检索结果-内蒙古大学图书馆

Line zonotopes: A tool for state estimation and fault diagnosis of unbounded and descriptor systems

AUTOMATICA 2025年 179卷

作者： Rego, Brenner S. Raimondo, Davide M. Raffo, Guilherme, V Univ Sao Paulo Dept Elect & Comp Engn BR-13566590 Sao Carlos SP Brazil Univ Trieste Dept Engn & Architecture I-34127 Trieste Italy Univ Fed Minas Gerais Dept Elect Engn BR-31270901 Belo Horizonte MG Brazil

This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear static constraints on state variables - typical of descriptor systems - into their mathematical representation, leading to less conservative enclosures. However, for LDS that are unstable or not fully observable, a bounded representation cannot ensure a valid enclosure of the states over time. To address this limitation, we introduce line zonotopes, a new representation for unbounded sets that retains key properties of CZs, including polynomial time complexity reduction methods, while enabling the description of strips, hyperplanes, and the entire n-dimensional Euclidean space. This extension not only generalizes the use of CZs to unbounded settings but can also enhance set-based estimation and AFD in both stable and unstable scenarios. Additionally, we extend the AFD method for LDS from Rego et al. (2020) to operate over reachable tubes rather than solely on the reachable set at the final time of the considered horizon. This reduces conservatism in input separation and enables more accurate fault diagnosis based on the entire output sequence. The advantages of the proposed methods over existing CZ-based approaches are demonstrated through numerical examples. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Descriptor systems set-based computing State estimation Fault diagnosis

来源：评论

学校读者我要写书评

暂无评论

Scalable Reachset-Conformant Identification of Linear Systems

引用

IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 520-525页

作者： Lutzow, Laura Althoff, Matthias Tech Univ Munich Sch Computat Informat & Technol D-85748 Garching Germany

By monitoring the set of reachable outputs, safety can be verified. However, to compute the reachable set of real-world systems, we require models that are able to produce all possible system behaviors. These kinds of models are called reachset-conformant, and their identification is a promising new research direction. While many existing reachset-conformant identification techniques require the computation of the halfspace representation of the zonotopic reachable sets, we propose an approach that leads to the same optimal identification results using the more scalable generator representation. Thus, our approach offers greater efficiency for high-dimensional systems and long time horizons. The scalability and accuracy of both approaches are compared in numerical experiments with linear time-variant systems.

关键词： Uncertainty Computational modeling Vectors Generators Trajectory Mathematical models Formal verification reachability analysis set-based computing

来源：评论

学校读者我要写书评

暂无评论

Inner Approximations of Reachable sets for Nonlinear Systems Using the Minkowski Difference

引用

IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 2033-2038页

作者： Wetzlinger, Mark Kulmburg, Adrian Althoff, Matthias Tech Univ Munich Sch Computat Informat & Technol D-85748 Garching Germany

Reachability analysis is a formal method that rigorously proves whether a dynamical system can reach certain states. Inner approximations of the exact reachable set contain only states that are definitely reachable and are therefore used to falsify specifications. While the majority of state-of-the-art approaches for nonlinear systems obtain an inner approximation via first computing an outer approximation of the reachable set, we directly obtain sound inner approximations by using the Minkowski difference in a reachability algorithm for nonlinear systems. Our implementation uses a combination of polytopes and constrained zonotopes as set representations, resulting in a low polynomial time complexity in the state dimension. A comparison with state-of-the-art approaches on several benchmarks demonstrates the advantages of our approach.

