Pierre Apkarian, Dominikus Noll
We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_\infty$-output feedback controllers which stabilize the infinite dimensional system exponentially in closed loop. The method is applied to control torsional vibrations in drilling systems with the goal to avoid slip-stick.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Uniformly exponentially stable approximations for a class of damped systems with unbounded feedbacks
本文研究了一类具有无界反馈的指数稳定无穷维系统的时间半离散逼近。最近的研究证明，对于时间半离散系统，由于高频寄生分量的存在，当时间步长趋于零时，系统的指数衰减特性可能丧失。我们证明了在数值格式中加入适当的数值粘性项，可以得到关于离散参数一致指数稳定的近似
Data-Driven Stable Neural Feedback Loop Design
本文提出一种数据驱动方法，通过将基于数据的稳定性条件转化为半定规划约束并整合到神经网络训练中，为未知动态系统设计具有稳定性保证的前馈控制器。
Output feedback stable stochastic predictive control with hard control constraints
针对离散线性定常系统，提出了一种不完全状态信息下的随机预测控制器。我们的方法是基于一个合适的选择的控制策略，稳定性约束，并雇用一个卡尔曼滤波器来估计不完整和腐败的观察系统的状态。我们证明，这种方法产生了一个计算上容易处理的问题，应该定期在线解决，所得到的闭环系统是均方有界的任何正界的控制行动。我们的研究结果允许一个解决最大的一类线性定常系统已知的服从随机稳定有界控制行动通过输出反馈随机预测控制。
This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. …
In this paper we study how high-gain anti-windup schemes can be used to implement projected dynamical systems in control loops that are subject to saturation on a (possibly unknown) set of admissible inputs. This insight is especially useful for the design of autonomous optimization schemes that realize a closed-loop behavior which approximates a particular optimization algorithm (e.g., projected gradient or Newton descent) while requiring only limited model information. In our analysis we show that a saturated integral controller, augmented with an anti-windup scheme, gives rise to a perturbe…
Feedback approximate controllability of blowup points for the heat equation with anti-interference blowup profile
本文研究热方程爆破点的反馈近似可控性，证明系统在反馈控制下近似可控且爆破剖面对初始数据稳定，仅发生微小时空平移，表明反馈策略具有抗干扰性。
Convergence Rate of Learning a Strongly Variationally Stable Equilibrium
本文研究凸博弈中零阶学习算法收敛到强变分稳定 Nash 均衡的速率，并在不假设强单调性的情况下，使单点与两点反馈速率均达到强单调博弈的已知最佳结果。
Some Remarks on Positive/Negative Feedback
本文通过例子表明，在非线性系统中，正反馈和负反馈可能同时增强稳定性，挑战了线性系统的传统观点。
Global tracking for an underactuated ships with bounded feedback controllers
针对欠驱动水面船舶，提出了一种全局状态反馈跟踪控制器。该控制器是基于饱和控制输入，并在参考轨迹的假设下，闭环系统是全局渐近稳定的（GAS）。它是使用海洋工程中使用的3自由度基准船模型设计的。我们的控制器的主要特点是控制输入的有界性，这是在现实生活中的一个重要考虑。在没有速度测量的情况下，控制器工作并且保持稳定，并且可以用作输出反馈控制器。仿真结果验证了该方法的有效性。
Dominant Mixed Feedback Design for Stable Oscillations
本研究提出一种通过混合反馈控制实现稳定振荡的设计框架，给出反馈增益与正负反馈平衡的鲁棒振荡条件，基于线性矩阵不等式推导抗有界动态不确定性、支持无源互连的系统化设计，为相关学科观察提供系统理论依据，并通过分布式神经动力学模拟电路验证。
Hovering Flight in Flapping Insects and Hummingbirds: A Natural Real-Time and Stable Extremum Seeking Feedback System
本文将昆虫和蜂鸟的悬停飞行建模为一种自然的极值搜索反馈系统，利用翅膀自然振荡实现简单、稳定、无模型且实时的悬停控制，并通过仿真验证了其有效性。
A linear state feedback switching rule for global stabilization of switched nonlinear systems about a nonequilibrium point
两个子系统切换系统的切换平衡点是两个子系统的向量场严格相互指向的点。利用Wicks-Peleties-DeCarlo（1998）为线性系提出的稳定凸组合的概念，Bolzern-Spinelli（2004）提供了一种状态反馈切换规则的设计，该规则能够将仿射切换系统稳定到任何切换平衡。Bolzern-Spinelli的状态反馈切换规则给出了通过切换平衡的非线性（二次）切换阈值。在本文中，我们证明了切换阈值（即相关的切换规则）可以选择线性，如果每个子系统的切换系统的考虑是稳定的。
Output feedback exponential stabilization of a nonlinear 1-D wave equation with boundary input
