This article addresses the consensus control and optimization issue for multiagent systems (MASs) with time-varying delay. Different from existing ones, an order-reduction method (ORM) is proposed to reduce the order of linear matrix inequalities (LMIs) without a complicated calculation process. The problem of complexity explosion caused by using LMI to analyze MASs is solved. To start with, we discuss and compare the existing ORMs and our ORM, respectively. Subsequently, under this improved ORM and the quadratic-delay-product method, a modified Lyapunov-Krasovskii functional (LKF) is constructed to obtain a less conservative consensus criterion. Then, we put forward a consensus controller which allows larger time delay upper bound. In addition, based on the self-adaptive differential evolution (DE) algorithm, the performance of the controller is significantly optimized. It is strictly proved that the designed controller can guarantee the realization of consensus and the LMI method used is feasible because it is independent of the number of agents. Finally, the simulation and comparison results illustrate the superiority of the theoretical results over others.

This article presents a two-degree-of-freedom structure of a fuzzy repetitive-control system that accurately tracks periodic signals and effectively suppresses aperiodic disturbances based on an enhanced equivalent-input-disturbance (EEID) method. To make full use of the learning characteristic, a 2-D model of the fuzzy repetitive-control system is established to independently regulate the control and learning behaviors. The EEID approach decouples the design of the observer and the estimator by adding a flexible controller to the estimator. This makes it possible to simultaneously reduce the estimated and filtered errors, which is a contradictory problem in the conventional EID method. The two errors cannot be eliminated due to the lack of an internal model of the external disturbance. To actively cancel the negative influence of the two errors, a new observation-error compensator is added to the observer input to improve the disturbance-suppression performance. Two low-conservative linear-matrix-inequality stability conditions are derived using the Lyapunov-Krasovskii functionals and zero equations with free-weighting matrices. The nondominated sorting genetic algorithm II and the particle swarm optimization algorithm are used to optimize the parameters of the controllers for the tracking and disturbance-suppression systems based on the stability conditions and performance indexes. The effectiveness and superiority of the design are verified by numerical simulation and comparison results.

Offshore drilling platforms are exposed to wind, waves, currents, and other unknown disturbances. Accurately estimating and rejecting these disturbances is the key to ensuring reliable station-keeping of the platforms. In this study, a novel dynamic positioning method using an improved equivalent-input-disturbance (EID) approach is proposed for offshore drilling platforms. An improved EID estimator is employed to estimate and suppress unknown disturbances, significantly enhancing the disturbance-rejection performance of the dynamic positioning system. The input channels are decoupled through linear transformation, and the parameter tuning process of the observer and controller is optimized, thus improving system performance. The bounded-input bounded-output stability of the closed-loop system is proved. This study provides insights into the design of dynamic positioning systems for offshore drilling platforms.

This study focuses on the problem of disturbance rejection in nonlinear repetitive-control systems. The conventional method for rejecting disturbance based on equivalent-input-disturbance (EID) produces phase lag and disturbance estimation errors, which limit disturbance-rejection performance. To mitigate this issue, conventional EID approaches typically use high-gain control. This study presents a new technique utilizing an improved EID estimator. The method consists of three aspects. First, the nonlinear plant is formulated using a Takagi-Sugeno fuzzy model. Second, the exogenous disturbance is treated as an EID. The phase lag caused by the EID filter is characterized based on the output error. An estimator incorporating a high-order sliding-mode observer is devised to compensate for the EID. The variable about phase lag is imposed on the observer input and the output error is reduced by fast convergence. Third, an adjustable factor is inserted into the low-pass filter to implement the tuning of the disturbance rejection bandwidth. The stability criteria and design procedures are given. In the end, the effectiveness and superiority of the developed method are demonstrated using a rotating system.

