A matrix lower bound

Grcar, Joseph F.

doi:10.2172/836372

Cited by 7 publications

(18 citation statements)

References 8 publications

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“…Given A ∈ R n×m , rank(A), col(A), and A † ∈ R m×n denote the rank, the column space, and the Moore-Penrose inverse of A, respectively ( [19]. Matrix lower bounds satisfy the following properties, which are essential in our derivation of the proposed method: [19,Lemma 4.4]).…”

Section: Preliminariesmentioning

confidence: 99%

“…In this work, we present a novel approach that results in efficient under-approximations of forward reachable sets and tubes for a class of LTI uncertain systems, where approximations of the matrix exponential are used, first order convergence guarantees are provided, and approximations of the reachable sets and tubes are given as convex sets and finite unions of convex sets, respectively. Our approach is fundamentally based on set-based recursive relations that utilizes constant-input reachable sets (see, e.g., [17], [18]), where truncation errors are accounted for in an underapproximating manner by resorting the the concept of matrix lower bounds [19].…”

Section: Introductionmentioning

confidence: 99%

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Under-Approximate Reachability Analysis for a Class of Linear Uncertain Systems

Serry¹,

Li²

2021

Preprint

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Under-approximations of reachable sets and tubes have received recent research attention due to their important roles in control synthesis and verification. Available under-approximation methods designed for continuous-time linear systems typically assume the ability to compute transition matrices and their integrals exactly, which is not feasible in general. In this note, we attempt to overcome this drawback for a class of linear time-invariant (LTI) systems, where we propose a novel method to under-approximate finite-time forward reachable sets and tubes utilizing approximations of the matrix exponential. In particular, we consider the class of continuoustime LTI systems with an identity input matrix and uncertain initial and input values belonging to full dimensional sets that are affine transformations of closed unit balls. The proposed method yields computationally efficient under-approximations of reachable sets and tubes with first order convergence guarantees in the sense of the Hausdorff distance. To illustrate its performance, the proposed method is implemented in three numerical examples, where linear systems of dimensions ranging between 2 and 200 are considered.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Under-Approximate Reachability Analysis for a Class of Linear Uncertain Systems

Serry¹,

Li²

2021

Preprint

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“…The first equality holds since σ min (.) is a linear operator and the second equality is a special case of the matrix lower bound [22] when ℓ 2 -norms are considered. The inequality holds since t⋆ k 2 = 1 by Corollary 1, so t⋆ k is a feasible point for the minimization problem (i.e., min…”

Section: Mode Detectabilitymentioning

confidence: 99%

“…Now, by the matrix lower bound theorem [22] and a similar argument to the proof of Lemma 3, it is sufficient to require that ∃K ∈ N such that ∀k ≥ K, ∀q = q ′ ∈ Q :…”

Section: Mode Detectabilitymentioning

confidence: 99%

Simultaneous Mode, State and Input Set-Valued Observers for Switched Nonlinear Systems

Khajenejad,

Yong

2021

Preprint

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In this paper, we study the problem of designing a simultaneous mode, input and state set-valued observer for a class of hidden mode switched nonlinear systems with bounded-norm noise and unknown input signals, where the hidden mode and unknown inputs can represent fault or attack models and exogenous fault/disturbance or adversarial signals, respectively. The proposed multiplemodel design has three constituents: (i) a bank of mode-matched set-valued observers, (ii) a mode observer and (iii) a global fusion observer. The modematched observers recursively find the sets of compatible states and unknown inputs conditioned on the mode being the true mode, while the mode observer eliminates incompatible modes by leveraging a residual-based criterion. Then, the global fusion observer outputs the estimated sets of states and unknown inputs by taking the union of the mode-matched set-valued estimates over all compatible modes. Moreover, sufficient conditions to guarantee the elimination of all false modes (i.e., mode detectability) are provided and the effectiveness of our approach is demonstrated and compared with existing approaches using an illustrative example.

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“…Miha Grcar et al presented a semi-automatic categorization of video-recorded lectures into taxonomy through ML task [10]. This categorizer combined information present in texts related with lectures and information extracted from various links between lectures in a unified ML framework for efficient browsing.…”

Section: Literature Reviewmentioning

confidence: 99%

An Optimized E-Lecture Video Retrieval based on Machine Learning Classification

Medida¹,

Ramani²

2019

IJEAT

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The advent of internet has lead to colossal development of e-learning frameworks. The efficiency of such systems however relies on the effectiveness and fast content based retrieval approaches. This paper presents a methodology for efficient search and retrieval of lecture videos based on Machine Learning (ML) text classification algorithm. The text transcript is generated exclusively from the audio content extracted from the video lectures. This content is utilized for the summary and keyword extraction which is used for training the ML text classification model. An optimized search is achieved based on the trained ML model. The performance of the system is compared by training the system using Naive Bayes, Support Vector Machine and Logistic Regression algorithms. Performance evaluation was done by precision, recall, F-score and accuracy of the search for each of the classifiers. It is observed that the system trained on Naive Bayes classification algorithm achieved better performance both in terms of time and also with respect to relevancy of the search results

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A matrix lower bound

Cited by 7 publications

References 8 publications

Under-Approximate Reachability Analysis for a Class of Linear Uncertain Systems

Under-Approximate Reachability Analysis for a Class of Linear Uncertain Systems

Simultaneous Mode, State and Input Set-Valued Observers for Switched Nonlinear Systems

An Optimized E-Lecture Video Retrieval based on Machine Learning Classification

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