本文系统地研究了一类一维不稳定/反稳定波动方程的输出反馈指数镇定问题，其中控制边界同时受到内部非线性不确定性和外部扰动的影响.本文提出了一种扰动估计器，它不仅可以在误差小于$L^2(0,\infty)$的意义下成功地估计扰动，而且具有自由高增益。利用估计的扰动，设计了一个指数收敛于原系统状态的状态观测器。提出了一种基于滑模控制器的输出反馈镇定控制律。然后在反馈回路中通过其近似值消除干扰。闭环系统是指数稳定的，它可以保证所有的内部信号是一致有界的。
We discuss the role of monotonicity in enabling numerically tractable modular control design for networked nonlinear systems. We first show that the variational systems of monotone systems can be embedded into positive systems. Utilizing this embedding, we show how to solve a network stabilization problem by enforcing monotonicity and exponential dissipativity of the network sub-components. Such modular approach leads to a design algorithm based on a sequence of linear programming problems.
In this paper, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an anti-stable stochastic heat equation with Neumann boundary actuation and unknown boundary external disturbance generated by an exogenous system. A disturbance observer-based boundary control is designed based on the backstepping approach and estimation/cancellation strategy, where the unknown disturbance is estimated in real time by a disturbance observer and rejected in the closed-loop, while the in-domain multiplicative noise whose intensity is …
Asymptotic Stability and Strict Passivity of Port-Hamiltonian Descriptor Systems via State Feedback
本文研究了端口哈密顿描述系统的渐近稳定性与严格无源性问题，提出了在保持系统结构的前提下，通过状态反馈实现这些性质及正则性与指标一性质的充要条件。
Linear Quadratic Regulator (LQR) design is one of the most classical optimal control problems, whose well-known solution is an input sequence expressed as a state-feedback. In this work, finite-horizon and discrete-time LQR is solved under stability constraints and uncertain system dynamics. The resulting feedback controller balances cost value and closed-loop stability. Robustness of the solution is modeled using the scenario approach, without requiring any probabilistic description of the uncertainty in the system matrices. The new methods are tested and compared on the Leslie growth model, …
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it requires dynamic control laws that include delayed values of the output (directly or through state observers) which may not be robust to infinitesimal uncertainties on the characteristic velocities. The purpose of this paper is to highlight some features of this problem by addressing the feedback stabilization of an unstable open-loop system which is made up…
Boundary feedback stabilization by piecewise constant time delay for the wave equation
对于振动系统，反馈控制应用中的延迟会破坏控制的稳定效果。在本文中，我们考虑一个振动的弦，是固定在一端和稳定的边界反馈与延迟在另一端。我们证明了对于一定的反馈参数，系统是指数稳定的，具有形式为4L/c，8L/c，12 L/c的常数时滞。此外，我们证明了系统是指数稳定的分段常数时滞，达到值4L/c和8L/c。
This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using feedback controllers that emulate optimization algorithms have recently been proposed for the autonomous optimization of power systems and other infrastructures. In this paper, we consider feedback gradient flows that exploit physical input saturation with the help of anti-windup control to enforce constraints. We prove semi-global convergence of "projected" tr…
Linear State Feedback Stabilization on Time Scales
对于一般的一类动力系统（其规范连续和一致离散形式只是其特例），我们证明了存在状态反馈增益，使得所得到的闭环系统以给定的速率一致指数稳定.本文的方法将基于Gramian的线性状态反馈控制推广和扩展到更一般的时域，例如非均匀离散或连续和离散时间的组合。最后，我们讨论了这个理论的实验实施。
Sufficient and Necessary Conditions for the Solvability of the State Feedback Regulation Problem