关键词： Vectors Polynomials Nonlinear systems Time complexity Jacobian matrices Safety Reachability analysis Formal verification falsification reachability analysis nonlinear systems set-based computing

来源：评论

学校读者我要写书评

暂无评论

Fully Automated Verification of Linear Systems Using Inner and Outer Approximations of Reachable sets

引用

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第12期68卷 7771-7786页

作者： Wetzlinger, Mark Kochdumper, Niklas Bak, Stanley Althoff, Matthias Tech Univ Munich Dept Comp Sci D-85748 Garching Germany SUNY Stony Brook Dept Comp Sci Stony Brook NY 11794 USA

Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm parameters, such as the time step size, which requires expert knowledge. In this work, we solve this issue with a fully automated reachability algorithm that tunes all algorithm parameters internally such that the reachable set enclosure respects a user-defined approximation error bound in terms of the Hausdorff distance to the exact reachable set. Moreover, this bound can be used to extract an inner approximation of the reachable set from the outer approximation using the Minkowski difference. Finally, we propose a novel verification algorithm that automatically refines the accuracy of the outer and inner approximations until specifications given by time-varying safe and unsafe sets can be verified or falsified. The numerical evaluation demonstrates that our verification algorithm successfully verifies or falsifies benchmarks from different domains without requiring manual tuning.

关键词： Formal verification linear systems reachability analysis set-based computing

来源：评论

学校读者我要写书评

暂无评论

State Estimation and Leakage Detection in Water Distribution Networks Using Constrained Zonotopes

引用

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2022年第5期30卷 1920-1933页

作者： Rego, Brenner S. Vrachimis, Stelios G. Polycarpou, Marios M. Raffo, Guilherme V. Raimondo, Davide M. Univ Fed Minas Gerais Grad Program Elect Engn BR-31270901 Belo Horizonte MG Brazil Univ Fed Minas Gerais Dept Elect Engn BR-31270901 Belo Horizonte MG Brazil Univ Cyprus KIOS Res & Innovat Ctr Excellence CY-1678 Nicosia Cyprus Univ Cyprus Dept Elect & Comp Engn CY-1678 Nicosia Cyprus Univ Pavia Dept Elect Comp & Biomed Engn I-27100 Pavia Italy

State estimation in water distribution networks (WDNs) is a challenging task due to the scarcity of measurements and the presence of several modeling uncertainties. In the literature, pseudo-measurements are often required to obtain an observable model for state estimation, which are highly uncertain and mostly represented by bounded sets. This article proposes two new methods for set-based state estimation in WDNs, considering unknown-but-bounded measurement and model uncertainties to calculate bounds on the system states. A new interval method is proposed based on iterative computation of tight enclosures of the nonlinear head-loss functions, and bounding the solution of the algebraic equations using rescaling. This method, referred to as iterative slope approximation and rescaling (ISAR), is mildly more conservative than the iterative hydraulic interval state estimation (IHISE) method previously proposed by the authors, but significantly more computationally efficient. However, since intervals are not capable of capturing the dependencies between state variables, we propose the use of constrained zonotopes (CZs) as an additional step to both IHISE and ISAR. This yields two new algorithms for set-based state estimation of WDNs, capable of capturing the dependencies between hydraulic states, which result in sets with significantly smaller volumes than intervals. The benefits of CZs are also highlighted when the new enclosures are used for leakage detection. These provide higher leakage detection rates compared to intervals, as demonstrated in two case studies using benchmark WDNs.

关键词： State estimation Computational modeling Mathematical models Uncertainty Hydraulic systems Measurement uncertainty Water conservation Constrained zonotopes (CZs) intervals set-based computing state estimation water distribution networks (WDNs)

来源：评论

学校读者我要写书评

暂无评论

Unions and Complements of Hybrid Zonotopes

引用

IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 1778-1783页

作者： Bird, Trevor J. Jain, Neera Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA

Hybrid zonotopes have been recently introduced as a mixed-integer set representation that is equivalent to the union of up to 2(N) constrained zonotopes through the use of N binary factors. This letter further develops this new set representation by deriving identities for union and complement set operations of hybrid zonotopes. The addition of these set operations proves the hybrid zonotope's closure under linear mappings, Minkowski sums, intersections, unions, and complements, thus increasing the usefulness of the set representation to a broad class of set-theoretic controls problems. Beyond set operations, a major contribution of this letter is a demonstration of how linear mixed-integer constraints may be embedded within the hybrid zonotope set definition. A numerical example using hybrid zonotopes as a nonconvex safety constraint in an obstacle avoidance problem is provided.

