Covariance‐based hardware selection part IV: Solution using the generalized benders decomposition

Zhang, Jin; Wang, Xiaoxi; Chmielewski, Donald J.

doi:10.1002/aic.15285

Cited by 5 publications

(5 citation statements)

References 23 publications

(37 reference statements)

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“…no saturation effect). To that end, our future work will focus on (i) investigating different approaches to solve SASP other than using BnB algorithm such as the generalized Benders decomposition [31] and branch-and-cut algorithm [32], (ii) extending the proposed approach for addressing the robust SASP as well as the simultaneous selection of SA through output feedback control and observer-based control policies, and (iii) considering the effect of SA saturation in SASP.…”

Section: Paper Summary and Limitationsmentioning

confidence: 99%

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

Nugroho¹,

Taha²

2020

Preprint

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Sensor and actuator selection problems (SASP) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such that certain estimation/control objectives can be achieved. While the literature on SASP is indeed inveterate, the vast majority of the work focuses on linear(ized) representation of the network dynamics, resulting in the placements of sensors or actuators (SA) that are valid for confined operating regions. As an alternative, herein we propose a new general framework for addressing SASP in nonlinear dynamic systems (NDS), assuming that the inputs and outputs are linearly coupled with the nonlinear dynamics. This is investigated through (i) classifying and parameterizing the NDS into various nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations, and (iii) designing a new customized branch-and-bound (BnB) algorithm that exploits problem structure of the SASP. The newly designed BnB routines are computationally more attractive than the standard one and also directly applicable to solve SASP for linear systems. In contrast with contemporary approaches from the literature, our approach is suitable for finding the optimal SA combination for stable/unstable NDS that ensures stabilization of estimation error and closed-loop dynamics through a simple linear feedback control policy.

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Section: Paper Summary and Limitationsmentioning

confidence: 99%

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

Nugroho¹,

Taha²

2020

Preprint

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“…To employ the GBD approach, the attendance variable α i must be split into two partsone part for the cost of the component, α i (cc) , and a second for its impact on system performance, α i (sp) . Using an extension of theorem 1 of ref , the equivalent form of problem is obtained as …”

Section: Application Of Gbd To Value-optimal Snd For Steady-state Sys...mentioning

confidence: 99%

“…In 2016, a similar, though distinct, application of the GBD to the cost optimal SND problem (including the cost optimal SND involving residual precisions) also yielded orders of magnitude reductions in computational effort. 14 The current paper aims to apply the GBD algorithm to the value-optimal SND problem, which is essentially a combination of the ELOC and cost optimal SND problems.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the previous branch and bound procedure was replaced with an application of the generalized benders decomposition (GBD) and resulted in orders of magnitude reductions in computational effort. In 2016, a similar, though distinct, application of the GBD to the cost optimal SND problem (including the cost optimal SND involving residual precisions) also yielded orders of magnitude reductions in computational effort . The current paper aims to apply the GBD algorithm to the value-optimal SND problem, which is essentially a combination of the ELOC and cost optimal SND problems.…”

Section: Introductionmentioning

confidence: 99%

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Value-Optimal Sensor Network Design for Steady-State and Closed-Loop Systems Using the Generalized Benders Decomposition

Zhang

Chmielewski

2017

Ind. Eng. Chem. Res.

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The problem of value-optimal sensor network design for linear systems has been shown to be of the nonconvex mixed integer programming class. While the branch and bound search procedure can be used to obtain a global solution, such a method is limited to fairly small systems. The bottleneck is that during each iteration of the branch and bound search, a fairly slow semi-definite programming (SDP) problem must be solved to its global optimum. In this paper, it is demonstrated that an equivalent reformulation of the nonconvex mixed integer programming problem and subsequent application of the generalized benders decomposition (GBD) algorithm will result in massive reductions in computational effort. While the proposed algorithm has to solve multiple mixed integer linear programs, this increase in computational effort is significantly outweighed by a reduction in the number of SDP problems that must be solved.

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“…On the other hand, the generalized Benders decomposition has shown significant computational performance over the branch and bound approach. 25 Various information-theoretic measures, like entropy, correntropy, and mutual information entropy, have been used for data reconciliation. Entropy is a measure of uncertainty or randomness in a system.…”

Section: Introductionmentioning

confidence: 99%

Convex optimization approach to design sensor networks using information theoretic measures

Magbool Jan

2023

AIChE Journal

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Accurate and precise estimation of process variables is key to effective process monitoring. The estimation accuracy depends on the choice of the sensor network. Therefore, the article aims at developing convex optimization formulations for designing the optimal sensor network using information‐theoretic measures in linear steady‐state data reconciliation. To this end, the estimation errors are characterized by a multivariate Gaussian distribution, and thus the analytical form for entropy and Kullback–Leibler divergences (forward, reverse, and symmetric) of estimation errors can be obtained to formulate the optimal sensor network design. The proposed information theoretic‐based optimal sensor selection problems are shown to be integer semi‐definite programming problems where the relaxation of binary decision variables results in solving a convex optimization problem. Thus, we use a branch and bound method to obtain a globally optimal sensor network design. Demonstrative case studies are presented to illustrate the efficacy of the proposed optimal sensor selection formulations.

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Covariance‐based hardware selection part IV: Solution using the generalized benders decomposition

Cited by 5 publications

References 23 publications

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

Value-Optimal Sensor Network Design for Steady-State and Closed-Loop Systems Using the Generalized Benders Decomposition

Convex optimization approach to design sensor networks using information theoretic measures

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