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This paper is concerned with the input delay compensation problem for neutral-type systems with both state and input delays. Single/various cascaded-observers based output feedback controllers are designed to predict the future states such that the input delay that can be arbitrarily large yet exactly known is compensated completely. Compared with the existing techniques, some more simple necessary and sufficient conditions guaranteeing the stability of the closed-loop systems are offered in terms of the stability of retarded-type time-delay systems referred to as observer-error systems. Finally, the lossless transmission line control system is worked out to illustrate the effectiveness of the proposed controllers.

This study presents an approach to the H∞ control of linear input-delay systems. First, an H∞ state predictor is introduced for dead-time systems with disturbance input and measurable outputs. The author's proposed method focuses on optimisation of the disturbance propagation in sequential sub-predictors (SSP). Each of the predictors is employed to forecast the state for one portion of the delay. The H∞ performance of the prediction error can be improved by increasing the number of predictors. Consequently, an H∞ controller is designed for the standard H∞ problem of dead-time systems using SSP. More importantly, the SSP method is extended to the robust H∞ control in presence of uncertainties. Some examples are given to illustrate the effectiveness of proposed method.

In this paper, the problem of adaptive optimized tracking control design is addressed for a class of nonlinear systems in strict-feedback form. The system under consideration contains input delay and has unmeasurable and restricted states within predefined compact sets. First, neural networks (NNs) are employed to approximate the unknown nonlinear dynamics, and an adaptive neural network (NN) state observer is constructed to compensate for the absence of state information. Additionally, by utilizing an auxiliary system compensation method alongside the backstepping technique, the impact of input delay is eliminated, and the generation of intermediate variables is prevented. Second, tan-type barrier optimal cost functions are established for each subsystem within the backstepping method to prevent the state variables from exceeding preselected sets. Moreover, by establishing both actor and critic NNs to execute a reinforcement learning algorithm, the optimal controller and optimal performance index function are evaluated, while relaxing the persistence of excitation condition. According to the Lyapunov stability theorem, it is demonstrated that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the output signal accurately tracks a reference trajectory with the desired precision. Finally, a practical simulation example is provided to verify the effectiveness of the proposed control strategy, demonstrating its potential for real-world implementation.

In this paper, an adaptive dynamic surface control (DSC) strategy is studied for high-order nonlinear systems with unknown time-varying input delay and unmodelled dynamics. An error transform for a high-order nonlinear system is established by introducing an integral term and utilizing an upper bound of the input delay. On this basis, a new Lyapunov functional applicable to higher order systems is constructed, and with the help of integral mean value theorem, the unknown input delay is effectively handled. By using inequality transformation technique and selecting appropriate virtual controllers, the control error term caused by power disturbances in high-order nonlinear systems is eliminated, overcoming the difficulties in designing controllers for high-order systems with unknown input delays. The uncertainty of the system is processed by using dynamic signals and radial basis function neural networks. An adaptive tracking control scheme is designed to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the scheme is verified through simulation examples.

This paper investigates the problem of adaptive optimal tracking control for full-state constrained strict-feedback nonlinear systems with input delay. To facilitate the study, a novel control approach is developed by combining the backstepping design technique and adaptive dynamic programming (ADP) theory. At first, an intermediate variable is introduced to approximate the input delay using Pade approximation. Then, barrier Lyapunov functions are incorporated into the backstepping procedure to handle the state constraints. Moreover, neural networks are employed to approximate unknown functions in the presence of uncertainties. Based on this, an adaptive backstepping feedforward controller is developed, which converts the tracking task into an equivalent regulation problem for the affine form nonlinear system. To obtain the optimal control of the affine form nonlinear system, a critic network is constructed within the ADP framework to approximate the solution of Hamilton–Jacobi–Bellman equation, and online learning is utilized to obtain the optimal feedback control. The resulting controller consists of feedforward and feedback parts. Meanwhile, all signals in the closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, the effectiveness of the proposed control scheme is illustrated through a numerical example.

Motor dynamics in antagonistic variable stiffness actuator (AVSA) is generally disregarded in control system design. This ignorance can lead to an inaccurate system model, affecting the performance of the closed-loop system. The motor dynamics can be modeled as an input-delay in actuator model. In this paper, the motor dynamics is modeled as the input time-delay for an AVSA for the first time. The stiffness of AVSA is a nonlinear function of system states; thus, stiffness tracking for an AVSA is a challenging task. Specifically, many of the existing delay compensation controllers cannot be used for stiffness tracking when the model contains input delay. To handle this issue, a nonlinear transformation is introduced and a super-twisting sliding mode control is then utilized to reach position and stiffness tracking simultaneously. Prediction-based feedback is involved together with some disturbance observers for estimating the external disturbance to compensate for the input time-delay. Simulation results show that the proposed design approach is successful in position and stiffness tracking and simultaneously in attenuating the external disturbance effect.

This paper studied the problem of stability and stabilization for a coupling permanent magnet synchronous motors (CPMSMs) system with input delay. Input delays caused by communication or calculation were firstly considered in CPMSMs system. Firstly, the mathematical model of the CPMSMs system with input delay and nonlinear constraints was established, in which the input delay is modeled as: time-invariant input delay and time-varying input delay. Then, two novel Lyapunov–Krasovskii (L–K) functionals were constructed for different input delays. Furthermore, based on the proposed L–K functionals, stability conditions and synchronization controllers were derived in the form of linear matrix inequalities. Finally, the effectiveness of the proposed control strategy was shown by simulation results.

This paper deals with control design for interconnected nonlinear systems with time-varying input delay. Based on the truncated prediction of the system state over the delay period, the state feedback control law is constructed. In the framework of the Lyapunov–Krasovskii function, the stability equations of closed-loop system under state feedback law are established, and the feasibility of the controller is transformed into the problem of establishing a set of linear matrix inequality (LMI) conditions. Based on the Lyapunov stability theorem, it is proved that the closed-loop system is asymptotically stable. Finally, a simulation example is provided to demonstrate the effectiveness of the control scheme.

This paper addresses the new output-feedback H ∞ control problem for active half-vehicle suspension systems with time-varying input delay. By introducing multi-objective synthesis, a new dynamic output-feedback H ∞ controller is designed such that the closed-loop suspension system is asymptotically stable with guaranteed robust performance in the H ∞ sense. The proposed controller is formulated in terms of linear matrix inequality (LMI) based on the auxiliary function-based integral inequality method and the reciprocally convex approach. A new delay-dependent sufficient condition for the desired controller offers a wider range of control input delay. Numerical examples are provided to validate the effectiveness of the proposed design method.

This paper presents a function approximation technique (FAT) including a fractional-order (FO) compound learning controller in the framework of backstepping algorithm. The controller is applied to uncertain fractional-order nonlinear systems with time-varying input delay in the presence of unknown external disturbances. An FAT is adopted in the learning-based design to identify unknown terms in the system description. In addition, a FO-augmented controller compensates the delay effects and a FO command-filtered algorithm copes with the complexity of the backstepping-based design. The approximation of the FAT learning process is also considered by defining a prediction error, which is derived from the FO serial–parallel identifier. FO compound adaptive laws are then proposed. The stability of the overall system is verified through a Lyapunov analysis. The proposed concepts are illustrated using numerical examples.