基于眼到手视觉伺服的移动机器人模型预测控制

针对具有速度约束的移动机器人视觉轨迹跟踪问题,提出了一种基于LOQO内点法的模型预测控制方法;在眼到手框架下,首先建立了移动机器人误差模型,并对该误差模型进行离散化,给出了移动机器人视觉伺服跟踪的代价函数;同时考虑到实际中移动机器人存在速度约束问题,将代价函数的最小化问题转换为带输入约束的模型预测控制问题;然后采用障碍函数法将移动机器人的速度约束转化为等式约束并采用拉格朗日乘子法引入到代价函数中;进而,利用LOQO内点法求解具有速度约束的最小化问题,得到基于视觉的轨迹跟踪控制器;最后,通过仿真验证了所提算法的有效性和优越性.     

不确定离散切换系统具有极点约束的保性能控制

对一类含有范数有界不确定性的离散切换系统和一个二次型性能指标,研究其具有闭环极点约束的鲁棒状态反馈保性能控制问题．利用二次Lyapunov函数方法和线性矩阵不等式技术,给出了鲁棒保性能控制器存在的一个充分条件,在所构造切换规则下,闭环系统二次D稳定,且满足给定的性能指标．在此基础上,将次优保性能控制器设计问题转化为一组线性矩阵不等式约束下的凸优化问题．数值例子说明了所提方法的有效性．     

采用内点法和图像反馈的机器人视觉伺服预测控制

针对具有控制量约束和可视性约束的六自由度机器人的视觉伺服系统,研究了基于图像空间局部模型的预测控制器的设计问题.首先对特征点的投影图像的运动学方程进行离散化,得到系统的误差预测模型.然后通过选取合适的性能指标函数,将视觉伺服控制器设计问题转化为一个具有控制量约束和可视性约束的最优化问题.进一步,利用对数障碍函数处理约束,得到系统的牛顿方程,获得控制量的迭代求解公式.最后,利用数值仿真和实验验证了所提方法的有效性.     

线性不确定时滞系统的可靠保成本控制

讨论了执行器故障下,线性不确定时滞系统的可靠保成本控制问题。提出了更实际、更一般的执行器故障模型;给出了以LMI表达的故障系统渐近隐定以及成本函数有上界的充分条件;进一步对执行器故障情况下的成本函数上界进行了优化,该优化是通过一个LMI组的最小化问题来实现的,对扰动输入具有一定的衰减性能。仿真实例验证了所得结果的有效性。     

Guaranteed cost control analysis and iterative design for constrained Takagi–Sugeno systems

This paper presents a novel control design technique in order to obtain a guaranteed cost fuzzy controller subject to constraints on the input channel. This guaranteed cost control law is obtained via multi-parametric quadratic programming. The result is a piecewise fuzzy control law where the state partition is defined by fuzzy inequalities. The parameters of the Lyapunov function can be obtained previously using Linear Matrix Inequalities optimization.     

Neural-based online finite-time optimal tracking control for wheeled mobile robotic system with inequality constraints

In this study, a finite-time online optimal controller was designed for a nonlinear wheeled mobile robotic system (WMRS) with inequality constraints, based on reinforcement learning (RL) neural networks. In addition, an extended cost function, obtained by introducing a penalty function to the original long-time cost function, was proposed to deal with the optimal control problem of the system with inequality constraints. A novel Hamilton-Jacobi-Bellman (HJB) equation containing the constraint conditions was defined to determine the optimal control input. Furthermore, two neural networks (NNs), a critic and an actor NN, were established to approximate the extended cost function and the optimal control input, respectively. The adaptation laws of the critic and actor NN were obtained with the gradient descent method. The semi-global practical finite-time stability (SGPFS) was proved using Lyapunov's stability theory. The tracking error converges to a small region near zero within the constraints in a finite period. Finally, the effectiveness of the proposed optimal controller was verified by a simulation based on a practical wheeled mobile robot model.     

