Invariant sets in finite-time stability of multi-mobile robots

Béji, Lotfi; Mlayeh, Rhouma; Zoghlami, Naim

doi:10.1109/acc.2015.7170873

Cited by 2 publications

(2 citation statements)

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“…Since (13) guarantees ε(P ) to be attractive/invariant ellipsoid, and the trace of matrix P characterizes the size of invariant ellipsoid (represent the impact of external disturbance). Therefore, the external disturbance of system (10) can be optimally rejected by solving the following optimal problem: tr(X) → Min where X = P −1 under constraints ( 13) and ( 17), (28) where the constraint ( 17) is added to avoid the infinite input.…”

Section: Minimization Of Invariant Ellipsoidmentioning

confidence: 99%

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Observer-Based Leader Following Consensus of Nonlinear Multi-agent Systems with a Leader of Bounded Input

Wang

2019

Lecture Notes in Electrical Engineering

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The objective of the invariant ellipsoid method is to minimize the smallest invariant and attractive set of a linear control system operating under the influence of bounded external disturbances. In this paper, this method is extended into the leader-following consensus problem. Initially, a linear control protocol is designed for the Multi-agent System without disturbances. Subsequently, in the presence of bounded disturbances, by employing a similar linear control protocol, a necessary and sufficient condition is introduced to derive the optimal control parameters for the MAS such that the state of followers converge and remain in an minimal invariant ellipsoid around the state of the leader.

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Section: Minimization Of Invariant Ellipsoidmentioning

confidence: 99%

“…It provides a sufficient condition of being an invariant set for MAS. In [28], a finite-time control protocol of reaching the invariant set is designed. In [29], the invariant set method is proposed to analyze the limit behaviors of all the synchronous trajectories.…”

Section: Introductionmentioning

confidence: 99%