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This paper designs a preview repetitive control (PRC) policy for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and external disturbances. First, the T–S fuzzy model is employed to represent a nonlinear plant, once the nonlinear plant is represented by a T–S fuzzy model, a fuzzy improved-equivalent-input-disturbance (IEID)-based PRC law can be designed to achieve better tracking performance and disturbance rejection. Next, based on a new equality constraint, we derive a continuous-discrete two-dimensional (2D) system that paves the way to solve the design problem of the IEID-based PRC law using linear matrix inequality (LMI) approach. Then, by solving LMIs, the gains of the controller and state observer can be obtained. Finally, a numerical example is included to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A modified equivalent-input-disturbance compensation method is investigated for repetitive control systems with state time delays, which achieve effective rejection of unknown disturbance and effective tracking control of periodic reference input. By incorporating the sliding mode observer into the equivalent-input-disturbance theory, the equivalent-input-disturbance estimator structure is determined. The structure presented in this work can effectively estimate the unknown disturbance without making use of the inverse model of the system. Moreover, an asymptotic stability condition is devised to ensure that the repetitive control systems are stable, as well as the corresponding controller gains are designed with the aim to guarantee the performance of the system to suppress unknown disturbances. Numerical example simulations demonstrate the effectiveness and advantages of the devise scheme. [ABSTRACT FROM AUTHOR]

A novel multi‐input multi‐output adaptive control strategy applied to the combined active front steering (AFS) and direct yaw moment control (DYC) system is proposed in this paper. Studies have been conducted to show the potential for electric vehicles to be affected by time delay, which may appear in states. Aiming to address the state delay, radial basis function neural network (RBFNN) and Lyapunov‐Krakovskii functional‐based AFS and DYC controllers are constructed, which also can process the parameter uncertainties due to the powerful ability of RBFNN to approximate the unknown terms. Meanwhile, the controller is designed to incorporate the barrier Lyapunov function so that the state variables under control, including the sideslip angle and yaw rate, remain in their respective stable ranges while accurately tracking the corresponding desired values. Co‐simulations utilizing Simulink and CarSim are implemented for verifying the effectiveness of the proposed control scheme and comparing it with the traditional control scheme. [ABSTRACT FROM AUTHOR]

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This paper investigates the finite-horizon robust event-triggered control for nonlinear multi-agent systems (NMASs) with state delay. The consensus of NMASs has been studied extensively. Robustness, as another significant topic of NMASs, has not been given enough attention. To fill the gap in this field, we are committed to studying the robust problem for NMASs and a criterion that the robust problem of the NMASs is equivalent to the optimal problem of its nominal system is given. In terms of algorithms, compared with the traditional continuous-time policy iteration algorithm, the event-triggered policy iteration algorithm is utilized to study the event-triggered HJB equation which can effectively reduce controller updates and redundant communication. After that, through the actor-critic network with the time-varying activation function, the approximate event-triggered optimal controller for the nominal state-delay NMASs is designed. In addition, this paper also excludes the Zeno behavior of the closed-loop system. Finally, the effectiveness of the proposed scheme is further verified by two examples. [ABSTRACT FROM AUTHOR]

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and the follower in a general case. Then, we focus on the linear–quadratic (LQ) backward Stackelberg game with delay. The backward Stackelberg equilibrium is presented by the generalized fully coupled anticipated forward–backward stochastic differential delayed Equation (AFBSDDE), which is composed of anticipated stochastic differential equations (ASDEs) and BSDDEs. Moreover, we obtain the unique solvability of the AFBSDDE using the continuation method. As an application of the theoretical results, the pension fund problem with delay effect is considered. [ABSTRACT FROM AUTHOR]

We investigate infinite-time admissibility of a control operator B in a Hilbert space state-delayed dynamical system setting of the form z ˙ (t) = A z (t) + A 1 z (t - τ) + B u (t) , where A generates a diagonal C 0 -semigroup, A 1 ∈ L (X) is also diagonal and u ∈ L 2 (0 , ∞ ; C) . Our approach is based on the Laplace embedding between L 2 and the Hardy space H 2 (C +) . The results are expressed in terms of the eigenvalues of A and A 1 and the sequence representing the control operator. [ABSTRACT FROM AUTHOR]

