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Calculation Method of Static Friction Forces for Multi-Joint Manipulators 多关节机械手静摩擦力计算方法
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417454
Yusuke Murayama;Yoshiro Fukui
The static friction force is an important element of practical problems, such as the model-based control design of mechanical systems described by the Euler-Lagrange equations. The difficulty in calculating the static friction force, represented by a discontinuous function, lies in the fact that the differential equations representing the equations of motion become discontinuous differential-algebraic equations (DAEs). To solve the discontinuous DAEs using numerical methods, we need to solve a non-differential implicit algebraic equation at each step. In this letter, we propose an algorithm for calculating the static friction force by solving the implicit algebraic equation. Theoretical analysis shows that the friction force exists uniquely. This ensures that the proposed algorithm obtains a unique value for the static friction force. Moreover, the number of iterations in the proposed algorithm is only $3^{mathrm { n}}$ at worst, where $rm n$ denotes the number of manipulator joints. Hence, the proposed method matches numerical differential equation solvers, such as the Euler method. The effectiveness of the proposed method was validated through simulations using simple mechanical systems.
静摩擦力是实际问题中的一个重要因素,例如基于欧拉-拉格朗日方程描述的机械系统的模型控制设计。静摩擦力由不连续函数表示,计算静摩擦力的困难在于表示运动方程的微分方程变成了不连续微分代数方程 (DAE)。要使用数值方法求解不连续 DAE,我们需要在每一步求解一个非微分隐式代数方程。在这封信中,我们提出了一种通过求解隐式代数方程计算静摩擦力的算法。理论分析表明,摩擦力是唯一存在的。这确保了所提出的算法能获得唯一的静摩擦力值。此外,所提算法的迭代次数最多只需 3^{mathrm { n}}$,其中 $rm n$ 表示机械手关节的数量。因此,所提出的方法与欧拉法等数值微分方程求解器相匹配。通过使用简单机械系统进行仿真,验证了所提方法的有效性。
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引用次数: 0
A Continuous-Time Gradient-Tracking Algorithm for Directed Networks 有向网络的连续时间梯度跟踪算法
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417856
Mani H. Dhullipalla;Tongwen Chen
In this letter, we consider the problem of unconstrained convex optimization over directed networks and design a continuous-time (CT) gradient-tracking dynamics to address it. First, we establish that the optimum of the distributed optimization problem (DOP) is contained in the equilibrium of the designed dynamics under appropriate initialization. Subsequently, we construct a novel Lyapunov function to establish exponential convergence to the equilibrium. Specifically, for the Lyapunov function, we rely on the Lyapunov-like equations associated with the asymmetric graph Laplacians of the directed networks. As a result of the convergence analysis, we obtain sufficiency conditions on the gains involved in the dynamics. Additionally, we also present an adaptive variant of the designed gradient-tracking dynamics which converges to the aforementioned equilibrium asymptotically.
在这封信中,我们考虑了有向网络上的无约束凸优化问题,并设计了一种连续时间(CT)梯度跟踪动力学来解决这个问题。首先,我们确定在适当的初始化条件下,分布式优化问题(DOP)的最优值包含在所设计动力学的均衡中。随后,我们构建了一个新颖的 Lyapunov 函数,以建立对平衡的指数收敛。具体来说,对于 Lyapunov 函数,我们依赖于与有向网络的非对称图拉普拉斯相关的类 Lyapunov 方程。通过收敛性分析,我们获得了动力学中涉及的增益的充分条件。此外,我们还提出了设计的梯度跟踪动力学的自适应变体,它可以渐进地收敛到上述平衡。
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引用次数: 0
Nonlinear Feedback Control Design via NEOC 通过 NEOC 进行非线性反馈控制设计
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417891
Ayush Rai;Shaoshuai Mou;Brian D. O. Anderson
Quadratic performance indices associated with linear plants offer simplicity and lead to linear feedback control laws, but they may not adequately capture the complexity and flexibility required to address various practical control problems. One notable example is to improve, by using possibly nonlinear laws, on the trade-off between rise time and overshoot commonly observed in classical regulator problems with linear feedback control laws. To address these issues, non-quadratic terms can be introduced into the performance index, resulting in nonlinear control laws. In this letter, we tackle the challenge of solving optimal control problems with non-quadratic performance indices using the closed-loop neighboring extremal optimal control (NEOC) approach and homotopy method. Building upon the foundation of the Linear Quadratic Regulator (LQR) framework, we introduce a parameter associated with the non-quadratic terms in the cost function, which is continuously adjusted from 0 to 1. We propose an iterative algorithm based on a closed-loop NEOC framework to handle each gradual adjustment. Additionally, we discuss and analyze the classical work of Bass and Webber, whose approach involves including additional non-quadratic terms in the performance index to render the resulting Hamilton-Jacobi equation analytically solvable. Our findings are supported by numerical examples.
