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Learning Hamiltonian dynamics with reproducing kernel Hilbert spaces and random features 利用重现核希尔伯特空间和随机特征学习哈密顿动力学
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101128
Torbjørn Smith, Olav Egeland
A method for learning Hamiltonian dynamics from a limited and noisy dataset is proposed. The method learns a Hamiltonian vector field on a reproducing kernel Hilbert space (RKHS) of inherently Hamiltonian vector fields, and in particular, odd Hamiltonian vector fields. This is done with a symplectic kernel, and it is shown how the kernel can be modified to an odd symplectic kernel to impose the odd symmetry. A random feature approximation is developed for the proposed odd kernel to reduce the problem size. The performance of the method is validated in simulations for three Hamiltonian systems. It is demonstrated that the use of an odd symplectic kernel improves prediction accuracy and data efficiency, and that the learned vector fields are Hamiltonian and exhibit the imposed odd symmetry characteristics.
本文提出了一种从有限的噪声数据集学习哈密顿动力学的方法。该方法在哈密顿向量场,特别是奇数哈密顿向量场的重现核希尔伯特空间(RKHS)上学习哈密顿向量场。该方法使用交映核,并展示了如何将交映核修改为奇数交映核,以实现奇数对称性。针对所提出的奇数核开发了一种随机特征近似方法,以减小问题的规模。通过对三个哈密顿系统的模拟验证了该方法的性能。结果表明,奇对称核的使用提高了预测精度和数据效率,而且学习到的矢量场是哈密尔顿矢量场,并表现出所强加的奇对称特征。
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引用次数: 0
One superior pursuer and multiple-evader differential games with two lifelines 有两条生命线的一优一劣追逐者和多诱饵差分赛
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101130
Ningsheng Xu , Fang Deng , Weiwen Huang , Li Liang , Xiang Shi
This paper investigates a pursuit-evasion game with multiple evaders and a superior pursuer situated on a two-dimensional plane, divided by two lifelines into the play area and goal areas. The goal of the evaders is to reach one of the two goal areas, while the pursuer aims to capture them before they reach the lifeline. This paper constructs barriers without time delay and with time delay, respectively. For each evader, the entire barrier divides the game area into regions of dominance for the evader and pursuer, respectively. Cooperative and non-cooperative strategies between two evaders are studied when the evaders’ positions are within the pursuer’s dominance region. We consider the impact of different strategies adopted by the evaders and variations in the distance between the two lifelines on the number of captures by the pursuer. Furthermore, Apollonius circles and Cartesian ovals are used to determine optimal target points for the evaders under different circumstances. Subsequently, we extend the cooperative strategies of the evaders to multiplayer cooperative games, transform them into optimization problems, and use optimization algorithm to derive the cooperative strategies of multiple evaders. Finally, numerical simulations for various cases are presented in this paper.
本文研究的是一种追逐-逃避博弈,在一个二维平面上有多个逃避者和一个卓越的追逐者,平面被两条生命线分为游戏区和目标区。逃避者的目标是到达两个目标区域之一,而追击者的目标是在他们到达生命线之前抓住他们。本文分别构建了无时间延迟和有时间延迟的障碍。对于每个逃逸者,整个障碍将游戏区域划分为逃逸者和追捕者分别占优势的区域。当逃避者的位置位于追逐者的优势区域内时,我们将研究两个逃避者之间的合作和非合作策略。我们考虑了逃避者采取的不同策略以及两条生命线之间的距离变化对追逐者捕获数量的影响。此外,我们还利用阿波罗尼斯圆和笛卡尔椭圆来确定不同情况下逃逸者的最佳目标点。随后,我们将逃逸者的合作策略扩展到多人合作博弈中,将其转化为优化问题,并利用优化算法推导出多个逃逸者的合作策略。最后,本文介绍了各种情况下的数值模拟。
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引用次数: 0
A frequency-domain approach for enhanced performance and task flexibility in finite-time ILC 在有限时间 ILC 中提高性能和任务灵活性的频域方法
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101033
Max van Haren , Kentaro Tsurumoto , Masahiro Mae , Lennart Blanken , Wataru Ohnishi , Tom Oomen
Iterative learning control (ILC) techniques are capable of improving the tracking performance of control systems that repeatedly perform similar tasks by utilizing data from past iterations. The aim of this paper is to achieve both the task flexibility enabled by ILC with basis functions and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.
