Distributed Adaptive Fault-Tolerant Output Regulation of Heterogeneous Multi-Agent Systems With Coupling Uncertainties and Actuator Faults

In this paper, we consider the distributed adaptive fault-tolerant output regulation problem for heterogeneous multiagent systems with matched system uncertainties and mismatched coupling uncertainties among subsystems under the influence of actuator faults. First, distributed finite-time observers are proposed for all subsystems to observe the state of the exosystem. Then, a novel fault-tolerant controller is designed to compensate for the influence of matched system uncertainties and actuator faults. By using the linear matrix inequality technique, a sufficient condition is provided to guarantee the solvability of the considered problem in the presence of mismatched coupling uncertainties. Moreover, it is shown that the system in closed-loop with the developed controller can achieve output regulation by using the Lyapunov stability theory and cyclic-small-gain theory. Finally, a numerical example is given to illustrate the effectiveness of the obtained result.      

一类具有Markov跳跃参数的不确定混合线性时滞系统鲁棒稳定性研究

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒稳定性问题．分别给出了非匹配条件下不确定部分范数上界已知时使混合线性系统以概率1渐近稳定的充分条件,和匹配条件下不确定部分范数上界未知时同样可以实现混合系统以概率1渐近稳定的鲁棒自适应控制设计方案．文章研究结果表明,此控制方案对混合线性时滞系统的不确定部分是有效的．     

非匹配不确定性影响下的无人车路径跟踪控制

针对无人车在非匹配不确定性影响下的路径跟踪控制问题,设计一种基于线性矩阵不等式（LMI）的滑模控制器.首先,根据车辆运动学和动力学方程,同时考虑轮胎侧滑造成的不确定性、车辆侧偏约束以及随机干扰影响,建立车辆非线性不确定系统模型;然后,提出一种线性滑模路径跟踪控制方法,给出线性滑模面存在的充分条件,并推导出线性滑模面存在的显式公式,以保证约束于该滑模面的降阶等价系统的二次稳定性;最后,在SerretFrenet坐标系下验证车辆单、双移线运动时的路径跟踪控制效果.仿真结果表明,所设计的滑模控制器可以保证对参考路径的稳定跟踪,具有较强的鲁棒性.     

Model Based Robust Control Law for Linear Event‐Triggered System

This paper proposes a framework to design an event‐triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event‐triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and mismatched system uncertainties. Derivation of event‐triggering rule with a non‐zero positive inter‐event time and corresponding stability criteria for uncertain event‐triggered system are the key contributions of this paper. The efficacy of proposed algorithm is carried out through a comparative study of simulation results.     

非匹配不确定系统的自适应反步非奇异快速终端滑模控制

针对一类n阶非匹配不确定系统,提出一种自适应反步非奇异快速终端滑模控制方法.控制的前n-1步采用自适应反步控制策略,消除非匹配不确定性的影响;最后一步利用误差的积分构造非奇异快速终端滑模面,设计控制律使系统第n个状态有限时间收敛.该方法对系统中匹配和非匹配不确定项均具有鲁棒性,比自适应反步终端滑模方法具有更快的收敛速度.理论分析证明了闭环系统的稳定性,仿真结果验证了该方法的有效性.     

Feedback Linearization Control for Systems with Mismatched Uncertainties via Disturbance Observers

This paper focuses on a novel feedback linearization control (FLC) law based on a self‐learning disturbance observer (SLDO) to counteract mismatched uncertainties. The FLC based on BNDO (FLC‐BNDO) demonstrates robust control performance only against mismatched time‐invariant uncertainties while the FLC based on SLDO (FLC‐SLDO) demonstrates robust control performance against mismatched time‐invariant and ‐varying uncertainties, and both of them maintain the nominal control performance in the absence of mismatched uncertainties. In the estimation scheme for the SLDO, the BNDO is used to provide a conventional estimation law, which is used as the learning error for the type‐2 neuro‐fuzzy system (T2NFS), and T2NFS learns mismatched uncertainties. Thus, the T2NFS takes the overall control of the estimation signal entirely in a very short time and gives unbiased estimation results for the disturbance. A novel learning algorithm established on sliding mode control theory is derived for an interval type‐2 fuzzy logic system. The stability of the overall system is proven for a second‐order nonlinear system with mismatched uncertainties. The simulation results show that the FLC‐SLDO demonstrates better control performance than the traditional FLC, FLC with an integral action (FLC‐I), and FLC‐BNDO.     

