Optimal Robust Control for Rigid Serial Manipulators: A Fuzzy Approach

We first investigate the fundamental properties of rigid serial manipulators as related to the control design. Then, a new optimal robust control is proposed for serial‐link mechanical manipulators with fuzzy uncertainty. Fuzzy set theory is used to describe the uncertainty. The desirable system performance is deterministic (assuring the bottom line) and also fuzzy (enhancing the cost consideration). The proposed control is deterministic and is not the usual if‐then rules‐based control. The resulting controlled system is uniformly bounded and uniformly ultimately bounded proved via the Lyapunov minimax approach. A performance index (the combined cost, which includes average fuzzy system performance and control effort) is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the performance index. The resulting control design is systematic and is able to guarantee the deterministic performance as well as minimizing the cost. In the end, a cylindrical robot manipulator is chosen for demonstration.     

不确定线性系统鲁棒二次最优控制的时频域方法

利用时域和频域结合的方法,讨论了线性不确定系统鲁棒二次最优控制问题;提出了线性不确定系统鲁棒二次最优的概念,并证明了有关性质,建立了鲁棒回差方程,阐述了鲁棒二次最优控制系统的分析和综合方法;最后给出了工程应用设计实例。     

非完整移动机械手鲁棒自适应模糊控制

考虑系统存在的参数、外界扰动和未建模动态等不确定性,研究非完整移动机械手的鲁棒自适应控制器设计方法.基于用旋量理论建立的非完整移动机械手的动力学模型,设计了移动平台子系统的运动控制器,然后应用非线性反步控制技术和模糊逻辑系统的通用逼近性,用参数化线性模糊逻辑系统逼近非完整移动机械手动力学模型中的不确定项,基于Lyapu...     

A New High‐Order Adaptive Robust Control for Constraint Following of Mechanical Systems

A mechanical system is to follow a class of prescribed holonomic or nonholonomic constraints. The system contains time‐varying bounded uncertainty. However, the bound is unknown. The objective is to design a control which renders constraint following. A new high‐order adaptive robust control is proposed. The control guarantees uniform boundedness and uniform ultimate boundedness even in the presence of the uncertainty. Significant advantages of this new control are demonstrated both analytically and numerically. It is shown that the system performance, including the finite entering time, constraint‐following error, and control magnitude, can be improved by tuning the control order.     

基于状态观测器的一类非线性系统的模糊鲁棒控制

利用T－S模型对一类非线性不确定系统进行模糊建模,在此基础上研究模糊鲁棒观测器及模糊状态鲁棒控制器的设计,并证明所设计的模糊鲁棒观测器和模糊状态鲁棒控制器具有全局渐近稳定性质。     

Finite‐Time Optimal Formation Control for Second‐Order Multiagent Systems

This paper studies the problem of finite‐time optimal formation control for second‐order multiagent systems in situations where the formation time and/or the cost function need to be considered. The finite‐time optimal formation control laws are proposed for the cases with or without a leader, respectively. For the case of control being constrained, the time optimal formation problem is considered and an algorithm is designed to derive a feasible solution for the problem concerned. Although the feasible solution may not be optimal, it can provide a lower bound for time for the formation problem with control constraints. Once the given formation time is lower than this bound, the control constraints cannot be ensured. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.     

基于T-S模糊的欠驱动机械臂的平衡控制

针对欠驱动机械臂平衡控制精度低,鲁棒性差,抗干扰空间狭窄,起摆成功率低等问题,提出了一种基于T-S模糊结构和线性调节理论的欠驱动机械臂平衡控制策略,并实现了一种新的起摆-平衡控制方式.首先将系统设定的状态空间分为若干个模糊子空间,通过线性二次型最优理论和线性调节理论,在每个模糊子空间建立局部控制器,保证系统在每个局部子空间中平衡,并最终收敛于给定平衡点,然后使用隶属函数平滑的将各个局部控制器连接起来,最终得到非线性控制对象的模糊平衡控制器,实现了欠驱动机械臂在任意给定点的平衡控制.实验结果表明,所提出的控制策略控制精度高,抗干扰范围大,鲁棒性强,起摆成功率高,并且易于实现,具有较高的推广和应用价值.     

非线性系统的鲁棒采样最优控制

采样系统控制作为一种数字控制的直接设计方法,近年来引起了广泛的重视,另一方面系统的时域约束在工业控制中是不可避免的。利用实用稳定性理论,研究了具有输出约束的一类非线性系统的鲁棒采样最优控制问题,结果表示为一些矩阵不等式,最后给了出了一个迭代算法。     

一类不确定系统的最优鲁棒控制

运用最优方法探讨了一类模型不确定系统的鲁棒控制问题。定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,并通过调整标称控制器最小化加权敏感度误差在整个频段上的方差,从而为一类不确定系统提供了一种最优的鲁棒控制器设计方法,可使系统性能对模型误差具有良好的鲁棒性。针对控制工程领域典型的一阶时滞系统进行仿真研究,其结果说明了该方法的有效性。     

Robust Input Covariance Constraint Control for Uncertain Polytopic Systems

In this paper, the robust input covariance constraint (ICC) control problem with polytopic uncertainty is solved using convex optimization with linear matrix inequality (LMI) approach. The ICC control problem is an optimal control problem that optimizes the output performance subjected to multiple constraints on the input covariance matrices. This control problem has significant practical implications when hard constraints need to be satisfied on control actuators. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the robust ICC control problem for polytopic uncertain systems. Both continuous‐ and discrete‐time systems are considered. Parameter‐dependent and independent Lyapunov functions have been used for robust ICC controller synthesis. Numerical design examples are presented to illustrate the effectiveness of the proposed approach.     