迭代学习控制(ILC)技术能够利用过去迭代的数据,改善重复执行类似任务的控制系统的跟踪性能。本文的目的是通过直观的设计程序,实现基函数 ILC 的任务灵活性和频域 ILC 的性能。本文确定了能恢复频域 ILC 的规范最优 ILC 成本函数,并因此根据基函数和频域 ILC 对前馈信号进行了参数化。由此产生的方法既有频域 ILC 的性能和设计程序,又有基函数 ILC 的任务灵活性,两者相得益彰。在一个基准实例上的验证证实了该框架的能力。
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引用次数: 0
Decentralized PI-control and anti-windup in resource sharing networks 资源共享网络中的分散 PI 控制和防倒转功能
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101049
Felix Agner , Jonas Hansson , Pauline Kergus , Anders Rantzer , Sophie Tarbouriech , Luca Zaccarian
We consider control of multiple stable first-order agents which have a control coupling described by an M-matrix. These agents are subject to incremental sector-bounded input nonlinearities. We show that such plants can be globally asymptotically stabilized to a unique equilibrium using fully decentralized proportional–integral controllers equipped with anti-windup and subject to local tuning rules. In addition, we show that when the nonlinearities correspond to the saturation function, the closed loop asymptotically minimizes a weighted 1-norm of the agents state mismatch. The control strategy is finally compared to other state-of-the-art controllers on a numerical district heating example.
我们考虑对多个稳定的一阶代理进行控制,这些代理具有由 M 矩阵描述的控制耦合。这些代理受增量部门有界输入非线性的影响。我们的研究表明,使用配备防倒退功能的全分散比例积分控制器,并根据局部调整规则,可以将这些植物全局渐近地稳定在一个唯一的平衡点上。此外,我们还证明,当非线性与饱和函数相对应时,闭环可近似最小化代理状态失配的加权 1 正态。最后,我们在一个区域供热数值示例中将该控制策略与其他最先进的控制器进行了比较。
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引用次数: 0
Scaled graphs for reset control system analysis 用于复位控制系统分析的比例图
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101050
Sebastiaan van den Eijnden , Thomas Chaffey , Tom Oomen , W.P.M.H. (Maurice) Heemels
Scaled graphs allow for graphical analysis of nonlinear systems, but are generally difficult to compute. The aim of this paper is to develop a method for approximating the scaled graph of reset controllers. A key ingredient in our approach is the generalized Kalman–Yakubovich–Popov lemma to determine input specific input–output properties of a reset controller in the time domain. By combining the obtained time domain properties to cover the full input space, an over-approximation of the scaled graph is constructed. Using this approximation, we establish a feedback interconnection result and provide connections to classical input–output analysis frameworks. Several examples show the relevance of the results for the analysis and design of reset control systems.
缩放图可以对非线性系统进行图形分析,但通常难以计算。本文旨在开发一种近似复位控制器缩放图的方法。我们方法的一个关键要素是广义卡尔曼-雅库博维奇-波波夫定理,用于确定复位控制器在时域中的特定输入输出属性。通过结合所获得的时域属性以覆盖整个输入空间,我们构建了一个比例图的过度近似值。利用这个近似值,我们建立了反馈互连结果,并提供了与经典输入输出分析框架的联系。几个例子显示了这些结果与复位控制系统分析和设计的相关性。
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引用次数: 0
Aperiodic MPC for nonlinear systems with additive disturbances and input delays: A prediction self-triggered approach 具有添加干扰和输入延迟的非线性系统的非周期性 MPC:预测自触发方法
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101133
Yanxin Li , Ning He , Zhongxian Xu , Lile He , Huiping Li
This paper is concerned with the control problem of continuous-time nonlinear systems with additive disturbances and input delays. The main focus is to predict the actual state of the system at the triggering moment within the delay time caused by the controller and, on the other hand, to obtain the optimal input by solving the optimization problem based on this state advance delay time to compensate for the input delay. Based on the event-based strategy, a new prediction self-triggered model predictive control (PST-MPC) scheme is designed by considering the prediction error, delay time, and bounded disturbances, which ensures the desired control effect while decreasing the computational load. In addition, sufficient conditions for the stability of the closed-loop system and the recursive feasibility of the PST-MPC algorithm are developed, respectively. Finally, the validity of the presented method is proved by a simulation comparison.
