State‐bounding observer design for uncertain positive systems under <i>ℓ</i><sub>1</sub> performance

Chen, Xiaoming; Shen, Jun

doi:10.1002/oca.2360

Cited by 6 publications

(3 citation statements)

References 57 publications

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“…with any S ℓ , S ℓ ∈ R nL×n ℓ + . Due to (24) which always holds with existence of S ℓ , S ℓ , ℓ = 0, . .…”

Section: Run-time Safety Monitoring Designmentioning

confidence: 99%

Run-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Xiang

2021

Preprint

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Complex dynamical systems rely on the correct deployment and operation of numerous components, with stateof-the-art methods relying on learning-enabled components in various stages of modeling, sensing, and control at both offline and online levels. This paper addresses the run-time safety monitoring problem of dynamical systems embedded with neural network components. A run-time safety state estimator in the form of an interval observer is developed to construct lowerbound and upper-bound of system state trajectories in run time. The developed run-time safety state estimator consists of two auxiliary neural networks derived from the neural network embedded in dynamical systems, and observer gains to ensure the positivity, namely the ability of estimator to bound the system state in run time, and the convergence of the corresponding error dynamics. The design procedure is formulated in terms of a family of linear programming feasibility problems. The developed method is illustrated by a numerical example and is validated with evaluations on an adaptive cruise control system.

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“…with any S ℓ , S ℓ ∈ R nL×n ℓ + . Due to (24) which always holds with existence of S ℓ , S ℓ , ℓ = 0, . .…”

Section: Run-time Safety Monitoring Designmentioning

confidence: 99%

Run-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Xiang

2021

Preprint

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“…The estimated states can be employed for controller design. Over the past decades, the observer design problem has received considerable attention and has been one of the most interesting topics in the control theory 2‐4 …”

Section: Introductionmentioning

confidence: 99%

Observer‐based control with enlarged domain of attraction for one‐sided Lipschitz systems subject to input saturation

Shahbazzadeh

Salehifar

Sadati

2021

Optim Control Appl Methods

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This article deals with the problem of observer‐based controller (OBC) design for a class of nonlinear systems in the presence of input saturation. The nonlinearities are assumed to satisfy the one‐sided Lipschitz and the quadratically inner‐bounded conditions. Sufficient conditions for the existence of OBC are derived by Lyapunov stability theory. The designed OBC not only ensures the asymptotic stability of the overall closed‐loop system with a domain of attraction as large as possible, but also guarantees the actuator saturation avoidance. This problem is converted into a linear matrix inequality optimization problem by judicious use of Young's relation for straightforward computation of the OBC gains. Finally, the effectiveness of the proposed design method is demonstrated by simulation results.

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“…Moreover, there are few articles presenting observers for uncertain positive systems (Chen and Lam, 2014; Chen et al, 2014; Li and Lam, 2012), and also in the presence of unknown input or disturbances (Shafai et al, 2015). Furthermore, the interval uncertainty has been considered for continuous or discrete-time positive systems in Chen et al (2018), Li and Xiang (2016), Liu et al (2018), Shu et al (2008) and Zaidi et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

Motahhari

Shafiei

2020

Transactions of the Institute of Measurement and Control

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This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

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State‐bounding observer design for uncertain positive systems under ℓ₁ performance

Cited by 6 publications

References 57 publications

Run-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Run-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Observer‐based control with enlarged domain of attraction for one‐sided Lipschitz systems subject to input saturation

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

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State‐bounding observer design for uncertain positive systems under ℓ1 performance

Cited by 6 publications

References 57 publications

Run-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Run-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Observer‐based control with enlarged domain of attraction for one‐sided Lipschitz systems subject to input saturation

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

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State‐bounding observer design for uncertain positive systems under ℓ₁ performance