Analytical Upper Bound for the Error on the Discretization of Uncertain Linear Systems by using the Tensor Product Model Transformation

Campos, Víctor Costa da Silva; Braga, Márcio F.; Frezzatto, Luciano

doi:10.12700/aph.17.6.2020.6.4

Cited by 19 publications

(9 citation statements)

References 21 publications

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“…It is worth mentioning that obtaining an exact discretization for uncertain systems has been recently studied in the literature (see da Silva Campos et al [17] and references therein). Herein, the distinguished approach introduced by Braga et al [21] will be addressed.…”

Section: Problemmentioning

confidence: 99%

“…x(t) = E(𝛼 1 )x(t) + F(𝛼 1 )u(t − 𝜏), (24) and considering t = KT(𝛼 2 ) such that 𝜏 = dT(𝛼 2 ), for d ∈ N * , then .…”

Section: Augmented Model Based On Longer Network-induced Delaysmentioning

confidence: 99%

“…The augmented model ( 20) includes a matrix with Taylor series expansion remainders (22), which are indicated by means of Δ. Despite of others methods to compute exact values to Δ Â[g] (𝛼) ( [24]), in this paper an upper bound approximation θ Â is calculated by using a (N 1 + 2)−dimensional off line search over a fine grid in the parameter space 𝛼 = (𝛼 1 , 𝛼 2 ) ∈ Λ N 1 × Λ 2 , as done in [11,21]. In this case, one defines…”

Section: Augmented Model Based On Longer Network-induced Delaysmentioning

confidence: 99%

“…For 𝜆 A > 0, W [q] (𝛼) > 0, and Θ → 0 + , then |𝜉| < 𝜚 is guaranteed. Additionally from (55), the condition N T U HN U < 0 in (17) can be written as…”

Section: Lmi-based Conditions For Problemmentioning

confidence: 99%

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On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

Leandro¹,

Pereira

2023

Asian Journal of Control

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This paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network‐induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network‐induced delay and uncertain sampling periods can be incorporated from the original continuous‐time state‐space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete‐time model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.

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Section: Problemmentioning

confidence: 99%

“…x(t) = E(𝛼 1 )x(t) + F(𝛼 1 )u(t − 𝜏), (24) and considering t = KT(𝛼 2 ) such that 𝜏 = dT(𝛼 2 ), for d ∈ N * , then .…”

Section: Augmented Model Based On Longer Network-induced Delaysmentioning

confidence: 99%

Section: Augmented Model Based On Longer Network-induced Delaysmentioning

confidence: 99%

“…For 𝜆 A > 0, W [q] (𝛼) > 0, and Θ → 0 + , then |𝜉| < 𝜚 is guaranteed. Additionally from (55), the condition N T U HN U < 0 in (17) can be written as…”

Section: Lmi-based Conditions For Problemmentioning

confidence: 99%

See 2 more Smart Citations

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

Leandro¹,

Pereira

2023

Asian Journal of Control

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“…Human driver models and models of the closed-loop system based on a control theory (e.g., [8][9][10]) approach have been considered in [11]. A human model based on fractional order calculus has also been presented [12].…”

Section: Introductionmentioning

confidence: 99%

Handover Process of Autonomous Vehicles – Technology and Application Challenges

Drexler¹,

Takács²,

Nagy³

et al. 2019

ACTA POLYTECH HUNG

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Self-driving technologies introduced new challenges to the control engineering community. Autonomous vehicles with limited automation capabilities require constant human supervision, and human drivers have to be able to take back control at any time, which is called handover. This is a critical process in terms of safety, thus appropriate handover modeling is fundamental in design, simulation and education related to selfdriving cars. This article reviews the literature of handover processes, situation awareness and control-oriented human driver models. It unifies the psychological and physiological control theory models to create a parameterized engineering tool to quantify the handover processes.

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Study of tensor product model alternatives

Kuczmann

2020

Asian Journal of Control

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A tensor product (TP) model has an infinite number of alternatives. These variants can be readily derived by the TP model transformation that can variate the number of fuzzy rules, the number of antecedent and consequent sets and, further, the shape of the antecedent fuzzy sets. The related literature has quite deep analysis that modifying these features of a TP model has a crucial role in further design. The latest variants of the TP model transformation, emerged about a year ago, are capable of variating the input space of a TP model. The goal of this paper is to analyse this recently emerged new feature through the example of the gantry crane state space model.

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Analytical Upper Bound for the Error on the Discretization of Uncertain Linear Systems by using the Tensor Product Model Transformation

Cited by 19 publications

References 21 publications

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

Handover Process of Autonomous Vehicles – Technology and Application Challenges

Study of tensor product model alternatives

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