本文关注的是具有添加干扰和输入延迟的连续时间非线性系统的控制问题。主要重点是在控制器引起的延迟时间内预测系统在触发时刻的实际状态,另一方面,通过求解基于该状态提前延迟时间的优化问题获得最佳输入,以补偿输入延迟。在基于事件的策略基础上,考虑到预测误差、延迟时间和有界干扰,设计了一种新的预测自触发模型预测控制(PST-MPC)方案,在降低计算负荷的同时确保了理想的控制效果。此外,还分别提出了闭环系统稳定性和 PST-MPC 算法递归可行性的充分条件。最后,通过仿真对比证明了所提出方法的有效性。
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引用次数: 0
Peak estimation of rational systems using convex optimization 利用凸优化进行有理系统的峰值估计
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101088
Jared Miller, Roy S. Smith
This paper presents algorithms that upper-bound the peak value of a state function along trajectories of a continuous-time system with rational dynamics. The finite-dimensional but nonconvex peak estimation problem is cast as a convex infinite-dimensional linear program in occupation measures. This infinite-dimensional program is then truncated into finite-dimensions using the moment-Sum-of-Squares (SOS) hierarchy of semidefinite programs. Prior work on treating rational dynamics using the moment-SOS approach involves clearing dynamics to common denominators or adding lifting variables to handle reciprocal terms under new equality constraints. Our solution method uses a sum-of-rational method based on absolute continuity of measures. The Moment-SOS truncations of our program possess lower computational complexity and (empirically demonstrated) higher accuracy of upper bounds on example systems as compared to prior approaches.
本文提出了一些算法,可以沿具有合理动态的连续时间系统的轨迹对状态函数的峰值进行上限计算。有限维但非凸的峰值估计问题被投射为占领度量中的凸无限维线性程序。然后,利用半定量程序的矩平方和(SOS)层次,将这个无穷维程序截断到有限维。之前使用矩-平方和方法处理有理动力学的工作涉及将动力学清除为共同分母或添加提升变量,以处理新相等约束条件下的互易项。我们的求解方法采用基于绝对连续性度量的有理数总和法。与之前的方法相比,我们程序的矩-SOS截断具有更低的计算复杂度和(经验证明的)更高的示例系统上限精度。
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引用次数: 0
Optimized dead-zone inverse control using reinforcement learning and sliding-mode mechanism for a class of high-order nonlinear systems 利用强化学习和滑模机制对一类高阶非线性系统进行优化死区逆控制
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101132
Shuaihua Ma , Wenxia Sun , Guoxing Wen
An optimized control method is developed for a class of high-order nonlinear dynamic systems having controller dead-zone phenomenon. Dead-zone refers to the controller with zero behavior within a certain range, so it will inevitably affect system performance. In order to make the optimized control eliminate the effect of dead zone, the adaptive dead-zone inverse and reinforcement learning (RL) techniques are combined. The main idea is to find the desired optimized control using RL as the input of dead-zone inverse function and then to design the adaptive algorithm to estimate the unknown parameters of dead-zone inverse function, so that the competent system control can be yielded from the dead-zone function. However, most existing RL algorithms are difficult to apply in the dead zone inverse methods because of the algorithm complexity. The proposed RL greatly simplifies the algorithm because it derives the training rules from the negative gradient of a simple positive function yielded by the partial derivative of Hamilton–Jacobi–Bellman (HJB) equation. Meanwhile, the proposed dead-zone inverse method also requires fewer adaptive parameters. Finally, the proposed control is attested through theoretical proofs and simulation examples.