与线性植物相关的二次方性能指标具有简单性,并能产生线性反馈控制法则,但它们可能无法充分体现解决各种实际控制问题所需的复杂性和灵活性。一个值得注意的例子是,通过使用可能的非线性规律,可以改善在使用线性反馈控制规律的经典调节器问题中常见的上升时间和超调之间的权衡。为了解决这些问题,可以在性能指标中引入非二次项,从而产生非线性控制法则。在这封信中,我们利用闭环邻域极值最优控制(NEOC)方法和同调法解决了具有非四次性能指标的最优控制问题。在线性二次调节器(LQR)框架的基础上,我们引入了一个与成本函数中的非二次项相关的参数,该参数可从 0 到 1 连续调整。我们提出了一种基于闭环 NEOC 框架的迭代算法,以处理每次渐进调整。此外,我们还讨论并分析了 Bass 和 Webber 的经典研究成果,他们的方法是在性能指标中加入额外的非二次项,从而使得到的汉密尔顿-雅可比方程可以分析求解。我们的研究结果得到了数字实例的支持。
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引用次数: 0
A Trust-Region Method for Data-Driven Iterative Learning Control of Nonlinear Systems 非线性系统数据驱动迭代学习控制的信任区域法
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417805
Jia Wang;Leander Hemelhof;Ivan Markovsky;Panagiotis Patrinos
This letter employs a derivative-free trust-region method to solve the norm-optimal iterative learning control problem for nonlinear systems with unknown dynamics. The iteration process is composed by two kinds of trials: main and additional trials. The tracking error is reduced in each main trial, and the additional trials explore the nonlinear dynamics around the main trial input. Then the trust-region subproblem is constructed based on the additional trial data, and solved to generate the next main trial input. The convergence of the tracking error is proved under mild assumptions. Our method is illustrated in simulations https://github.com/JiaaaWang/TRILC.
本文采用无导数信任区域法求解未知动态非线性系统的规范最优迭代学习控制问题。迭代过程由两种试验组成:主要试验和附加试验。每次主试验都会减小跟踪误差,而附加试验则会探索主试验输入周围的非线性动态。然后根据附加试验数据构建信任区域子问题,并求解以生成下一个主试验输入。在温和的假设条件下,证明了跟踪误差的收敛性。我们的方法通过模拟 https://github.com/JiaaaWang/TRILC 进行了说明。
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引用次数: 0
Enhancing Data-Driven Stochastic Control via Bundled Interval MDP 通过捆绑区间 MDP 加强数据驱动的随机控制
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417852
Rudi Coppola;Andrea Peruffo;Licio Romao;Alessandro Abate;Manuel Mazo
The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic processes in terms of richer discrete stochastic models, whose actions lead to nondeterministic transitions over the space of probability measures. The data-driven component of the proposed methodology lies in the fact that we only assume samples from an unknown probability distribution. We also rely on the model of the underlying dynamics to build our abstraction through backward reachability computations. The nondeterminism in the probability space is captured by a collection of Markov Processes, and we identify how this model can improve upon existing abstraction techniques in terms of satisfying temporal properties, such as safety or reach-avoid. The connection between the discrete and the underlying dynamics is made formal through the use of the scenario approach theory. Numerical experiments illustrate the advantages and main limitations of the proposed techniques with respect to existing approaches.