基于块控原理的变结构控制

针对一类非匹配不确定性的线性系统 ,基于块控原理 ,提出了一种变结构控制设计方法 .利用反演设计方法来处理系统中的非匹配不确定性 ,再用变结构控制方法来改善系统的性能 .仿真实例证明了所提出的方法的正确性和有效性     

Discrete-time sliding mode control for uncertain systems with state and input delays

This article presents a discrete-time sliding mode control method for the robust stabilisation of linear uncertain multi-input discrete-time systems with state and input delays. The systems are assumed to have structured mismatched time-varying parameter uncertainties. A specified switching surface is proposed and a sliding mode controller is derived to ensure the existence of the quasi-sliding mode. Based on the improved Lyapunov function and linear matrix inequality technique, delay-independent sufficient conditions for the design of a stable switching surface are given and the stability of the overall closed-loop system is guaranteed. Neither chattering phenomenon will occur nor the knowledge of upper bound of uncertainties is required. Finally, simulation results demonstrate the efficacy of the proposed control methodology.     

不匹配不确定性系统的近似变结构输出跟踪控制

针对一类具有不匹配不确定性的非线性系统,提出一种结合变结构控制方法及自适应控制方法输出跟踪控制器。首先提出一种保证不确定性系统跟踪误差指数稳定的近似变结构控制器;进而得到一种具有不确定性范数上界估计能力的自适应近似变结构控制器,并证明了所提出的自适应近似变结构控制器使跟踪误差在时间趋于无穷时收敛于零。     

基于RBF神经网络的块控制器设计

针对一类非匹配不确定性的线性系统,基于块控原理,提出了一种结合块控制、神经网络控制和backstepping控制技术的设计方法。利用反演设计方法来处理系统中的非匹配不确定性,利用神经网络来估计系统中的不确定性,再利用鲁棒控制方法来改善系统的性能,利用Lyapunov稳定性定理证明了系统的渐近稳定性。最后,给出的仿真实例证明了所提出的方法的正确性和有效性。     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

A novel interpretation of the invariance condition of mismatched uncertain large-scale systems

This paper presents a novel interpretation of the invariance condition of mismatched uncertain large-scale systems in which uncertainties and interconnections do not satisfy the conventional invariance condition. A new sliding mode that consists of two sets of switching surfaces is proposed. In every subsystem, uncertainties and interconnections are all separated into matched and mismatched components to reduce the conservatism. As a result, new invariance conditions are derived such that each subsystem in the new sliding mode is completely invariant to both uncertainties and interconnections. We also show that these conditions are not only necessary but also sufficient. In addition, sufficient conditions are derived such that the equivalent reduced-order system in the new sliding mode is asymptotically stable within the framework of linear matrix inequalities. A decentralized controller is synthesized to assure stability of the overall system. Finally, illustrative example is given to show the effectiveness of the proposed approach.     

Variable structure control of dynamical systems with mismatched norm-bounded uncertainties: An LMI approach

In this paper, we propose a new sliding surface design method for a class of uncertain systems with mismatched unstructured uncertainties. We relax the matching assumption of traditional VSC design methods, and the uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as the input matrix. In terms of linear matrix inequalities (LMIs), we give a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. We give an LMI parameterization of such sliding surfaces together with a switched feedback control strategy. We also give an LMI existence condition of linear sliding surfaces guaranteeing the prescribed decay rate. Finally, we give simulation results to show the effectiveness of our method.     

Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.     