针对一类存在控制器死区现象的高阶非线性动态系统,开发了一种优化控制方法。死区是指控制器在一定范围内的行为为零,因此不可避免地会影响系统性能。为了使优化控制消除死区的影响,自适应死区反演和强化学习(RL)技术被结合起来。其主要思想是利用 RL 作为死区反函数的输入,找到所需的优化控制,然后设计自适应算法来估计死区反函数的未知参数,从而从死区函数中得到合格的系统控制。然而,由于算法复杂,现有的大多数 RL 算法很难应用于死区反演方法。所提出的 RL 算法从汉密尔顿-雅各比-贝尔曼(Hamilton-Jacobi-Bellman,HJB)方程偏导数产生的简单正函数的负梯度推导出训练规则,从而大大简化了算法。同时,所提出的死区反演方法所需的自适应参数也更少。最后,通过理论证明和仿真实例对所提出的控制方法进行了验证。
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引用次数: 0
Robust convex LPV control of a Helicopter-UAV transporting a suspended payload 运输悬挂有效载荷的直升机-无人机的鲁棒凸LPV控制
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101121
P. Gasga , F.R. López-Estrada , G. Valencia-Palomo , S. Gómez-Peñate , M.E. Guerrero-Sánchez
This paper develops a robust integral sliding mode controller for a helicopter-type unmanned aerial vehicle with a suspended payload. The nonlinear model is rewritten by considering a convex Linear Parameter Varying model that captures the nonlinear system dynamics. Then, a controller is developed by considering a nominal integrator comparator scheme and a discontinuous control based on sliding modes. The first part of the controller is dedicated to tracking the desired trajectory, while the second is devoted to attenuating the effect of external disturbance through a sliding surface. A set of linear matrix inequalities obtained from a Lyapunov quadratic function gives sufficient conditions to compute the controller gains. Numerical simulations are carried out to illustrate the effectiveness of the proposed approach in tracking the desired trajectory and attenuating the load oscillations under the presence of external disturbance.
本文为带有悬挂有效载荷的直升机型无人飞行器开发了一种鲁棒积分滑动模式控制器。通过考虑能捕捉非线性系统动态的凸线性参数变化模型,对非线性模型进行了重写。然后,通过考虑标称积分器比较器方案和基于滑动模态的非连续控制,开发了一个控制器。控制器的第一部分专门用于跟踪预期轨迹,第二部分则通过滑动面减弱外部干扰的影响。从 Lyapunov 二次函数得到的一组线性矩阵不等式给出了计算控制器增益的充分条件。我们进行了数值模拟,以说明所提出的方法在外部扰动存在的情况下,在跟踪理想轨迹和减弱负载振荡方面的有效性。
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引用次数: 0
A novel MATLAB toolbox for Control101 courses 用于 Control101 课程的新型 MATLAB 工具箱
IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.ejcon.2024.101041
J.A. Rossiter
In recent years the educationally focused parts of the global control community have given some focus to what constitutes a sensible first course in control (Rossiter et al., 2020) and how to support this with high quality learning and teaching resources. This paper contributes to that overall effort in that it provides an example of high quality, open-access resources to support students in their independent learning. One aspect of the ideal first course in control is the suggestion that we (the community) focus more on concepts and understanding and less on tedious paper and pen calculations; to do this the community needs suitable easy to use software for performing computations and producing illustrations. Hence the author is leading what he hopes will be a collaborative community project on creating a MATLAB toolbox to provide such software. The purpose of this paper is to highlight the toolbox, present its current contents and thus enable staff to evaluate and adopt this toolbox and moreover, to reflect on how it might be improved.
近年来,全球控制界以教育为重点的部分已经开始关注什么是合理的第一门控制课程(Rossiter 等人,2020 年),以及如何用高质量的学习和教学资源来支持这门课程。本文为这一总体努力做出了贡献,提供了一个高质量、开放式资源的范例,以支持学生的自主学习。理想的第一门控制课程的一个方面是建议我们(社区)更多地关注概念和理解,而不是乏味的纸笔计算;为此,社区需要合适的、易于使用的软件来执行计算和制作插图。因此,作者正在领导一个社区合作项目,希望通过创建 MATLAB 工具箱来提供此类软件。本文旨在重点介绍该工具箱,介绍其现有内容,从而使工作人员能够评估和采用该工具箱,并思考如何对其进行改进。
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引用次数: 0
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European Journal of Control
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