基于强化学习的一类具有输入约束非线性系统最优控制

针对部分系统存在输入约束和不可测状态的最优控制问题,本文将强化学习中基于执行–评价结构的近似最优算法与反步法相结合,提出了一种最优跟踪控制策略.首先,利用神经网络构造非线性观测器估计系统的不可测状态.然后,设计一种非二次型效用函数解决系统的输入约束问题.相比现有的最优方法,本文提出的最优跟踪控制方法不仅具有反步法在处理...     

An approximated scalar sign function approach to optimal anti-windup digital controller design for continuous-time nonlinear systems with input constraints

This article presents an approximated scalar sign function-based digital design methodology to develop an optimal anti-windup digital controller for analogue nonlinear systems with input constraints. The approximated scalar sign function, a mathematically smooth nonlinear function, is utilised to represent the constrained input functions, which are often expressed by mathematically non-smooth nonlinear functions. Then, an optimal linearisation technique is applied to the resulting nonlinear system (with smooth nonlinear input functions) for finding an optimal linear model, which has the exact dynamics of the original nonlinear system at the operating point of interest. This optimal linear model is used to design an optimal anti-windup LQR, and an iterative procedure is developed to systematically adjust the weighting matrices in the performance index as the actuator saturation occurs. Hence, the designed optimal anti-windup controller would lie within the desired saturation range. In addition, the designed optimal analogue controller is digitally implemented using the prediction-based digital redesign technique for the effective digital control of stable and unstable multivariable nonlinear systems with input constraints.     

输入饱和及输出受限的纯反馈非线性系统控制

针对具有输入饱和和输出受限的纯反馈非线性系统,设计了神经网络自适应控制器.首先利用隐函数定理和中值定理将非仿射形式的纯反馈非线性系统转换成有显式输入的非线性系统,基于李雅普诺夫第二方法以及反推法并采用障碍型李雅普诺夫函数进行控制器的设计,最后通过稳定性分析证明了闭环控制系统是半全局一致最终有界的,利用仿真例子验证了控制...     

Nonsmooth multi-objective synthesis with applications

Nonsmooth optimization is used to design feedback controllers subject to closed-loop performance specifications both in time and frequency-domains. In time domain the nonlinear plant is submitted to a set of test input signals and the closed-loop responses so generated are called scenarios. A design technique is proposed which computes a controller with a prescribed structure that satisfies performance specifications for a given set of scenarios in tandem with robustness constraints in the frequency-domain, and is locally optimal among other controllers with these properties.     

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line reconfiguration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modified to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is defined in terms of virtual commands. A suitable terminal cost weighting for the reconfigurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a defined subset of faults. The proposed method is demonstrated by means of a numerical example.     

Guaranteed‐cost fuzzy controller design for a self‐sustaining bicycle with practical constraints

This study presents a guaranteed‐cost fuzzy controller for a self‐sustaining bicycle. First, the nonlinear dynamics of the bicycle are exactly transformed into a T‐S fuzzy system with model uncertainty. The guaranteed‐cost fuzzy controller is then designed for the transformed T‐S fuzzy system. For practical considerations, the input/state constraints are also satisfied in the design. The main contribution of this study is the guaranteed‐cost control design for a T‐S fuzzy system with model uncertainty and input/state constraints. Finally, simulation results show the validity of the proposed controller design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

风电介入下的多区域互联电力系统分布式经济模型预测负荷频率控制

针对风电介入下的多区域互联电力系统,提出一种分布式经济模型预测负荷频率控制策略.通过将大规模互联电力系统分解成若干个动态耦合的子系统,这些子系统能够利用网络交流并共享信息,使得各区域的控制器实现各自优化问题的求解.同时,在满足状态约束和控制输入约束的前提下,遵循传统火力发电优先、风力发电配合的原则,通过在线求解优化问题,实现风电介入下的多区域互联电力系统的负荷频率控制.为了提高系统整体运行经济性,所提出的分布式经济模型预测控制器将负荷调频成本、燃料消耗成本以及风力发电成本等经济性指标考虑在内.仿真结果表明,在阶跃负荷扰动下,所设计的控制器不仅可以满足调频要求,在降低计算负担和提高经济性能方面也具有一定优势.     