关键词： Hybrid systems predictive control set-based computing zonotopes

来源：评论

学校读者我要写书评

暂无评论

Robust Successor and Precursor sets of Hybrid Systems Using Hybrid Zonotopes

引用

IEEE CONTROL SYSTEMS LETTERS 2022年 7卷 355-360页

作者： Siefert, Jacob A. Bird, Trevor J. Koeln, Justin P. Jain, Neera Pangborn, Herschel C. Penn State Univ Dept Mech Engn University Pk PA 16802 USA Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA Univ Texas Dallas Dept Mech Engn Richardson TX 75080 USA

This letter presents identities for calculating robust successor and precursor sets of discrete-time linear hybrid systems. The proposed technique relies on generating a set containing all possible state transitions of a dynamic system over a region of interest, named the state-update set. Forward and backward reachability can then be performed using only projection, intersection, and Minkowski difference set operations with the state-update set. It is shown how state-update sets may be defined as hybrid zonotopes for mixed logical dynamical systems and linear systems in closed loop with model predictive control.

关键词： Complexity theory Time complexity Predictive control Mechanical engineering Linear systems Jacobian matrices Iterative methods Hybrid systems predictive control set-based computing zonotopes

来源：评论

学校读者我要写书评

暂无评论

Joint state and parameter estimation based on constrained zonotopes

引用

AUTOMATICA 2022年 142卷

作者： Rego, Brenner S. Locatelli, Diego Raimondo, Davide M. Raffo, Guilherme, V Univ Fed Minas Gerais Grad Program Elect Engn BR-31270901 Belo Horizonte MG Brazil Univ Pavia Dept Elect Comp & Biomed Engn Pavia Italy Univ Fed Minas Gerais Dept Elect Engn BR-31270901 Belo Horizonte MG Brazil

This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Nonlinear state estimation Parameter identification set-based computing Constrained zonotopes

来源：评论

学校读者我要写书评

暂无评论

Hierarchical MPC for coupled subsystems using adjustable tubes

引用

AUTOMATICA 2022年 143卷

作者： Raghuraman, Vignesh Koeln, Justin P. Univ Texas Dallas Richardson TX 75080 USA

A hierarchical Model Predictive Control (MPC) formulation is presented for coupled discrete-time linear systems with state and input constraints. Compared to a centralized approach, a two-level hierarchical controller, with one controller in the upper-level and one controller per subsystem in the lower-level, can significantly reduce the computational cost associated with MPC. Hierarchical coordination is achieved using adjustable tubes, which are optimized by the upper-level controller and bound permissible lower-level controller deviations from the system trajectories determined by the upper-level controller. The size of these adjustable tubes determines the degree of uncertainty between subsystems and directly affects the required constraint tightening under a tube-based robust MPC framework. sets are represented as zonotopes to enable the ability to optimize the size of these adjustable tubes and perform the necessary constraint tightening online as part of the MPC optimization problems. State and input constraint satisfaction is proven for the two-level hierarchical controller with an arbitrary number of controllers at the lower-level and a numerical example demonstrates the key features and performance of the approach. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Hierarchical control Robust model predictive control set-based computing Zonotopes

来源：评论

学校读者我要写书评

暂无评论

set operations and order reductions for constrained zonotopes

引用

AUTOMATICA 2022年 139卷

作者： Raghuraman, Vignesh Koeln, Justin P. Univ Texas Dallas Richardson TX 75080 USA

This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to represent sets resulting from operations including halfspace intersections, convex hulls, robust positively invariant sets, and Pontryagin differences. Order reduction techniques are also presented that provide lower-complexity inner-approximations of zonotopes and constrained zonotopes. Numerical examples are used to demonstrate the efficacy and computational advantages of using zonotope-based set representations for dynamic system analysis and control. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： set-based computing Zonotopes Computational methods Linear systems

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：