In this paper, we discuss event-triggered consensus control for a heterogeneous second-order multi-agent systems with unknown nonlinear functions and state delays (SODMASs). Firstly, a broad adaptive dynamic event-triggered mechanism (ETM), which includes many existing ETM, is proposed. Based on this ETM and the approximation property of neural networks, an adaptive event-triggered protocol with weight estimation of neural network and time-varying integral gain compensation is designed to reduce communication frequency and to eliminate the uncertainty of nonlinear function and state delays. Then, the consensus problem for the heterogeneous SODMASs under the protocol is solved successfully by selecting a suitable Lyapunov–Krasovskii functional. In addition to these, it is also proved that all agents can exclude Zeno behavior under the proposed event-triggered protocol. Finally, a numerical example is given to verify the effectiveness of the proposed consensus protocol algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the optimal disturbance suppression problem of disturbed underwater vehicle with state delay is studied. Firstly, we establish the mathematical model of the motion of the disturbed underwater vehicle and linearize it. Secondly, the mathematical model with state delay is transformed into a formal mathematical model without time-delay by using the no time-delay transformation method. Then, according to the optimal control theory, the optimal disturbance suppression control law of the disturbed underwater vehicle with state delay is designed based on the quadratic performance index. This control law can be obtained by solving the Riccati matrix equation and Sylvester matrix equation. Finally, the effectiveness of the method is verified by an AUV system simulation example.

This paper proposes a discrete‐time sliding mode control design for a class of discrete‐time dynamic systems with time delays, parameter uncertainties, and external disturbances. The robust design implements an adaptive discrete‐time reaching law in order to reduce the effect of the chattering phenomena and improve system robustness. It also considers a lumped disturbance function for the unknown parameters and time‐delayed terms in order to estimate both at the same time. Additionally, the proposed sliding function ensures that the states of the control system are put on the switching surface right from the beginning, thus eliminating the reaching phase. The effectiveness of the proposed scheme was assessed using the longitudinal and lateral dynamics of an Osprey plane model. The obtained results indicated that the proposed approach guarantees system stability and ensures excellent tracking performance in the simultaneous presence of time delays, parameter uncertainties, and external disturbances. [ABSTRACT FROM AUTHOR]

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and the follower in a general case. Then, we focus on the linear–quadratic (LQ) backward Stackelberg game with delay. The backward Stackelberg equilibrium is presented by the generalized fully coupled anticipated forward–backward stochastic differential delayed Equation (AFBSDDE), which is composed of anticipated stochastic differential equations (ASDEs) and BSDDEs. Moreover, we obtain the unique solvability of the AFBSDDE using the continuation method. As an application of the theoretical results, the pension fund problem with delay effect is considered.

In this paper, the problem of secure state estimation for cyber physical systems (CPSs) with state delay and sparse sensor attacks is studied. An algorithm combining set cover approach and adaptive switching mechanism is proposed, which can realize off-line acquisition of candidate set and accurately locate the real attack mode. The contributions of this algorithm are that it can greatly reduce the search space, eliminate the impact of attacks on state estimation, improve the estimation speed and ensure the real-time performance of state estimation under the premise of effective estimation. The sufficient condition for the existence of the observer is obtained. Finally, the rapidity and effectiveness of the designed observer are verified by two examples.

• Bifurcation dynamic analysis of a new model for trimming process was performed by computing nonlinear stability diagrams and basins of attraction. • The undertaken investigations show a good agreement between theoretical prediction and experiments. • Whilst increasing radial depth of cut, transitions from stability to chatter and shifts between periodic and quasi-period oscillations were observed. Our previous study [1] revealed that trimming of thin-walled structures has a strongly nonlinear nature, hence this investigation delves into nonlinear dynamic analysis. Specifically, a perturbation method was applied to analyze the linear stability, whilst a direct numerical integration approach was employed to construct bifurcation diagrams, where unsafe cutting caused by multiple stabilities had been found. Basins of attraction were computed to evaluate the cutting safety. Finally, the stability charts for both linearized and fully nonlinear models were constructed showing a good degree of similarity but the linear one has a larger area of stable trimming. The data from our focused experimental studies was then superimposed on both diagrams and it is clear that more refinements in models' calibration are needed. This work has laid firm foundations for further advanced modelling investigations and experimental studies to gain more insights into nonlinear dynamics of the machining process. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper studies the problem of the secure state estimation of cyber-physical systems. The system model we studied is a class of discrete-time systems with state delay and sparse sensor attacks. In the design of the observer, a Projection Operator is utilized to determine the correct attack set, and the gain matrix will be switched accordingly. In this way, the excessive estimation error could be avoided effectively. In addition, based on the generalization of the classical Krasovskii Stability Theorem for stability analysis of time-delay systems, a Lyapunov-Krasovskii functional is chosen and a sufficient condition for the existence of the observer together with its design method is determined. The designed observer overcomes the difficulties caused by state delay and sensor attacks, and has good performance in secure estimation. Finally, two examples are given to verify that the observer can restore the desired estimate in a short time when a sudden attack occurs.