Repetitive control involves two different behaviors: continuous control in a period and discrete learning between two periods, which together determine the fast and precise tracking control. Using a 2-D method, previous methods could only preferentially design the two behaviors rather than independently, because of the coupling of control and learning in the conventional modified repetitive control, which limits further improvement of tracking performance. This article presents a generalized modified repetitive control structure that separates control and learning and allows them to be designed independently using a 2-D method. Using a Takagi Sugeno (T-S) fuzzy model and a parallel distribution compensation scheme, a linear-matrix-inequality (LMI)-based condition is derived to ensure the stability of a nonlinear repetitive-control system. Three adjustable parameters in the LMIs are used to tune the weights of control and learning. After that, dual indexes are devised to evaluate the control-learning performance, respectively. Thus, the regulation of the control-learning behavior is transformed into a standard multiobjective optimization problem. The nondominated sorting genetic algorithm-II is used to solve the problem. Finally, numerical simulations are performed to illustrate the process of independent regulation of control and learning, and experimental comparisons with related approaches are performed to show the validity and superiority.

Repetitive control has learning properties and exhibits high accuracy in periodic control but struggles with nonlinearities and disturbances. To address this issue, the study presents a composite method of repetitive control and equivalent input disturbance based on the Takagi-Sugeno fuzzy model. The control structure takes into account both the continuous-discrete two-dimensional characteristics of the repetitive control and the membership function of the fuzzy system. As the first component of the control configuration, a repetitive controller is adopted for the high-precision tracking of periodic references. Then, an equivalent-input-disturbance estimator is used to compensate for exogenous disturbances. The closed-loop system is stabilized using the state feedback and the state observer. To ensure stability, membership function-dependent Lyapunov candidates are used to derive a less conservative stability condition. Consequently, all gains in the controller switch with the derivative sign of the premise variables. Finally, the developed approach is validated through comparisons with typical methods, demonstrating its effectiveness and advantages.

This article presents an adaptive integral sliding mode control-based amplitude and phase compensation repetitive-control method that achieves precise tracking control for nonlinear systems. An adaptive integral sliding mode controller handles system nonlinearity and helps stabilize the system, thus simplifying the system structure. An adaptive law removes the requirement of knowing the nonlinear information and helps quickly enter the sliding surface. An amplitude and phase compensation repetitive controller achieves precise control of periodic signals. This controller makes small changes in the positive-feedback loop to compensate for the amplitude and phase changes caused by the low-pass filter, which greatly improves the steady-state tracking performance compared with the conventional modified repetitive controller. Simulation and experimental results verify the effectiveness and superiority.

This study presents a two-dimensional (2-D) repetitive control method to address the issues of periodic tracking and disturbance suppression in uncertain Takagi-Sugeno systems. The disturbance and uncertainty are treated as an equivalent-input-disturbance (EID). However, the conventional EID estimators typically suppress the EID through high gain. Meanwhile, the low-pass filter associated with EID causes a certain degree of phase lag. A proportional-integral (PI) filter is integrated with an EID estimator to develop a PI-EID structure to improve the estimation accuracy. Based on the self-learning mechanism of repetitive control, the 2-D repetitive controller is used to achieve a high level of tracking. Unlike the conventional nonlinear repetitive control methods, the state observer and the PI-EID estimator are membership function dependent. The gains of both controllers switch in line with the signs of the time derivative of the normalized premise variables, and this framework takes full account of the information of the nonlinear membership functions. The controller design procedures and the stability conditions are detailedly presented. Finally, a rotation speed control experiment is conducted to validate the developed PI-EID method.

This article presents a phase-compensated equivalent-input-disturbance approach-based repetitive-control system that aims to precisely track periodic signals and effectively suppress aperiodic signals. A generalized modified repetitive control, which completely separates control and learning through two gains, is constructed to achieve independent control-learning regulation without using a 2-D model. On the other hand, the low-pass filter in the equivalent-input-disturbance estimator introduces a phase offset while ensuring causality. Such a phase delay reduces the suppression accuracy of time-varying disturbances. A phase compensator is added to accurately compensate for the phase delay through detailed analysis, thus improving the disturbance-rejection performance. Finally, theoretical analysis and experimental results demonstrate the effectiveness and superiority of the method.

