Compositional performance certification of interconnected systems using ADMM

Meissen, Chris; Lessard, Laurent; Arcak, Murat; Packard, Andrew

doi:10.1016/j.automatica.2015.07.027

Cited by 28 publications

(26 citation statements)

References 23 publications

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“…Follow the formulation developed by , the plantwide control synthesis problem can be written in the form of as follows:

\begin{matrix} \underset{Φ_{1 : N}, {\tilde{Φ}}_{1 : N}}{minimize} & \sum_{i = 1}^{N} I_{L_{i}} (Φ_{i}) + I_{G} ({\tilde{Φ}}_{1 : N}) \\ subject to & Φ_{i} - {\tilde{Φ}}_{i} = 0, i = 1, 2, \dots, N, \end{matrix}

where Φ 1: N = (Φ 1 ,Φ 2 ,…,Φ N ),

{\overset{normalΦ}{true}}_{1 : N} = ((), {\overset{normalΦ}{true}}_{1}, {\overset{normalΦ}{true}}_{2}, \dots, {\overset{normalΦ}{true}}_{N})

, the cost functions

{double-struckI}_{{scriptL}_{i}} ({normalΦ}_{i})

and

{double-struckI}_{scriptG} ({\overset{normalΦ}{true}}_{1 : N})

can be written as

{double-struckI}_{{scriptL}_{i}} ({normalΦ}_{i}) = ({, \begin{matrix} 0 & Φ_{i} \in L_{i} \\ \infty & otherwise \end{matrix}), {double-struckI}_{scriptG} (

…”

Section: Plantwide Control Synthesismentioning

confidence: 99%

“…It can be seen that the local and global optimization processes are linked in the feedback interconnection. The convergence update works as an integral control action, which can force the distance between Φ i and

{\overset{normalΦ}{true}}_{i}

converges to zero .…”

Section: Plantwide Control Synthesismentioning

confidence: 99%

“…It was extended to different types of dissipativity properties in [3,28]. Finding the suitable differential dissipativity property for the plantwide system is a feasibility problem, which can be derived in a similar way as [28]. Assume that the differential supply rate of the ith close-loop subsystem is…”

Section: Plantwide Differential Dissipativity Planningmentioning

confidence: 99%

“…In this paper, open source Matlab toolbox -YALMIP [40] and semidefinite programming solver -SeDuMi [41] are used for finding the Q matrix. Distributed plantwide control synthesis based on differential dissipativity is a large-scale feasibility problem, which requires to solve the LMI in (28) for plantwide dissipativity analysis and the state-dependent LMI constraints in (18) for dissipativity shaping of individual subsystem simultaneously. Those state-dependent LMIs are converted into SOS programming problem through relaxation method in Section 4.2.…”

Section: Plantwide Control Synthesismentioning

confidence: 99%

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Distributed plantwide control based on differential dissipativity

Wang

Bao

2016

Intl J Robust & Nonlinear

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Summary Modern chemical plants are becoming very complex, often consisting of a number of nonlinear process units (subsystems) with strong interactions due to material recycle and energy integration. The operation setpoint may need to be adjusted from time to time based on the market demand. To address the aforementioned challenges, a plantwide distributed nonlinear control scheme based on differential dissipativity is proposed in this paper, which can ensure plantwide incremental exponential stability and achieve bounded incremental L2 gain performance. As a non‐unique property, the differential dissipativity of individual subsystem is shaped by a setpoint‐independent control structure – differential state feedback control. The dissipativity properties of subsystems and individual controllers are determined simultaneously as a large‐scale feasibility problem to ensure the plantwide stability and performance. It is converted into an LMI condition for plantwide supply rate planning and small‐scale sum‐of‐squares programming problems for individual subsystem dissipativity shaping, by using the alternating direction method of multipliers method. The proposed approach is illustrated using a chemical reactor network with a recycle stream. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Follow the formulation developed by , the plantwide control synthesis problem can be written in the form of as follows:

\begin{matrix} \underset{Φ_{1 : N}, {\tilde{Φ}}_{1 : N}}{minimize} & \sum_{i = 1}^{N} I_{L_{i}} (Φ_{i}) + I_{G} ({\tilde{Φ}}_{1 : N}) \\ subject to & Φ_{i} - {\tilde{Φ}}_{i} = 0, i = 1, 2, \dots, N, \end{matrix}

where Φ 1: N = (Φ 1 ,Φ 2 ,…,Φ N ),

{\overset{normalΦ}{true}}_{1 : N} = ((), {\overset{normalΦ}{true}}_{1}, {\overset{normalΦ}{true}}_{2}, \dots, {\overset{normalΦ}{true}}_{N})

, the cost functions

{double-struckI}_{{scriptL}_{i}} ({normalΦ}_{i})

and

{double-struckI}_{scriptG} ({\overset{normalΦ}{true}}_{1 : N})

can be written as

{double-struckI}_{{scriptL}_{i}} ({normalΦ}_{i}) = ({, \begin{matrix} 0 & Φ_{i} \in L_{i} \\ \infty & otherwise \end{matrix}), {double-struckI}_{scriptG} (

…”

Section: Plantwide Control Synthesismentioning

confidence: 99%

{\overset{normalΦ}{true}}_{i}

converges to zero .…”

Section: Plantwide Control Synthesismentioning

confidence: 99%

Section: Plantwide Differential Dissipativity Planningmentioning

confidence: 99%

Section: Plantwide Control Synthesismentioning

confidence: 99%

See 2 more Smart Citations

Distributed plantwide control based on differential dissipativity

Wang

Bao

2016

Intl J Robust & Nonlinear

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show abstract

“…Then, Equation (24) can be solved by the alternate direction method of multipliers method (ADMM), the detailed ADMM algorithms of which are given in [33][34][35]. Finally, all the IMF models obtained from this solution are written as:…”

Section: Review Of Vmdmentioning

confidence: 99%

Incipient Fault Feature Extraction for Rotating Machinery Based on Improved AR-Minimum Entropy Deconvolution Combined with Variational Mode Decomposition Approach

Liang

2017

Entropy

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Aiming at the issue of extracting the incipient single-fault and multi-fault of rotating machinery from the nonlinear and non-stationary vibration signals with a strong background noise, a new fault diagnosis method based on improved autoregressive-Minimum entropy deconvolution (improved AR-MED) and variational mode decomposition (VMD) is proposed. Due to the complexity of rotating machinery systems, the periodic transient impulses of single-fault and multiple-faults always emerge in the acquired vibration signals. The improved autoregressive minimum entropy deconvolution (AR-MED) technique can effectively deconvolve the influence of the background noise, which aims to enhance the peak value of the multiple transient impulses. Nevertheless, the envelope spectrum of simulation and experimental in this work shows that there are many interference components exist on both left and right of fault characteristic frequencies when the background noise is strong. To overcome this shortcoming, the VMD is thus applied to adaptively decompose the filtered output vibration signal into a number of quasi-orthogonal intrinsic modes so as to better detect the single-and multiple-faults via those sub-band signals. The experimental and engineering application results demonstrate that the proposed method dramatically sharpens the fault characteristic frequencies (FCFs) from the impacts of bearing outer race and gearbox faults compared to the traditional methods, which show a significant improvement in early incipient faults of rotating machinery.

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