本文讨论了具有无限维外系统的无限维线性控制系统的状态反馈输出调节问题。在多项式可稳定性假设下，给出了SFRP可解的充分条件和必要条件。这个问题的可解性的特点是一对线性调节器方程的可解性。给出了多项式稳定SISO系统SFRP可解性的一个应用。
Synchronizing continuous-time neutrally stable linear systems via partial-state coupling
研究了一般情况下耦合连续线性系的同步问题。对于输出可检测的中立稳定线性系，证明了在所有固定（有向）连通网络拓扑下，存在线性输出反馈律，使得耦合系统全局渐近同步.提供了一种算法来计算一个这样的反馈规律的基础上，个别系统参数。对偶的情况下，其中个别系统是中立稳定和稳定的，从他们的输入，也被认为是平行的结果建立。
Synchronizing discrete-time neutrally stable linear systems via partial-state coupling
本文给出了线性系通过输出耦合实现同步的一个基本结果。对于输出可检测且中立稳定的全同离散线性系，证明了存在线性输出反馈律，使得耦合系统对所有固定连接（非对称）网络拓扑全局渐近同步.提供了一种算法来计算这样的反馈规律的基础上的个别系统参数。提出并解决了一个对偶问题。
For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems. Response lags are required by most of physical systems and play a key role in the feedback control. The aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching diffusion system (SDS) to be exponentially stable in $p$th moment and probability one as well as stable in $H_\infty$. The designed control principles are impl…
Asymptotic stabilization of stationnary shock waves using a boundary feedback law
本文研究了具有凸通量的标量守恒律。对于定常激波，我们给出了一个作用在边界点的反馈律，使得该解在熵解类中按L1-范数渐近稳定。
Gain and phase type multipliers for feedback robustness
本文证明了线性时不变反馈系统对结构化不确定性的鲁棒稳定性蕴含特定形式的乘子存在性，建立了增益型与相位型不确定性的对偶乘子关系，推广了小增益和小相位定理。
Stabilization of linear Port-Hamiltonian Descriptor Systems via Output Feedback
针对可能非正则的线性pHDAE系统，本文给出比例和/或微分输出反馈使其正则化、指数至多为一并渐近稳定的充要条件及完整刻画。
Variance reduction for antithetic integral control of stochastic reaction networks
本文提出结合抗异性积分反馈与负反馈策略以降低随机反应网络中方差，通过理论和数值分析验证了负反馈可减少方差，但会增加均值收敛速度。
We investigate input-to-state stability (ISS) of infinite-dimensional collocated control systems subject to saturated feedback. Here, the unsaturated closed loop is dissipative and uniformly globally asymptotically stable. Under an additional assumption on the linear system, we show ISS for the saturated one. We discuss the sharpness of the conditions in light of existing results in the literature.
Boundary Output Feedback Stabilization for a Novel Magnetizable Piezoelectric Beam Model
针对两端自由可磁化压电梁强耦合PDE模型同位控制器的局限性，首次设计非同位边界输出反馈控制器与观测器，通过Lyapunov函数证明其一致指数稳定性，为有限差分模型降阶奠定基础。
Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation
本文提出一种新框架，通过经验证伪与策略性正则化联合学习神经网络控制器和李雅普诺夫证书，扩大可验证吸引域，并首次实现具有形式化稳定性保证的神经网络输出反馈控制。
In this note, a novel observer-based output feedback control approach is proposed to address the distributed optimal output consensus problem of uncertain nonlinear multi-agent systems in the normal form over unbalanced directed graphs. The main challenges of the concerned problem lie in unbalanced directed graphs and nonlinearities of multi-agent systems with their agent states not available for feedback control. Based on a two-layer controller structure, a distributed optimal coordinator is first designed to convert the considered problem into a reference-tracking problem. Then a decentraliz…
Converse negative imaginary theorems
本文推导了线性时不变系统的逆负虚定理，给出了反馈系统对各类负虚不确定性具有鲁棒稳定性的充要条件，并证明了考虑具有增益约束的NI系统子类的必要性。
Finite Difference Method for Global Stabilization of the Viscous Burgers' Equation with Nonlinear Neumann Boundary Feedback Control
本文提出一种θ方案用于黏性Burgers方程的非线性Neumann边界反馈控制，通过有限差分方法实现全局稳定化并验证了其理论稳定性与收敛性。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。