移动机械手鲁棒自适应模糊控制

基于旋量理论建立了非完整移动机械手系统的动力学模型,通过反步控制技术,应用非线性参数化模糊逻辑系统设计了移动机械手的鲁棒自适应模糊控制器.该控制器放松了移动机械手控制器设计中斜对称性的要求,对移动机械手系统中存在的参数或外界扰动等不确定性具有较强的鲁棒性和自适应能力.理论证明和仿真结果表明,所设计的控制器是有效的.     

Control Design for Artificial Swarm Mechanical Systems: Dynamics,Uncertainty, and Constraint

We consider an artificial swarm system consisting of multiple agents. The agents influence each other through the attraction/repulsion, which is related to the relative positions among them. Here the collective behavior of the agents mimics some biological swarm systems. The dynamic model for each agent is built by taking the uncertainty into account. Based on the dynamic model, we propose three types adaptive robust controls, including switching type, non‐switching type and fractional type, for each agent. The control design weaves together several intrinsic features of kinematics, dynamics, d'Alembert's principle, constraint, and uncertainty.     

Robust Decentralized Adaptive Fuzzy Control of Large‐Scale Nonaffine Nonlinear Systems With Strong Interconnection and Application to Automated Highway Systems

A novel decentralized adaptive fuzzy controller is developed for a class of large‐scale uncertain nonaffine nonlinear systems in this paper. Incorporating the benefits of fuzzy systems, implicit function theorem, and robust control technique, the interconnections between subsystems are extended to general unknown nonlinear functions. No a priori knowledge of lower and upper bounds on lumped uncertainties is required to implement each local controller. The resulting closed‐loop large‐scale system is proved to be asymptotically stable. The controller design is applicable to an automated highway system and simulation results confirm its practical usefulness.     

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.     

A Nonlinear Robust Control Using a Fuzzy Reasoning and Its Application to a Robot Manipulator

A simplified adaptive nonlinear robust controller (SANROC) has beenstudied in the literature. However, this is based on using the so-calledmatching condition. The present controller is not based on using such acondition. The estimate of an upper bound for uncertainties is usuallyincreased by using the adaptive mechanism, e.g., by consisting of amonotonically increased function. In this paper, instead of using such ananalytically adaptive mechanism, a fuzzy reasoning technique is alsoincorporated with the adaptive mechanism of SANROC. The proposed method isapplied to a pantagraph type robot manipulator. The effectiveness of thepresent method is illustrated by some experiments.     

动态不确定多输入多输出系统的变结构鲁棒控制

本文仅利用输入输出数据给出了一种动态不确定多输入多输出系统的变结构控制器设计机制，控制系统的设计中引入了一个严格正实的模型．应用适当逻辑切换的状态变量滤波器实现变结构控制．证明了所提方案能保证全局输出有界稳定并能实现滑模控制和渐近跟踪参考模型的输出．该设计方案对结构不确定性具有一定的鲁棒性．仿真结果表明了所提方案的有效性．     

模糊神经网络补偿的伺服系统二次型最优控制

针对伺服系统二次型最优控制存在的问题,提出了基于模糊神经网络补偿的二次型最优控制方法,该控制方法利用模糊神经网络的实时学习能力,能够及时补偿被控对象建模不准确、参数摄动和外界干扰等非线性因素对控制系统性能的影响,增强控制系统的自适应能力,有效提高控制系统的跟踪性能和抗干扰鲁棒性能.仿真试验结果验证了该控制方法的有效性.     

基于自适应模糊补偿的机械臂复合控制策略

针对刚性机械臂存在摩擦和扰动等不确定因素给轨迹跟踪控制带来的困难,本文基于李亚普诺夫稳定性理论,给出了一种机械臂的自适应控制方案．该方案针对机械臂的标称部分,采用计算力矩的方法设计相应的控制量,在此基础上,构造模糊系统逼近摩擦得到补偿控制量,并针对随机扰动的上界设计反馈控制率,以克服扰动带来的影响,保证系统的稳定性．仿真结果表明,该复合控制对于具有不确定性摩擦以及扰动的机械臂轨迹跟踪问题效果良好．     

Fuzzy Optimal Control for Bilinear Stochastic Systems with Fuzzy Parameters

In this paper we consider the control problem for a class of partially observed bilinear stochastic systems with fuzzy parameters. Using Takagi–Sugeno fuzzy model, the problem is described by three sets of fuzzy stochastic differential equations: one for the state process, one for the observed process and one for the controller which is assumed to be driven by the observed process. With this formulation, the original stochastic control problem can be treated as a deterministic identification problem in which the controller parameters and the corresponding membership functions are the unknowns. Using a suitable performance index, we have developed a set of necessary conditions for determining the parameters of the controller and the corresponding membership functions. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed fuzzy control scheme.     

Robust Adaptive Fuzzy Control of Nonlinear Systems with Unknown and Time‐Varying Saturation

In this paper, a robust adaptive fuzzy control approach is proposed for a class of nonlinear systems in strict‐feedback form with the unknown time‐varying saturation input. To deal with the time‐varying saturation problem, a novel controller separation approach is proposed in the literature to separate the desired control signal from the practical constrained control input. Furthermore, an optimized adaptation method is applied to the dynamic surface control design to reduce the number of adaptive parameters. By utilizing the Lyapunov synthesis, the fuzzy logic system technique and the Nussbaum function technique, an adaptive fuzzy control algorithm is constructed to guarantee that all the signals in the closed‐loop control system remain semiglobally uniformly ultimately bounded, and the tracking error is driven to an adjustable neighborhood of the origin. Finally, some numerical examples are provided to validate the effectiveness of the proposed control scheme in the literature.