The disturbance rejection problem of T–S fuzzy systems is concerned. Since the T–S fuzzy system is characterised by its membership function, less conservative stabilisation conditions can be derived from membership function-dependent Lyapunov function which contributes to the improvement of disturbance rejection performance. Specifically, we utilise a configuration composed of a membership function-dependent state observer for the state estimation, a membership function-dependent equivalent-input-disturbance estimator for the estimation and compensation of disturbance and an internal model for the reference tracking. It is revealed that this membership function-dependent Lyapunov function naturally leads to control gains switching in accordance with the derivative signs of the normalised premise variables. The switching rules and the design conditions for all control gains are obtained explicitly. In particular, the free-weighting-matrix approach is used to lessen the conservatism in the stability condition. Moreover, a concrete procedure for the controller design including the switching rule is given. Finally, the developed method is tested via simulations. The advantage of the membership function-dependent equivalent-input-disturbance method is validated by comparing with conventional methods.

This study focuses on the performance design issue of nonlinear repetitive control (RC) systems subject to harmonic disturbances. First, a Takagi-Sugeno fuzzy model is used to describe a nonlinear plant. Then, a repetitive controller featuring a harmonic disturbance period is integrated with an EID estimator to form an RC-EID structure. The structure has a learning feature that gradually reduces the harmonic disturbance estimation error by self-learning. The linear inequality matrices guarantee the stability of nonlinear RC systems. A case study with two permanent magnet synchronous motors shows that the presented RC-EID estimator enhances the harmonic disturbance-suppression performance while compensating for the phase lag caused by the conventional EID filter.

This paper presents an optimization design method for a two-dimensional (2D) modified repetitive control system (MRCS) with an anti-windup compensator. Using lifting technology, a 2D hybrid model of the MRCS considering actuator saturation is established to describe the control and learning of the repetitive control. A linear-matrix-inequality (LMI)-based sufficient condition is derived to ensure the stability of the MRCS. Two tuning parameters, the selection of which is critical to the system design, are used in the LMI to adjust the control and learning, and hence the reference-tracking performance. A new cost function, developed through time domain analysis, directly evaluates the control performance of the system without calculating control errors, thus reducing the optimization time. Based on this cost function, an adaptive multi-population particle swarm optimization algorithm is presented to select an optimal pair of tuning parameters in which multiple populations cooperatively search in non-intersecting search intervals. An anti-windup term is added between the low-pass filter and the time delay in the modified repetitive controller to mitigate the undesirable effect of actuator saturation on system performance and stability. Simulations and experiments on the speed control of a rotation control system demonstrate the validity of the approach.

This paper uses the wave equation to explain the torsional motion of the drill-string system. Solving the wave equation with the D'Alembert method, a neutral time-delay model of the drill-string system is obtained. The disturbance input, caused by the bit-rock interaction, is given consideration, and an equivalent-input-disturbance (EID) based controller is designed to mitigate the disturbance in the established model. In the actual drilling procedure, the system input time-delay increases as the length of the drill columns increases. If the influence of system input time-delay in the drilling procedure is ignored, it will most likely lead to the drill-string system instability and cause serious consequences. The essential contribution of this paper is the incorporation of input time-delay into the EID based control structure. Considering the system's input time-delay, the proposed model is more practical and has significant implications for stick-slip vibration assessment and control in drilling procedures.

煤矿井下施工瓦斯抽采孔作业过程中，钻孔机器人给进系统用于钻进过程加压、减压和给进。针对复杂地层不确定性扰动影响钻孔机器人工作性能和钻孔施工质量及效率的问题，首先分析钻孔机器人的结构组成和钻进施工工艺，根据其给进系统的工作原理，建立了减压阀控制数学模型，获得了控制输入量电磁铁电流与控制输出量减压阀出口压力的映射关系，并在明确给进力驱动方式的基础上对整个给进系统进行控制建模。随后设计了钻孔机器人给进力跟踪控制系统，使用Luenburger全维状态观测器重构被控对象状态，建立基于等价输入干扰估计（EID）与补偿的控制结构，设计了状态反馈控制器、状态观测器和干扰估计器增益矩阵，实现给进力闭环控制系统稳定的同时具有满意的跟踪与扰动抑制性能。最后利用Matlab软件搭建数值仿真模型，以某煤矿井下实际钻进施工时给进系统的实测钻进数据信号为例进行仿真研究，以给进力为控制目标，实测减压阀输出压力波动为依据设计外部扰动信号，分别采用所提EID控制方法和PID控制方法进行了对比仿真。结果表明：所提方法获得了比PID方法更小的稳态跟踪误差峰峰值，且跟踪误差更小，保证了给进系统稳定运行，具有较好的跟踪与扰动抑制性能。研究结果对提高钻孔机器人适应复杂煤层负载变化，保证其工作性能和安全高效施工提供了控制理论基础。