一类非匹配不确定性系统的变结构控制

研究一类非匹配不确定性系统的变结构控制问题. 引入适当的状态变换, 将非匹配不确定系统描述成具有分级形式的两个子系统. 在保证第一个子系统二次渐近稳定的条件下, 利用线性矩阵不等式方法得到第二个状态变量的期望值, 并由第二个状态变量与其期望值之差构造滑动模, 并利用滑模运动的到达条件, 得到变结构控制律.     

非匹配不确定和状态时滞扰动下的车道线保持

针对车道线保持控制中存在的不确定性扰动及时滞问题, 提出一种自校正滑模控制方法. 该方法利用线性矩阵不等式理论给出滑动模态存在的充分条件; 系统在滑动模态下对于存在的非匹配不确定性扰动以及状态时滞具有完全不变性. 接下来引入双极性sigmoid函数代替常规滑模控制中的符号函数并设计自校正律; 在自校正律的作用下使sigmoid函数的边界层厚度以及切换增益可根据系统状态进行自适应调节, 从而达到削弱控制器输出抖振的目的. 基于Lyapunov理论对该方法的稳定性进行了证明, 最后通过车辆的车道线保持仿真实验对该控制方法的可行性及有效性进行了验证.     

Output feedback variable structure control for linear systems with uncertainties and disturbances

This paper proposes a dynamic output feedback variable structure controller for linear MIMO systems with mismatched and matched norm-bounded uncertainties and matched nonlinear disturbances. The proposed controller consists of nonlinear and linear parts, similar to the unit vector type of controller. The nonlinear part of the new controller takes care only of matched uncertainties and disturbances and, on the other hand, the linear part with full dynamics completely handles mismatched uncertainties. Designing such a linear part leads to use a Lyapunov function associated with the full states, which achieves the global stability against the mismatched uncertainties. The resulting criteria are, furthermore, converted into solvable ones, by using the so-called cone complementary linearization algorithm for bi-convex problems.     

Extended sliding mode observer-based high-accuracy motion control for uncertain electro-hydraulic systems

In this paper, a novel robust backstepping control strategy is introduced to achieve high-accuracy tracking performance for electro-hydraulic servo systems (EHSSs) without velocity information in the presence of uncertainties and disturbances. Firstly, system dynamics of the studied EHSS considering parameter deviations, modeling errors, and unknown external loads which are grouped into lumped mismatched and matched disturbances in the mechanical system and pressure dynamics, respectively, are developed. On the basis of the sliding mode theory, two extended sliding mode observers (ESMOs) are originally established to simultaneously estimate the immeasurable angular velocity of the actuator, and lumped mismatched and matched uncertainties. As a consequence, an observer-based controller is designed using the conventional backstepping technique to ensure a highly accurate tracking position control. In addition, the stability of the observer and overall closed-loop control system is conclusively proven through the Lyapunov theory. Finally, several numerical simulations for an EHSS with a hydraulic rotary actuator are conducted to demonstrate the advantage of the recommended method compared to the existing well-known extended state observer-based control approaches.     

线性时滞不确定系统的鲁棒稳定控制

对于线性时滞不确定系统,给出一种鲁棒渐近稳定控制器的设计方法,且对匹配与不匹 配两类不确定系统进行了研究.与现有结果相比,按此方法设计的系统不但控制器增益较小, 实现方便,而且可以容许较大的系统不确定性.     

Decentralised variable gain robust controller design for a class of large-scale interconnected systems with mismatched uncertainties

In this paper, we propose an LMI-based design method of a decentralised variable gain robust controller for large-scale interconnected systems with mismatched uncertainties. The mismatched uncertainties under consideration are composed of the matched part and the mismatched one, and the proposed decentralised robust controller consists of a state feedback with a fixed gain and one with a variable gain tuned by parameter adjustment laws. Sufficient conditions for the existence of the proposed decentralised variable gain robust controller are given in terms of linear matrix inequalities (LMIs). Finally, a numerical example is illustrated to validate the proposed design procedure.