Mathematics of Control Signals and Systems最新文献

Overcoming limitations in stability theorems based on multiple Nussbaum functions 克服基于多重努斯鲍姆函数的稳定性定理的局限性

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-09-09 DOI: 10.1007/s00498-024-00400-w

Caiyun Liu, Yungang Liu

{"title":"Overcoming limitations in stability theorems based on multiple Nussbaum functions","authors":"Caiyun Liu, Yungang Liu","doi":"10.1007/s00498-024-00400-w","DOIUrl":"https://doi.org/10.1007/s00498-024-00400-w","url":null,"abstract":"Among system uncertainties, unknown control direction is a rather essential one, whose compensation should entail the so-called Nussbaum function. Recently, strategies based on multiple Nussbaum functions (MNFs) have been proposed to make possible continuous adaptive control for the systems with nonidentical unknown control directions, such as large-scale systems and multi-agent systems, which cannot be addressed by a single Nussbaum function. But the existing stability theorems required: MNFs have explicit expressions; MNFs are all odd or all even. This paper aims to overcome the limitations of the theorems. We first delineate MNFs by two aspects of basic properties, replacing their explicit expressions as in the literature. Specifically, MNFs have the bivariate-product form, where one variate delineates frequent changes of signs and persistent intensity of MNFs, and the other delineates the rapid growth of MNFs. Such a delineation can capture the essence of MNFs and cover as many MNFs as possible. Based on the delineated MNFs, we present two stability theorems overcoming the aforementioned limitations. Notably, the two theorems do not require MNFs to have explicit expressions. Specifically, Theorem 1 allows nonmonotonic dynamic variables of MNFs while requiring MNFs to be odd, avoiding too large gains and excessive control cost. Theorem 4 does not require all MNFs to be odd while requiring dynamic variables of MNFs to be monotonic, giving users more freedom in selecting MNFs. The two stability theorems are applied to a large-scale system and a nonlinear system with parameterized uncertainties, both with nonidentical unknown control directions, to avoid monotonicity of dynamic gains and overparameterization, respectively, in control design.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability analysis of systems with delay-dependent coefficients and commensurate delays 具有延迟相关系数和相应延迟的系统稳定性分析

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-08-31 DOI: 10.1007/s00498-024-00399-0

Chi Jin, Keqin Gu, Qian Ma, Silviu-Iulian Niculescu, Islam Boussaada

{"title":"Stability analysis of systems with delay-dependent coefficients and commensurate delays","authors":"Chi Jin, Keqin Gu, Qian Ma, Silviu-Iulian Niculescu, Islam Boussaada","doi":"10.1007/s00498-024-00399-0","DOIUrl":"https://doi.org/10.1007/s00498-024-00399-0","url":null,"abstract":"This paper develops a method of stability analysis of linear time-delay systems with commensurate delays and delay-dependent coefficients. The method is based on a D-decomposition formulation that consists of identifying the critical pairs of delay and frequency, and determining the corresponding crossing directions. The process of identifying the critical pairs consists of a magnitude condition and a phase condition. The magnitude condition utilizes the Orlando’s formula, and generates frequency curves within the delay interval of interest. Such frequency curves correspond to the delay-frequency pairs such that the decomposition equation has at least one solution on the unit circle. The delay interval of interest is divided into continuous frequency curve intervals (CFCIs). Under some nondegeneracy assumptions, the number of frequency curves remains constant within each CFCI, and the associated decomposition equation has one and only one solution on the unit circle at any point on a frequency curve. By traversing through the frequency curves, all the crossing points can be identified. The crossing direction is related to the sign of the lowest-order nonzero derivative of the phase angle with respect to the delay, which is a generalization of the existing literature even for the case with single delay. This conclusion allows one to determine the crossing direction by examining the phase angle vs delay diagram. An example is presented to illustrate how a stability analysis can be conducted if some nondegeneracy assumptions are violated.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Controllability with one scalar control of a system of interaction between the Navier–Stokes system and a damped beam equation 用一个标量控制纳维-斯托克斯系统和阻尼梁方程之间的相互作用系统的可控性

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-08-28 DOI: 10.1007/s00498-024-00397-2