For a class of stochastic nonlinear systems (SNSs) with state delay and unknown control directions (UCDs), the global asymptotic regulation problem is investigated in this brief. Based on the key Lyapunov-Krasovskii functional (KLF), a dynamic feedback control strategy is designed to solve the time delay and UCDs problems. The proposed dynamic compensator guarantees the global asymptotic convergence of the systems state in probability at the origin and the global boundedness of the closed-loop system (TCLS) in probability. Finally, an example is given to verify the effectiveness of the developed scheme. [ABSTRACT FROM AUTHOR]

In this article, the problem of adaptive finite-time prescribed performance control (FTPPC) is discussed for stochastic non-triangular structure time-delay systems. The mean value theorem (MVT) is employed to convert the non-triangular structure systems to the equivalent systems with affine structure. A finite-time performance function (FTPF) is constructed to guarantee that the system achieves the predefined tracking accuracy within a finite time. Combining the FIPF and adaptive neural network (NN) technology, a newly controller is presented, under which both the specified tracking accuracy and convergence time can be ensured, and the whole variables in the closed-loop system are bounded in probability. Simulation results verify the effectiveness and suitability of the scheme. [ABSTRACT FROM AUTHOR]

This article deals with the robust control design for linear systems with input and state delays, subject to nonvanishing matched disturbances. The controller is synthesized with the Lyapunov redesign technique in two stages: first, an optimal predictor compensates the input delay of the nominal system while a quadratic performance index is minimized. Then, the robust component guarantees that the solutions are ultimately bounded. The theoretical results are experimentally validated through a dehydration process, with the controller digital implementation on an industrial programmable automation controller cDAQ-9132. [ABSTRACT FROM AUTHOR]

Abstract We discuss the controllability for a damped fractional differential system with impulses and state delay, which involves Caputo fractional derivatives. Deriving the condition based on the Gramian matrix defined by the Mittag-Leffler matrix function and Laplace transformation, we establish necessary and sufficient conditions of controllability criteria. Finally, we construct two numerical examples to support the result.

Abstract In this study, we are currently investigating the controllability of nonlinear fractional differential control systems with delays in the state function. The solution representations of fractional delay differential equations have been established by using the delayed Mittag-Leffler function. Firstly we obtain the result of the controllability of a linear fractional control system with delay. Then, for the controllability criteria of nonlinear fractional delay system, we establish the set of sufficient conditions of nonlinear fractional differential systems with delay in their state function by using Schauder’s fixed point theorem. In the end, a numerical example is constructed to support the results.

Abstract In this research work, we investigate the controllability of linear fractional differential control systems with state and control delay. By using an explicit solution formula, a rank criterion for controllability is established. For the controllability criteria, we establish necessary and sufficient conditions of a fractional differential systems with state and control delay. In the end, a numerical example is constructed to support the results.

This article explores the problems of robust information fusion for wireless sensor networks with state delay, parameter uncertainty, and communication constraints. Based on a data-driven transmission strategy, the robust fusion estimator proposed in this article can greatly reduce the possibility of network congestion, while ensuring the accuracy of the estimation fusion. The uncertainty of random parameters in the model is not limited to special forms, which means that this estimator is applicable to a wide range of situations. The pseudo cross covariance matrix used for estimation fusion is derived by local robust state estimation algorithm, which is based on state augmentation and expectation minimization of estimation errors. Furthermore, we prove that the error variance of this fusion estimator is uniformly bounded, and the corresponding condition is given. According to this condition, the selection of key matrices and vectors in the transmission strategy is determined. Finally, some numerical simulations are utilized to verify the performance of this algorithm.

The aim of this study is to address the challenge of H∞ filtering for 2-D systems with time delays. We will employ the well-known Fornasini-Marchesini state model with delay to mathematically describe these 2-D systems. Our objective is to develop a full-order filter that not only ensures the asymptotic stability of the expanded system but also maintains H∞ performance. Our approach will rely on Linear Matrix Inequalities (LMIs) to establish the conditions for the filter’s existence and convert the filter design problem into a convex optimization problem. Finally, we conclude with an illustrative example to demonstrate the effectiveness of the proposed filter design.