对动态系统进行抽象是一种强大的工具,可以利用 "按设计纠正 "框架设计反馈控制器。我们研究了一种新方案,通过更丰富的离散随机模型获得数据驱动的离散时间随机过程抽象,这些模型的动作会导致概率度量空间上的非确定性转换。所提方法的数据驱动部分在于,我们只假设样本来自未知概率分布。我们还依靠底层动力学模型,通过后向可达性计算建立我们的抽象。概率空间中的非确定性由马尔可夫过程集合来捕捉,我们确定了这一模型如何在满足时间属性(如安全性或到达-避免)方面改进现有的抽象技术。通过使用情景方法理论,离散模型与底层动态模型之间的联系变得正式起来。数值实验说明了所提出的技术相对于现有方法的优势和主要局限性。
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引用次数: 0
Convergence Rates of Online Critic Value Function Approximation in Native Spaces 原生空间中在线批评值函数逼近的收敛率
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417178
Shengyuan Niu;Ali Bouland;Haoran Wang;Filippos Fotiadis;Andrew Kurdila;Andrea L’Afflitto;Sai Tej Paruchuri;Kyriakos G. Vamvoudakis
This letter derives rates of convergence of online critic methods for the estimation of the value function for a class of nonlinear optimal control problems. Assuming that the underlying value function lies in reproducing kernel Hilbert space (RKHS), we derive explicit bounds on the performance of the critic in terms of the kernel functions, the number of basis functions, and the scattered location of centers used to define the RKHS. The performance of the critic is precisely measured in terms of the power function of the scattered bases, and it can be used either in an a priori evaluation of potential bases or in an a posteriori assessments of the value function error for basis enrichment or pruning. The most concise bounds in this letter describe explicitly how the critic performance depends on the placement of centers, as measured by their fill distance in a subset that contains the trajectory of the critic. To the authors’ knowledge, precise error bounds of this form are the first of their kind for online critic formulations used in optimal control problems. In addition to their general and immediate applicability to a wide range of applications, they have the potential to constitute the groundwork for more advanced “basis-adaptive” methods for nonlinear optimal control strategies, ones that address limitations due to the dimensionality of approximations.
这封信推导了在线批判者方法的收敛率,用于估计一类非线性最优控制问题的值函数。假定基础值函数位于重现核希尔伯特空间(RKHS),我们根据核函数、基函数数量以及用于定义 RKHS 的中心散布位置,推导出批判器性能的明确界限。批判器的性能可以用散布基点的幂函数来精确测量,它既可以用于潜在基点的先验评估,也可以用于基点富集或剪枝的值函数误差的后验评估。这封信中最简洁的界限明确描述了批判者的性能如何取决于中心的位置,而中心的位置是通过中心在包含批判者轨迹的子集中的填充距离来衡量的。据作者所知,这种形式的精确误差边界是首次用于最优控制问题中的在线批判公式。除了可直接应用于广泛的应用领域外,它们还有可能为非线性最优控制策略中更先进的 "基础自适应 "方法奠定基础,解决近似维度带来的局限性。
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引用次数: 0
Learning-Based Prescribed-Time Safety for Control of Unknown Systems With Control Barrier Functions 带控制障碍功能的未知系统控制中基于学习的规定时间安全性
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417175
Tzu-Yuan Huang;Sihua Zhang;Xiaobing Dai;Alexandre Capone;Velimir Todorovski;Stefan Sosnowski;Sandra Hirche
In many control system applications, state constraint satisfaction needs to be guaranteed within a prescribed time. While this issue has been partially addressed for systems with known dynamics, it remains largely unaddressed for systems with unknown dynamics. In this letter, we propose a Gaussian process-based time-varying control method that leverages backstepping and control barrier functions to achieve safety requirements within prescribed time windows for control affine systems. It can be used to keep a system within a safe region or to make it return to a safe region within a limited time window. These properties are cemented by rigorous theoretical results. The effectiveness of the proposed controller is demonstrated in a simulation of a robotic manipulator.
在许多控制系统应用中,需要在规定时间内保证满足状态约束。虽然已知动力学系统已部分解决了这一问题,但对于未知动力学系统,这一问题在很大程度上仍未得到解决。在这封信中,我们提出了一种基于高斯过程的时变控制方法,该方法利用反向步进和控制障碍函数,在规定的时间窗口内实现仿射系统控制的安全要求。它可用于将系统保持在安全区域内,或使其在有限的时间窗口内返回安全区域。严格的理论结果巩固了这些特性。在一个机器人机械手的仿真中,演示了所提出的控制器的有效性。
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引用次数: 0
An Observer-Based Extremum Seeking Controller Design for a Class of Second-Order Nonlinear Systems 为一类二阶非线性系统设计基于观测器的极值寻优控制器
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417172
Seyed Mohammadmoein Mousavi;Martin Guay
In this letter, an extremum seeking controller (ESC) is designed for stabilization and output minimization for a class of second-order control-affine nonlinear systems. The main difficulty with such design lays in the fact that the relative degree between the measured output and the system’s input is two. As a result, the classical ESC approaches which use a high-pass filter for differentiation, are not suitable. We propose a perturbation-based controller in the feedback loop that utilizes a high-gain like observer with bounded derivatives of first and second-order. The closed-loop system is shown to be practically stable while maintaining the output in a small neighborhood of its optimum value. Simulation results demonstrate the effectiveness of the proposed approach.
