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Eigenvalue assignment of second-order singular systems by acceleration–velocity–displacement feedback 通过加速度-速度-位移反馈实现二阶奇异系统的特征值赋值
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-01-27 DOI: 10.1007/s00498-023-00379-w
{"title":"Eigenvalue assignment of second-order singular systems by acceleration–velocity–displacement feedback","authors":"","doi":"10.1007/s00498-023-00379-w","DOIUrl":"https://doi.org/10.1007/s00498-023-00379-w","url":null,"abstract":"<h3>Abstract</h3> <p>The eigenvalue assignment problem of second-order singular system is investigated by using acceleration–velocity–displacement feedback. The conditions are established to ensure the solvability of partial eigenvalue assignment problem of second-order singular system. The derived results are extended to complete eigenvalue assignment problem of second-order singular system. The presented solvability conditions are easily tested. Then, the methods are given to solve the eigenvalue assignment problem of second-order singular systems. Finally, several examples are given to validate our results and algorithms.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"12 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139581122","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
State observation for heterogeneous quasilinear traffic flow system with disturbances 带干扰的异构准线性交通流系统的状态观测
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-12-07 DOI: 10.1007/s00498-023-00377-y
Lina Guan, Christophe Prieur, Liguo Zhang, Rafael Vazquez
{"title":"State observation for heterogeneous quasilinear traffic flow system with disturbances","authors":"Lina Guan, Christophe Prieur, Liguo Zhang, Rafael Vazquez","doi":"10.1007/s00498-023-00377-y","DOIUrl":"https://doi.org/10.1007/s00498-023-00377-y","url":null,"abstract":"<p>This paper studies state observation for a heterogeneous quasilinear traffic flow system with disturbances at the inlet of a considered road section. Based on the backstepping method, an observer is designed for the quasilinear traffic flow system with only the boundary measurements at the inlet of the considered road section. The observer is constructed by duplicating the quasilinear system and adding the output injection terms to the partial differential equations and boundary conditions. Making use of the backstepping transformation, the injection gains of the observer system are derived by the computation of kernel equations, which are obtained by mapping the error system into an integral input-to-state stable target system. The applicability of the observer for the design of an output feedback controller stabilizing the quasilinear system is discussed. Finally the assumptions of the design of the observer are numerically checked on a realistic congested traffic scenario.\u0000</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"34 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553785","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
Well-posedness and properties of the flow for semilinear evolution equations 半线性演化方程流动的好求和特性
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-12-07 DOI: 10.1007/s00498-023-00378-x
Andrii Mironchenko
{"title":"Well-posedness and properties of the flow for semilinear evolution equations","authors":"Andrii Mironchenko","doi":"10.1007/s00498-023-00378-x","DOIUrl":"https://doi.org/10.1007/s00498-023-00378-x","url":null,"abstract":"<p>We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general <span>(C_0)</span>-semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers’ equation with nonlinear local dynamics and both distributed and boundary disturbances.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554021","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 discrete-time dissipative port-Hamiltonian (descriptor) systems 关于离散时间耗散端口-哈密顿(描述)系统
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-12-06 DOI: 10.1007/s00498-023-00376-z
Karim Cherifi, Hannes Gernandt, Dorothea Hinsen, Volker Mehrmann
{"title":"On discrete-time dissipative port-Hamiltonian (descriptor) systems","authors":"Karim Cherifi, Hannes Gernandt, Dorothea Hinsen, Volker Mehrmann","doi":"10.1007/s00498-023-00376-z","DOIUrl":"https://doi.org/10.1007/s00498-023-00376-z","url":null,"abstract":"<p>Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. This manuscript presents a discrete-time pH descriptor formulation for linear, completely causal, scattering passive dynamical systems based on the system coefficients. The relation of this formulation to positive and bounded real systems and the characterization via positive semidefinite solutions of Kalman–Yakubovich–Popov inequalities is also studied.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138541359","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: 1
The difference between port-Hamiltonian, passive and positive real descriptor systems 波特-哈密顿系统、被动实描述子系统和正实描述子系统的区别
4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-11-11 DOI: 10.1007/s00498-023-00373-2
Karim Cherifi, Hannes Gernandt, Dorothea Hinsen
{"title":"The difference between port-Hamiltonian, passive and positive real descriptor systems","authors":"Karim Cherifi, Hannes Gernandt, Dorothea Hinsen","doi":"10.1007/s00498-023-00373-2","DOIUrl":"https://doi.org/10.1007/s00498-023-00373-2","url":null,"abstract":"Abstract The relation between passive and positive real systems has been extensively studied in the literature. In this paper, we study their connection to the more recently used notion of port-Hamiltonian descriptor systems. It is well-known that port-Hamiltonian systems are passive and that passive systems are positive real. Hence it is studied under which assumptions the converse implications hold. Furthermore, the relationship between passivity and KYP inequalities is investigated.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"11 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135042854","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: 6
The minimum principle of hybrid optimal control theory 混合最优控制理论的最小原理
4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-11-10 DOI: 10.1007/s00498-023-00374-1
Ali Pakniyat, Peter E. Caines