执行器约束下基于数据驱动的参数化前馈控制器设计

针对执行器约束下非重复性点到点运动的轨迹跟踪问题, 提出了一种在执行器约束下基于数据驱动的参数化输入整形滤波器和前馈控制器优化设计算法. 首先对输入整形滤波器以及前馈控制器进行参数化, 然后在目标函数中加入控制信号变化量与控制信号能量的约束, 再采用基于数据驱动的迭代寻优算法得到最优参数, 在该参数下可以实现满足执行器约束条件下的运动控制系统轨迹最优跟踪性能. 并且由于采用了前馈参数化设计方法, 在点到点轨迹发生变化时所提出算法依然能够保持良好的轨迹跟踪性能. 仿真与实验结果表明在执行器约束下所提出算法能够实现最优点到点轨迹跟踪性能, 并且对非重复性点到点轨迹跟踪具有一定的鲁棒性.     

Model predictive control of axial dispersion chemical reactor

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints.     

伺服电机驱动的连铸结晶器振动系统受限状态下预设性能控制

以伺服电机驱动的连铸结晶器振动位移系统为研究对象,针对系统输入和状态受限问题,考虑系统存在的参数不确定性和负载转矩扰动影响,设计一种基于观测器的预设性能自适应控制器.首先,针对系统存在的参数不确定性、负载转矩扰动等问题,基于Lyapunov函数设计变增益扩张状态观测器,在保证观测精度的同时,削弱峰值现象;其次,考虑状态和输入受限的情况,将预设性能函数与Backstepping技术相结合设计控制器,构建指令滤波器解决“计算膨胀”问题,引入动态补偿量对观测器及受限状态产生的误差进行补偿,并对所设计的控制器进行稳定性分析;最后,通过仿真对比实验验证控制器的有效性.     

Guaranteed cost stabilization for a class of uncertain discrete-time systems

A technique to design stabilizing state feedback controllers is presented for a class of linear discrete-time systems subject to possibly time-varying uncertainties that affect the system and input matrices. The controller design procedure is based on the solution of one of three modified algebraic Riccati matrix equations. Stability considerations rely on the second method of Lyapunov. To evaluate the system's performance degradation due to uncertainly, an upper bound (guaranteed cost) is derived for the cost of the controlled uncertain system with respect to a designer-chosen quadratic cost function. An example adapted from the literature is used to illustrate the method.     

LMI-based robust model predictive control and its application to an industrial CSTR problem

In this paper, robust model predictive control (MPC) is studied for a class of uncertain linear systems with structured time-varying uncertainties. This general class of uncertain systems is useful for nonlinear plant modeling in many circumstances. The controller design is characterizing as an optimization problem of the “worst-case” objective function over infinite moving horizon, subject to input and output constraints. A sufficient state-feedback synthesis condition is provided in the form of linear matrix inequality (LMI) optimizations, and will be solved on-line. The stability of such a control scheme is determined by the feasibility of the optimization problem. To demonstrate its usefulness, this robust MPC technique is applied to an industrial continuous stirred tank reactor (CSTR) problem with explicit input and output constraints. Its relative merits to conventional MPC approaches are also discussed.     

TS-based sampled-data model predictive controller for continuous-time nonlinear systems

This paper proposes a new fuzzy model predictive control approach for continuous-time nonlinear systems in terms of linear matrix inequalities (LMIs). The proposed approach is based on the Takagi–Sugeno fuzzy modeling, a quadratic Lyapunov function, and a sampled-data parallel distributed compensation controller with constant sampling time. The goal is designing the sampled-data controller such that at each sampling time, the stability of the closed-loop system is guaranteed and an infinite horizon cost function is minimised. The main advantage of the proposed approach is to eliminate the approximations induced from discretizing the original system and cost function upper bound minimisation. Consequently, a lower bound of the cost function is obtained and the performance of the proposed model predictive controller is improved compared to the recently published papers in the same field of interest. In addition, the Euclidean norm constraint of the control input vector is derived in terms of LMIs. To illustrate the merits of the proposed approach, the proposed technique is applied to a continuous stirred tank reactor system.