Analysis of SDC matrices for successfully implementing the SDRE scheme

Liang, Yew Wen; Li, Lin

doi:10.1016/j.automatica.2013.07.026

Cited by 46 publications

(29 citation statements)

References 12 publications

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“…Given the results in Section 3.1 (Liang & Lin, 2013), with extension to the case of A l , Problem 1 can be easily solved by direct calculation, which alleviates the computational burden to determine the property of the solution of the corresponding SDDRE/SDRE ((3)/(6)). For brevity, we explain in detail the solutions only for Problems 2-3.…”

Section: Lemma 4 (I) a Simentioning

confidence: 99%

“…Besides, in accordance with Liang and Lin (2013), if W ∈ R p×n with p < n and rank(W ) = p, then we define W ⊥ = N(W ), null space of W , and W ⊥ ∈ R n×(n−p) as a selected constant matrix having orthonormal columns and satisfying WW ⊥ = 0. Similarly, if W ∈ R n×q and rank(W ) = q < n, then we define W ⊥ = {w T | w ∈ N(W T )} and W ⊥ ∈ R (n−q)×n as a selected constant matrix having orthonormal rows and satisfying W ⊥ W = 0.…”

Section: Mathematical Representationsmentioning

confidence: 99%

“…Then, we summarize the following lemma to provide fundamental requirements/assumptions on the solvability of SDDRE/SDRE ((3)/(6)) (proof at Heydari et al (2014); Liang and Lin (2013); Zhou, Doyle, and Glover (1996)). …”

Section: Mathematical Representationsmentioning

confidence: 99%

“…Çimen (2010, 2012); Liang and Lin (2013); Lin (2014)), the SDRE scheme is known to include many beneficial properties, and most of them are also possessed by the SDDRE scheme due to the similarity between both schemes. Besides, many practical applications successfully performed by the SDRE scheme have also been reported.…”

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confidence: 97%

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Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems

2015

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Section: Lemma 4 (I) a Simentioning

confidence: 99%

Section: Mathematical Representationsmentioning

confidence: 99%

Section: Mathematical Representationsmentioning

confidence: 99%

mentioning

confidence: 97%

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Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems

2015

Self Cite

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“…However, the continuous control system is more di cult to achieve in engineering practice. Using a LQR (linear quadratic regulator) optimal control algorithm and SDRE (state-dependent Riccati equation) optimal control algorithm to maintain the formation ying [3,4]. Through simulation, it was found that when using the SDRE controller in the system transition process time is shorter than when the LQR controller is used, and fuel consumption is less for the SDRE controller than for the LQR controller.…”

mentioning

confidence: 99%

Study on maintaining formations during satellite formation flying based on SDRE and LQR

Zhang

2017

Open Physics

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Due to the in uence of various perturbations of space, satellites ying in formation cannot maintain speci c con gurations for long durations [1,2]. In order to ensure that formation con gurations are able to meet the requirements of space missions, it is important to maintain control of formation con gurations. This is an urgent problem to be solved. The traditional control method for controlling formations is based on the average orbit element, and uses the assumption that the average orbit element deviation and the instantaneous orbit element deviation are approximately equal. However, the continuous control system is more di cult to achieve in engineering practice. Using a LQR (linear quadratic regulator) optimal control algorithm and SDRE (state-dependent Riccati equation) optimal control algorithm to maintain the formation ying [3,4]. Through simulation, it was found that when using the SDRE controller in the system transition process time is shorter than when the LQR controller is used, and fuel consumption is less for the SDRE controller than for the LQR controller.

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On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

Batmani

2017

Asian Journal of Control

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In this paper, two suboptimal event-triggered control techniques are proposed for both the regulation and the tracking problems in a broad class of nonlinear networked control systems. The proposed techniques are based on the state-dependent Riccati equation (SDRE) methodology. In the case of the regulation problem, the asymptotic stability of the origin of the closed-loop system under the proposed event-triggered control law is investigated. In addition, for the tracking problem, it is proved that the tracking error between the system output and its desired trajectory converges asymptotically to zero under some mild conditions. It is shown that the proposed methods can considerably reduce the information exchange between the controller and the actuator. Due to the implementation procedures of the proposed techniques, no Zeno behavior is occurred. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed event-triggered control techniques.

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Analysis of SDC matrices for successfully implementing the SDRE scheme

Cited by 46 publications

References 12 publications

Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems

Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems

Study on maintaining formations during satellite formation flying based on SDRE and LQR

On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

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