在这封信中,我们设计了一种极值寻优控制器(ESC),用于一类二阶控制-非线性非线性系统的稳定和输出最小化。这种设计的主要难点在于测量输出与系统输入之间的相对度为二。因此,使用高通滤波器进行微分的经典 ESC 方法并不适用。我们在反馈环中提出了一种基于扰动的控制器,该控制器利用具有一阶和二阶有界导数的高增益观测器。结果表明,闭环系统实际上是稳定的,同时能将输出保持在最佳值的小范围内。仿真结果证明了所提方法的有效性。
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引用次数: 0
Online Nonstochastic Control Versus Retrospective Cost Adaptive Control 在线非随机控制与追溯成本自适应控制
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-20 DOI: 10.1109/LCSYS.2024.3417450
Usman Syed;Yingying Li;Bin Hu
Recently, online optimization methods have been leveraged to develop the online nonstochastic control framework which is capable of learning online gradient perturbation controllers in the presence of nonstochastic adversarial disturbances. Interestingly, using online optimization for adapting controllers in the presence of unknown disturbances is not a completely new idea, and a similar algorithmic framework called Retrospective Cost Adaptive Control (RCAC) has already appeared in the controls literature in 2000s. In this letter, we present the connections between online nonstochastic control and RCAC, and discuss the different strengths of both approaches: i.e., RCAC is able to stabilize unknown unstable plants via the use of target models, while online nonstochastic control enjoys provably near optimal regret bounds given a stabilizing policy a priori. We further propose an integration of these two approaches. We hope that our insights will help the development of new algorithms that complement the two approaches.
最近,人们利用在线优化方法开发了在线非随机控制框架,该框架能够在非随机对抗性干扰下学习在线梯度扰动控制器。有趣的是,在存在未知干扰的情况下使用在线优化来调整控制器并不是一个全新的想法,早在 2000 年代,控制领域的文献中就已经出现了一个类似的算法框架,名为 "回溯成本自适应控制"(RCAC)。在这封信中,我们介绍了在线非随机控制与 RCAC 之间的联系,并讨论了这两种方法的不同优势:即 RCAC 能够通过使用目标模型来稳定未知的不稳定工厂,而在线非随机控制在给定一个先验稳定策略的情况下,享有可证明的接近最优的遗憾边界。我们进一步提出了这两种方法的整合方案。我们希望我们的见解将有助于开发新的算法来补充这两种方法。
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引用次数: 0
Controller Design for Constrained Discrete-Time Uncertain Linear Systems Using Implicit Functions 利用隐函数为受限离散时间不确定线性系统设计控制器
IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-06-19 DOI: 10.1109/LCSYS.2024.3416475
Diego A. Muñoz-Carpintero;Giorgio Valmorbida
This letter shows a controller design procedure for constrained discrete-time uncertain linear systems, where the control law and piece-wise functions implicitly defined by ramps give the associated invariant set and Lyapunov function. This structure enables non-symmetric invariant sets of larger sizes than other structures, yielding symmetric invariant sets. The procedure is iterative, and each iteration solves a semi-definite program. A simulation example illustrates the attributes of the proposed design procedure.
这封信展示了受约束离散时间不确定线性系统的控制器设计程序,其中斜坡隐式定义的控制法则和片断函数给出了相关的不变集和 Lyapunov 函数。与其他结构相比,这种结构能使非对称不变集的规模更大,从而产生对称不变集。该程序是迭代式的,每次迭代都会求解一个半定式程序。一个模拟示例说明了拟议设计程序的特性。
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引用次数: 0
期刊
IEEE Control Systems Letters
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