Rémi Buffe, Takéo Takahashi

{"title":"Controllability with one scalar control of a system of interaction between the Navier–Stokes system and a damped beam equation","authors":"Rémi Buffe, Takéo Takahashi","doi":"10.1007/s00498-024-00397-2","DOIUrl":"https://doi.org/10.1007/s00498-024-00397-2","url":null,"abstract":"We consider the controllability of a fluid–structure interaction system, where the fluid is modeled by the Navier–Stokes system and where the structure is a damped beam located on a part of its boundary. The motion of the fluid is bidimensional, whereas the deformation of the structure is one-dimensional, and we use periodic boundary conditions in the horizontal direction. Our result is the local null-controllability of this free-boundary system by using only one scalar control acting on an arbitrary small part of the fluid domain. This improves a previous result obtained by the authors where three scalar controls were needed to achieve the local null-controllability. In order to show the result, we prove the final-state observability of a linear Stokes-beam interaction system in a cylindrical domain. This is done by using a Fourier decomposition, proving Carleman inequalities for the corresponding system for the low-frequency solutions and in the case where the observation domain is an horizontal strip. Then, we conclude this observability result by using a Lebeau–Robbiano strategy for the heat equation and a uniform exponential decay for the high-frequency solutions. Finally, the result on the nonlinear system can be obtained by a change of variables and a fixed-point argument.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the relations between stability optimization of linear time-delay systems and multiple rightmost characteristic roots 论线性时延系统的稳定性优化与多最右特征根之间的关系

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-08-23 DOI: 10.1007/s00498-024-00398-1

Wim Michiels, Silviu-Iulian Niculescu, Islam Boussaada, Guilherme Mazanti

{"title":"On the relations between stability optimization of linear time-delay systems and multiple rightmost characteristic roots","authors":"Wim Michiels, Silviu-Iulian Niculescu, Islam Boussaada, Guilherme Mazanti","doi":"10.1007/s00498-024-00398-1","DOIUrl":"https://doi.org/10.1007/s00498-024-00398-1","url":null,"abstract":"Several recent results on spectrum-based analysis and control of linear time-invariant time-delay system concern the characterization and exploitation of situations where the so-called multiplicity-induced dominancy property holds, that is, the higher multiplicity of a characteristic roots implies that it is a rightmost root. This direction of research is inspired by observed multiple roots after minimizing the spectral abscissa as a function of controller parameters. However, unlike the relation between multiple roots and rightmost roots, barely theoretical results about the relation of the former with minimizers of the spectral abscissa are available. Consequently, in the first part of the paper the characterization of rightmost roots in such minimizers is briefly revisited for all second-order systems with input delay, controlled with state feedback. As the main theoretical results, the governing multiple root configurations are proved to correspond not only to rightmost roots, but also to global minimizers of the spectrum abscissa function. The proofs rely on perturbation theory of nonlinear eigenvalue problems and exploit the quasi-convexity of the spectral abscissa function. In the second part, a computational characterization of minima of the spectral abscissa is made for output feedback, yielding a more complex picture, which includes configurations with both multiple and simple rightmost roots. In the analysis, the pivotal role of the invariant zeros is highlighted, which translate into restrictions on the tunable parameters in the closed-loop quasi-polynomial.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The local representation of incrementally scattering passive nonlinear systems 增量散射被动非线性系统的局部表示法

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-08-05 DOI: 10.1007/s00498-024-00396-3

Shantanu Singh, George Weiss

引用次数: 0

Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups 零potent 群上线性控制系统非空内部控制集存在的弱条件

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-07-24 DOI: 10.1007/s00498-024-00395-4

Adriano Da Silva, Anderson F. P. Rojas

引用次数: 0

On the convergence of the linear tracking differentiator for signals with KH-integrable derivatives 论具有 KH 可积分导数的信号的线性跟踪微分器的收敛性

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-07-22 DOI: 10.1007/s00498-024-00394-5

Salvador Sánchez-Perales, Juan Carlos Felipe-Figueroa, Silvia Reyes-Mora

引用次数: 0

Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis 利用自感应压电致动器稳定横梁的控制设计：管理迟滞的存在和不存在

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-07-15 DOI: 10.1007/s00498-024-00393-6

Andrea Mattioni, Christophe Prieur, Sophie Tarbouriech

引用次数: 0

Control sets on maximal compact subgroups 最大紧凑子群上的控制集

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-07-02 DOI: 10.1007/s00498-024-00391-8

Mauro Patrão, Laércio dos Santos

引用次数: 0

Port-Hamiltonian descriptor systems are relative generically controllable and stabilizable 端口-哈密顿描述子系统具有相对的通用可控性和稳定性

IF 1.2 4区计算机科学

Mathematics of Control Signals and Systems Pub Date : 2024-06-24 DOI: 10.1007/s00498-024-00392-7

Achim Ilchmann, Jonas Kirchhoff, Manuel Schaller

引用次数: 0