不确定非线性系统的自适应反推高阶终端滑模控制

针对一类非匹配不确定非线性系统,提出一种神经网络自适应反推高阶终端滑模控制方案.反推设计的前1步利用神经网络逼近未知非线性函数,结合动态面控制设计虚拟控制律,避免传统反推设计存在的计算复杂性问题,并抑制非匹配不确定性的影响;第步结合非奇异终端滑模设计高阶滑模控制律,去除控制抖振,使系统对于匹配和非匹配不确定性均具有鲁棒性.理论分析证明了闭环系统状态半全局一致终结有界,仿真结果表明了所提出方法的有效性.     

Dynamic output feedback integral sliding mode control design for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. Once the system is in the sliding mode, the proposed output‐dependent integral sliding surface can robustly stabilize the closed‐loop system and obtain the desired system performance. Two types of mismatched disturbances are considered and their effects on the sliding mode are explored. By introducing an additional dynamics into the controller design, the developed control law can guarantee that the system globally reaches and is maintained on the sliding surface in finite time. Finally, the feasibility of the proposed method is illustrated by numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.     

Discrete-time adaptive sliding mode control for uncertain systems based on multi-rate output measurement

This article presents the design of a discrete-time adaptive sliding mode control (SMC) for uncertain systems using the noisy multi-rate output measurement. It is assumed that the dynamic systems are described by a discrete-time state equation with mismatched uncertainties. The proposed discrete-time adaptive SMC is composed of the equivalent and the nonlinear switching controls, and it is derived based on a new sliding surface. A new least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed without the information of the statistics for the measurement noises and the initial state. In the design of the proposed discrete-time adaptive SMC, the un-measurable states and the uncertainties are, respectively, replaced as their estimates obtained from the proposed LSE, and the sliding coefficient matrices are selected such that the states for the systems are ultimately bounded, and the effect of the external disturbances to give the states is reduced as small as possible. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

基于调节函数的一类三角结构非线性系统的自适应滑模控制

针对一类三角结构的非线性系统,基于状态参考自适应控制算法和滑模控制技术,研究了其在非匹配未知参数和不确定性干扰下的跟踪控制问题,提出了自适应滑模控制策略,实现了不确定非线性系统的鲁棒输出跟踪.与一般自适应控制相比,允许系统存在非参数化的不确定性和未知扰动,增强了控制系统鲁棒性.仿真算例证明了理论研究成果的正确性和可行性.     

非匹配不确定非线性系统的自适应反演滑模控制

针对一类具有非匹配不确定性的最小相位仿射非线性系统,研究其在未知扰动作用下的调节问题。基于自适应反演设计方法和变结构控制设计了控制方案,实现不确定系统的鲁棒调节。与经典反演设计相比,本方案允许非参数化不确定性,增强了控制系统的鲁棒性。     

不确定时滞切换系统的鲁棒滑模控制

该文研究了一类具有非匹配不确定性和非线性扰动的时滞切换系统的滑模控制问题.首先,针对每个子系统设计对应的时滞依赖滑模面,利用驻留时间方法,给出了由滑动模态方程组成的切换系统鲁棒渐近稳定的充分条件;然后设计了滑模控制器,使得闭环系统的状态能够到达滑模面上,产生滑动模态.最后,仿真实例说明所提出方法的有效性.     

Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach of an adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. A fuzzy terminal sliding mode controller is designed to retain the advantages of the terminal sliding mode controller and to reduce the chattering occurred with the terminal sliding mode controller. The sufficient condition is provided for the uncertain system to be invariant on the sliding surface. The parameters of the output fuzzy sets in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy sliding mode control system. The bounds of the uncertainties are not required to be known in advance for the presented adaptive fuzzy sliding mode controller. The stability of the fuzzy control system is also guaranteed. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed adaptive fuzzy terminal sliding mode controller.     

Terminal滑模自适应控制实现一类不确定混沌系统的同步

应用Terminal滑模控制技术和选择指数趋近律来综合滑模控制器,实现一类混沌系统的状态同步．在控制器中引入一类简单的自适应律,用以在线估计界参数．该设计方案消除了滑模控制的到达阶段,状态始终保持在滑模面上,并能在有限时间内趋近于原点．与一般滑模控制同步实现相比,具有更小的同步时间和鲁棒性．通过对Duffing—Holmes系统的同步仿真,验证了该方法的可行性．     

一类非线性不确定系统的自适应积分滑模控制

针对一类具有不确定参数的复杂非线性系统,提出了一种自适应积分滑模控制方法。控制器的设计分两步进行：首先,基于被控对象模型构造一个简化子系统,设计出该子系统的一个全局渐近稳定控制律;然后构造一个积分滑模面,设计自适应积分滑模补偿器以处理系统中含有不确定参数的部分,保证了滑模面的可达性和原系统的闭环稳定性。补偿后,系统的完整自适应控制律由简化子系统的控制律加补偿控制器两部分组成。所提设计方法简单,便于工程实现。最后,通过仿真结果验证了设计方案的有效性。     