The stabilization of receding horizon control (RHC) for a class of discrete-time stochastic systems with multiple state delay is concerned. Firstly, a cost function with the type of conditional expectation is designed. Secondly, the sufficient RHC stabilization condition has been obtained in terms of a linear matrix inequalities (LMI). And under some appropriate assumptions, it is shown that the stochastic system with state delay can be stabilized in the mean square sense if the terminal weighting matrices satisfy the given inequalities. Lastly, the explicit stabilizing controller is derived by solving a finite horizon optimal control problem. Numerical examples show that the proposed RHC can effectively stabilize stochastic systems with state delay.

In this paper, the problem of secure state estimation for cyber physical systems (CPSs) with state delay and sparse sensor attacks is studied. An algorithm combining set cover approach and adaptive switching mechanism is proposed, which can realize off-line acquisition of candidate set and accurately locate the real attack mode. The contributions of this algorithm are that it can greatly reduce the search space, eliminate the impact of attacks on state estimation, improve the estimation speed and ensure the real-time performance of state estimation under the premise of effective estimation. The sufficient condition for the existence of the observer is obtained. Finally, the rapidity and effectiveness of the designed observer are verified by two examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of stability analysis, controller design, and H∞ control for singular systems with state delay and disturbance based on event‐triggered control. Firstly, the corresponding model of this system is proposed, taking into consideration issues of regular, impulse free, and stability. According to the model, the admissible condition is derived in terms of Lyapunov‐Krasovskii stability theory, and the co‐design method of the H∞ controller and event‐triggered scheme is also presented based on the above results. The presented method emphasizes the employment of event‐triggered control to a class of singular systems with time delay. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Exogenous disturbances largely affect the control performance of systems with time delays. This study considers a control problem of rejecting a disturbance in a PI control system for a time-varying state-delay plant. The equivalent-input-disturbance (EID) approach is integrated in a PI control system. An EID estimator estimates the overall effects of a time-varying delay and a disturbance. An EID estimate is combined into a PI control law to improve control performance. A less-conservative stability condition of the control system is derived using a Lyapunov–Krasovskii functional together with the Jensen's integral inequality and the reciprocally convex combination lemma. Parameters of the controllers in the system are calculated using the condition. Engine idle speed control is used to verify the effectiveness of this approach. Compared with the generalized extended-state observer and the sliding-mode control methods, our method reduced the tracking error to about one third and one sixth, respectively. This demonstrates the validity and superiority of our method. • The equivalent-input-disturbance (EID) approach is incorporated into a PI control system to improve disturbance-rejection performance. • The EID approach is also extended to deal with a time-varying delay. • A less-conservative stability condition is derived to design the gains of the PI controller and state observer. • A comparison of our method with the GESO and SMC methods for engine idle speed control show the validity of this method and its superiority over others. [ABSTRACT FROM AUTHOR]

This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDa). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation. [ABSTRACT FROM AUTHOR]

This article focuses on the model reduction problem of discrete-time time-delay interval type-2 Takagi-Sugeno (T–S) fuzzy systems. Compared with the type-1 T–S fuzzy system, the interval type-2 T–S fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties. In addition, in order to simplify the analysis process, complex high-order systems can be approximated as low-order systems, which is called model reduction. In previous studies, there are few researches on model reduction of the interval type-2 T–S fuzzy system with time delay. Hankel norm is adopted to limit the error after model reduction. Based on Jensen's inequality, a linear matrix inequality (LMI) condition for the Hankel norm performance of the error system is obtained. A membership-function-dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results. Next, by a convex linearization design, the model reduction problem is formulated as a convex LMI feasibility/optimization condition. Numerical examples are given to verify the validity of the analysis. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the iterative learning control problem for a class of discrete-time singular systems. According to the characteristics of the systems, a closed-loop PD-type learning algorithm is proposed and the convergence condition of the algorithm is established. It is shown that the algorithm can guarantee the system output converges to the desired trajectory on the whole time interval. Moreover, the presented algorithm is also suitable for discrete-time singular systems with state delay. Finally, the validity of the presented algorithm is verified by two numerical examples.

