

This article proposes a novel robust adaptive sliding control mode law for time unknown varying delay in state uncertain systems. In this work, the upper limit of disruption and uncertainty is assumed to be unknown. The model is adjusted so that the system looks like a certain one with unknown added disturbances on the bounds of which are unknown too. Accordingly, new control law for this kind of systems has been defined based on a Lypunov function choice. The main results of this paper are that the conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices and the determination of the control law based on a sliding surface will converge to zero. This proposed approach has been validated in simulation on an uncertain system with comparative study proved the efficiency of the proposed resulting methodology after has been validated in real system.

Asynchronous $$H_{\infty }$$ Control of Uncertain Switched Singular Systems with Time-Varying Delays

This paper is concerned with the problem of $$H_{\infty }$$ control for a class of uncertain switched singular systems with time-varying state delays under asynchronous switching. The asynchronous phenomenon is caused by the choice of controller lagging behind the corresponding subsystem in practice. First, sufficient conditions by finding a novel piecewise Lyapunov–Krasovskii function combining with average dwell time technique are given to guarantee the exponential admissibility of the system. The algebraic equations and differential equations of the original system are proved to be exponentially stable. Then, a condition guaranteeing the $$H_{\infty }$$ performance of the original system is derived based on the above analysis. Furthermore, strict LMI formulas for solving the state feedback controller are given. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

Event-triggered observer-based H ∞ control of switched linear systems with time-varying delay

This paper is devoted to study the issue of event-triggered observer-based control of switched linear systems subject to time-varying state delay and exogenous disturbance. Firstly, an observer-based event-triggered controller is provided under the proposed event-triggered mechanism. Then, based on the average dwell time scheme and Jensen's Inequality technique, delay-dependent less conservative sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are obtained to guarantee the resulting augmented switched systems is exponential stabilisation and satisfies a prescribed control performance. Furthermore, observer-based event-triggered controller is designed, and it is shown that there exists a positive lower bound of inter-event intervals. Finally, numerical example and comparison results are provided to illustrate the effectiveness and advantages of the proposed method.

Finite-Time Tracking Control for Nonstrict-Feedback State-Delayed Nonlinear Systems with Full-State Constraints and Unmodeled Dynamics

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.