This paper concerns the design and optimisation of two-dimensional (2D) repetitive control of nonlinear systems based on the Takagi-Sugeno (T-S) fuzzy model. First, a continuous-discrete 2D model of nonlinear repetitive-control systems based on T-S fuzzy model is constructed by utilizing the 2D characteristics of continuous control and discrete learning actions in the repetitive-control process. Next, a fuzzy Lyapunov-Krasovskii functional derives the linear-matrix-inequality-based stability condition with a low conservatism. Two positive and two nonzero parameters in the fuzzy Lyapunov-Krasovskii functional tune the control and learning actions. Then the particle swarm optimisation algorithm based on a 2D performance index searches for the best parameter combination, resulting in the optimal 2D controller gains. A numerical example is given to demonstrate the effectiveness of the method.

In this paper, the issue of disturbance rejection of nonlinear repetitive control system (RCS) based on a continuous-discrete two-dimensional (2D) model is studied. Since a RCS involves continuous control and discrete learning, higher tracking performance may be realizable by taking into account these two different actions in system design. This paper construct a fuzzy RCS based on T-S model at first. Then, an improved fuzzy-equivalent-input-disturbance (IFEID)-based 2D RCS is presented to achieve both high tracking precision of periodic input and satisfactory rejection of aperiodic disturbances. Stability conditions of two subsystems are derived by exploiting separation theorem to ease the solution of state-feedback and observer gains. A design algorithm is presented via the concept of parallel distributed compensation. A simulation and a comparison demonstrate the availability and advantage of the IFEID-based 2D RCS approach.

This paper deals with the problem of designing a two-dimensional (2D) modified repetitive-control system based on a Takagi–Sugeno (T-S) fuzzy model to achieve high tracking performance for a nonlinear plant. First, a nonlinear plant is represented by a T-S fuzzy model, and a modified repetitive controller with two repetitive loops is used to increases design flexibility. Next, a continuous-discrete 2D model is established to make use of the 2D characteristics in the modified repetitive-control system. Then, a sufficient stability condition is derived in terms of linear matrix inequalities. Three parameters are used to balance continuous control and discrete learning actions: one in a repetitive loop and two in a Lyapunov–Krasovskii functional. A particle swarm optimisation algorithm yields optimal parameters and the gains of the modified repetitive and state-feedback controllers. Finally, simulation and comparison results demonstrate the effectiveness of our method.

This paper concerns robust stabilization for a class of nonlinear systems with uncertainties and disturbaces. The equivalent-input-disturbance (EID) approach is utilized to estimate the influence of nonlinearities and exogenous disturbances on the output of the system. A robust stability condition is derived in terms of linear matrix inequalities. Moreover, two parameters are used to tune the robustness of the system. Simulation results show that it is more effective to stabilize the system using the developed method than using the sliding-mode control (SMC) method.

Aiming at the problems of slow recognition, low efficiency and degree of automation in handwritten letter recognition system at present, a handwritten letter recognition system based on extreme learning machine is designed in this paper. The system is implemented by mixed programming with MATLAB and visual studio, it can reads, normalize, binarize and extract the handwritten letter images. The real-time interactive recognition of handwritten letters can be realized on the basis of training the simple pictures by using the identification model of the extreme learning machine algorithm. The experimental results show that the handwriting recognition system based on extreme learning machine designed in this paper can recognize 98.82% of handwritten letters and greatly reduce learning and testing time. Compared with BP neural network and other recognition algorithms, its training times have been reduced by hundreds or even thousands of times. At the same time, there is no manual intervention in the entire learning and testing process, which improves the automation of handwriting recognition.