This paper presents an observer for a class of nonlinear systems, suitably affine in the input and the delayed terms, with constant, known, and arbitrarily large time-delays in both internal and output variables. It is assumed that the system at hand is globally drift-observable and that the function describing the dynamics is globally Lipschitz. Moreover, it is assumed that the system at hand admits full uniform observation relative degree. A differential geometry-based approach is followed. The well-known chain procedure is employed in order to deal with arbitrarily large output delay. It is proved that, for any given delays at states and output, there exist a suitable gain matrix and a Hurwitz matrix, involved in the observer algorithm, such that, when a sufficiently large number of chain elements are employed, the observation error converges asymptotically to zero. The effectiveness of the proposed method is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

Transmission control protocol, in the transport layer of a network, can usually detect congestion after its occurrence. Therefore, designing a robust active queue management (RAQM) is imperative to prevent congestion along with being robust against wireless environment issues such as packet error rate and fading. Moreover, a communication network suffers from input delay as well as the state delay which is multiplied to the control input signal. The main contribution of the authors' study is to design a predictive sliding mode control (PSMC) procedure as a RAQM to guarantee the input delay system stability and to regulate the queue length to the desired value. Firstly, a predictor is designed for the original system to obtain an input delay free model. Then, a RAQM is designed based on PSMC for the system with non‐singular and singular control gain. The disturbance observer ensures that the estimation error tends to zero. Unlike the prevalent procedures designed for the networks, the proposed method can avoid the singular gain problem in the control design. Furthermore, it can stabilise the system and can prevent congestion with robustness against external disturbances. Finally, the simulation results, obtained from SIMULINK and professional network simulator 2, confirm the analytical consequences. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive perimeter control problem is studied for urban traffic networks with multiple regions, time-varying state, and input delays. After defining state variables by partition the accumulation variable of each region, a system model is formulated as nonlinear ordinary differential equations based on the concept of macroscopic fundamental diagram. Both the travel times of vehicles as well as evacuation process of traffic jams are first introduced into the system dynamics, and they are modeled as input and state delays, respectively. The control objective is to stabilize the number of vehicles in each region to desired values. By employing the model reference adaptive control scheme and asymptotical sliding mode technique, two filters and adaptive laws for control parameters are designed by using only the information of the reference model. With properly constructed Lyapunov functions, the stability of tracking error with regard to the reference signals is analyzed. Lastly, a simulation example is given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

We discuss the controllability for a damped fractional differential system with impulses and state delay, which involves Caputo fractional derivatives. Deriving the condition based on the Gramian matrix defined by the Mittag-Leffler matrix function and Laplace transformation, we establish necessary and sufficient conditions of controllability criteria. Finally, we construct two numerical examples to support the result. [ABSTRACT FROM AUTHOR]

Enhancing macroscopic fundamental diagram (MFD) dynamic models and improving perimeter control algorithms are the current main research challenges in the MFD research area. Over the last decade, different accumulation-based dynamic models, describing the traffic flow dynamics of one or multi-region systems, have been developed in different forms relying on vehicle conservation equations. In this research, two enhanced accumulation-based models are developed by incorporating into model structure the time-delay (time-lag) effects as an important factor. The first model incorporates state delay in the MFD output to improve the dynamics, to better represent wave propagation and travel time evolution within the region, especially when the change in demand is fast. While in the second model delayed interconnections are introduced in the dynamic equations to model data processing and communication delays between interconnected regions. The two linearized models are formulated in interconnected forms. Then, the reference model adaptive control approach has been implemented to allow us designing distributed adaptive perimeter control laws. The developed adaptive control scheme postulates one controller structure, however, the controllers' gains vary with time to adapt themselves against the model parameter uncertainties and state delays. The numerical results demonstrate the flexibility of the distributed adaptive perimeter controllers in handling different cases and various traffic situations with state delays. [ABSTRACT FROM AUTHOR]

In this study, we are currently investigating the controllability of nonlinear fractional differential control systems with delays in the state function. The solution representations of fractional delay differential equations have been established by using the delayed Mittag-Leffler function. Firstly we obtain the result of the controllability of a linear fractional control system with delay. Then, for the controllability criteria of nonlinear fractional delay system, we establish the set of sufficient conditions of nonlinear fractional differential systems with delay in their state function by using Schauder's fixed point theorem. In the end, a numerical example is constructed to support the results. [ABSTRACT FROM AUTHOR]

In this research work, we investigate the controllability of linear fractional differential control systems with state and control delay. By using an explicit solution formula, a rank criterion for controllability is established. For the controllability criteria, we establish necessary and sufficient conditions of a fractional differential systems with state and control delay. In the end, a numerical example is constructed to support the results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of actuator fault estimation for continuous-time switched systems with state delay. The proposed fault estimation approach uses a switching proportional–integral observer which allows to obtain fast and exact fault information. Sufficient conditions are achieved by using a multiple Lyapunov–Krasovskii functional. These conditions are manipulated in a simple way in order to obtain a new linear matrix inequality different from the existing ones. To prove the effectiveness of the proposed results, an example of a switched electrical circuit is performed. [ABSTRACT FROM AUTHOR]