一种基于反步法的鲁棒自适应终端滑模控制

针对不确定严格反馈块控非线性系统, 提出了一种基于反步法的鲁棒自适应终端滑模变结构控制方法. 系统的未知不确定及外界干扰由模糊系统在线逼近, 利用反步法设计了变结构控制的终端滑模面, 并由此得到了鲁棒自适应终端滑模控制器, 使系统的跟踪误差在有限时间内趋于给定轨迹的任意小的邻域内. 通过Lyapunov定理证明了闭环系统所有信号最终有界. 对某战斗机6自由度机动仿真结果表明, 该方法具有强鲁棒性.     

Extended filtering high‐gain output feedback controller for a class of uncertain nonlinear systems subject to external disturbances

In this article, an extended filtering high‐gain output feedback controller is developed for a class of uncertain nonlinear systems subject to external disturbances. The nonlinearities under consideration satisfy a semiglobal Lipschitz condition. The proposed control architecture integrates the extended state observer (ESO), high gain, and low‐pass filter together. None of them is used alone. The ESO can not only estimate the unknown internal state, but also deliver a good property of disturbance rejection simultaneously due to the presence of high gain. Since the high gain deteriorates the robustness of the system, a low‐pass filtering mechanism is added in the control law to filter away aggressive signals and recover the robustness. The filtering control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed stability. The matched uncertainties are canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. Numerical examples are provided to illustrate the effectiveness of the novel design via comparisons with the model reference adaptive control method and L₁ adaptive controller.     

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.     

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

A robust consensus controller is proposed for heterogeneous higher‐order nonlinear multi‐agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time‐varying nonhomogeneous finite‐time disturbance observer and sliding mode control is designed to realize the network consensus of higher‐order multi‐agent systems. The time‐varying finite‐time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite‐time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Parallel Distributed Fuzzy Sliding Mode Control for Nonlinear Mismatched Uncertain Systems

A new design approach of a parallel distributed fuzzy sliding mode controller for nonlinear systems with mismatched time varying uncertainties is presented in this paper. The nonlinear system is approximated by the Takagi–Sugeno fuzzy linear model. The approximation error between the nonlinear system and the fuzzy linear model is considered as one part of the uncertainty in the uncertain nonlinear system. The time varying uncertainties are assumed to have the format which enables the design of the coefficient matrix of the sliding function to satisfy a sliding coefficient matching condition. With the sliding coefficient matching condition satisfied, a parallel distributed fuzzy sliding mode controller (PDFSC) is designed. The stability and the sliding mode of the fuzzy sliding control system are guaranteed. Also, the nonlinear system is shown to be invariant on the sliding surface. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed fuzzy sliding mode controller. This work is partly supported by the the R.O.C. National Science Council through Grant NSC93-2213-E-197-004.     

Robust tracking control for a class of MIMO nonlinear systems with measurable output feedback

This paper proposes a robust output feedback controller for a class of nonlinear systems to track a desired trajectory. Our main goal is to ensure the global input-to-state stability (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. Our approach consists of constructing a nonlinear observer to reconstruct the unavailable states, and then designing a discontinuous controller using a back-stepping like design procedure to ensure the ISS property. The observer design is realized through state transformation and there is only one parameter to be determined. Through solving a Hamilton–Jacoby inequality, the nonlinear control law for the first subsystem specifies a nonlinear switching surface. By virtue of nonlinear control for the first subsystem, the resulting sliding manifold in the sliding phase possesses the desired ISS property and to certain extent the optimality. Associated with the new switching surface, the sliding mode control is applied to the second subsystem to accomplish the tracking task. As a result, the tracking error is bounded and the ISS property of the whole system can be ensured while the internal stability is also achieved. Finally, an example is presented to show the effectiveness of the proposed scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Fixed-time sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems

This paper investigates a fixed-time convergence issue using the sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems. This observer-based controller is designed assuming that only the first state measurement is available and there is no information about external disturbances and modeling uncertainties. A new form of sliding mode observer in combination with a sliding mode controller is designed to estimate unmeasured state and unknown disturbances and uncertainties as well as provide the estimated data in the control law. A novel form of sliding surfaces for the robust observer-based controller is proposed for which fixed-time convergence is guaranteed to achieve trajectory tracking. In the proposed fixed-time scheme, the bound on the settling time is user-defined using design parameters regardless of the system's initial conditions. The control law and observer law are designed such that the chattering issue is alleviated in the control signal. The stability analysis of the closed-loop system using the observer-based controller is established via the Lyapunov theory. The validity of the controller design is tested by applying and simulating an example of a robot manipulator in Simulink/MATLAB. The superiority of the proposed method is demonstrated by comparing it with two other methods from the relevant literature.     

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.