{"title":"The minimum principle of hybrid optimal control theory","authors":"Ali Pakniyat, Peter E. Caines","doi":"10.1007/s00498-023-00374-1","DOIUrl":"https://doi.org/10.1007/s00498-023-00374-1","url":null,"abstract":"","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"120 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135136187","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 admissibility and input–output representation for a class of Volterra integro-differential systems 一类Volterra积分-微分系统的容许性与输入-输出表示
4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-11-10 DOI: 10.1007/s00498-023-00375-0
H. Bounit, M. Tismane
{"title":"On the admissibility and input–output representation for a class of Volterra integro-differential systems","authors":"H. Bounit, M. Tismane","doi":"10.1007/s00498-023-00375-0","DOIUrl":"https://doi.org/10.1007/s00498-023-00375-0","url":null,"abstract":"","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"102 46","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135138002","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
Control problems on infinite horizon subject to time-dependent pure state constraints 受时变纯状态约束的无限视界控制问题
4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-10-25 DOI: 10.1007/s00498-023-00372-3
Vincenzo Basco
{"title":"Control problems on infinite horizon subject to time-dependent pure state constraints","authors":"Vincenzo Basco","doi":"10.1007/s00498-023-00372-3","DOIUrl":"https://doi.org/10.1007/s00498-023-00372-3","url":null,"abstract":"In the last decades, control problems with infinite horizons and discount factors have become increasingly central not only for economics but also for applications in artificial intelligence and machine learning. The strong links between reinforcement learning and control theory have led to major efforts toward the development of algorithms to learn how to solve constrained control problems. In particular, discount plays a role in addressing the challenges that come with models that have unbounded disturbances. Although algorithms have been extensively explored, few results take into account time-dependent state constraints, which are imposed in most real-world control applications. For this purpose, here we investigate feasibility and sufficient conditions for Lipschitz regularity of the value function for a class of discounted infinite horizon optimal control problems subject to time-dependent constraints. We focus on problems with data that allow nonautonomous dynamics, and Lagrangian and state constraints that can be unbounded with possibly nonsmooth boundaries.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"72 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973230","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
Newton and interior-point methods for (constrained) nonconvex–nonconcave minmax optimization with stability and instability guarantees 具有稳定性和不稳定性保证的(约束)非凸非凹极小极大优化问题的牛顿和内点法
4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-10-10 DOI: 10.1007/s00498-023-00371-4
Raphael Chinchilla, Guosong Yang, João P. Hespanha
{"title":"Newton and interior-point methods for (constrained) nonconvex–nonconcave minmax optimization with stability and instability guarantees","authors":"Raphael Chinchilla, Guosong Yang, João P. Hespanha","doi":"10.1007/s00498-023-00371-4","DOIUrl":"https://doi.org/10.1007/s00498-023-00371-4","url":null,"abstract":"Abstract We address the problem of finding a local solution to a nonconvex–nonconcave minmax optimization using Newton type methods, including primal-dual interior-point ones. The first step in our approach is to analyze the local convergence properties of Newton’s method in nonconvex minimization. It is well established that Newton’s method iterations are attracted to any point with a zero gradient, irrespective of it being a local minimum. From a dynamical system standpoint, this occurs because every point for which the gradient is zero is a locally asymptotically stable equilibrium point. We show that by adding a multiple of the identity such that the Hessian matrix is always positive definite, we can ensure that every non-local-minimum equilibrium point becomes unstable (meaning that the iterations are no longer attracted to such points), while local minima remain locally asymptotically stable. Building on this foundation, we develop Newton-type algorithms for minmax optimization, conceptualized as a sequence of local quadratic approximations for the minmax problem. Using a local quadratic approximation serves as a surrogate for guiding the modified Newton’s method toward a solution. For these local quadratic approximations to be well-defined, it is necessary to modify the Hessian matrix by adding a diagonal matrix. We demonstrate that, for an appropriate choice of this diagonal matrix, we can guarantee the instability of every non-local-minmax equilibrium point while maintaining stability for local minmax points. Using numerical examples, we illustrate the importance of guaranteeing the instability property. While our results are about local convergence, the numerical examples also indicate that our algorithm enjoys good global convergence properties.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295467","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 of periodic linear systems, the Poincaré sphere, and quasi-affine systems 周期线性系统的可控性，庞卡罗球，和准仿射系统
4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2023-10-04 DOI: 10.1007/s00498-023-00369-y
Fritz Colonius, Alexandre Santana, Juliana Setti
{"title":"Controllability of periodic linear systems, the Poincaré sphere, and quasi-affine systems","authors":"Fritz Colonius, Alexandre Santana, Juliana Setti","doi":"10.1007/s00498-023-00369-y","DOIUrl":"https://doi.org/10.1007/s00498-023-00369-y","url":null,"abstract":"Abstract For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here, a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere, one obtains a compactification of the state space allowing us to describe the behavior “near infinity” of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior.","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135591189","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
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