Ellipsoidal approximations to attraction domains of linear systems with bounded control

Polyak, B. T.; Shcherbakov, Pavel

doi:10.1109/acc.2009.5160175

Cited by 14 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [28], the authors use ellipsoids to approximate polytopes. Ellipsoidal approximation is also widely used in control problems to describe the attraction domain [29] and to approximated polyhedral sets in power systems [30].…”

Section: A Prior Resultsmentioning

confidence: 99%

A tractable ellipsoidal approximation for voltage regulation problems

Jin

Xiong

et al. 2019

2019 American Control Conference (ACC)

View full text Add to dashboard Cite

We present a machine learning approach to the solution of chance constrained optimizations in the context of voltage regulation problems in power system operation. The novelty of our approach resides in approximating the feasible region of uncertainty with an ellipsoid. We formulate this problem using a learning model similar to Support Vector Machines (SVM) and propose a sampling algorithm that efficiently trains the model. We demonstrate our approach on a voltage regulation problem using standard IEEE distribution test feeders.

show abstract

Section: A Prior Resultsmentioning

confidence: 99%

A tractable ellipsoidal approximation for voltage regulation problems

Jin

Xiong

et al. 2019

2019 American Control Conference (ACC)

View full text Add to dashboard Cite

show abstract

“…x = x − x s and ū = u − u s . Following the linearization, a semi-definite program (SDP) is formulated according to the work by Polyak and Shcherbakov [25]. The SDP to be solved is presented in Optimization problem (18).…”

Section: Modification Of the Target Zonementioning

confidence: 99%

Robust economic MPC of the absorption column in post-combustion carbon capture through zone tracking

Decardi‐Nelson¹,

Liu²

2022

Preprint

View full text Add to dashboard Cite

Several studies have reported the importance of optimally operating the absorption column in a post-combustion CO 2 capture (PCC) plant. It has been demonstrated in our previous work how economic Model Predictive Control (EMPC) has a great potential to improve the operation of the PCC plant. However, the use of a general economic objective such as maximizing the absorption efficiency of the column can cause EMPC to drive the state of the system close to the constraints. This may often than not lead to solvent overcirculation and flooding which are undesirable. In this work, we present an EMPC with zone tracking algorithm as an effective means to address this problem. The proposed control algorithm incorporates a zone tracking objective and an economic objective to form a multi-objective optimal control problem. To ensure that the zone tracking objective is achieved in the presence of model uncertainties and time-varying flue gas flow rate, we propose a method to modify the original target zone with a control invariant set. The zone modification method combines both ellipsoidal control invariant set techniques and a back-off strategy. The use of ellipsoidal control invariant sets ensure that the method is applicable to large scale systems such as the absorption column. We present several simulation case studies that demonstrate the effectiveness and applicability of the proposed control algorithm to the absorption column in a post-combustion CO 2 capture plant.

show abstract

“…x s ,u s are matrices of appropriate dimensions, and x and ū denote the system states and input in deviation form, i.e., x = x − x s and ū = u − u s . Following the linearization, a semi-definite program (SDP) is formulated according to the work by Polyak and Shcherbakov [28]. The SDP to be solved is presented in Optimization problem described by Equations ( 40…”

Section: Modification Of the Target Zonementioning

confidence: 99%

Robust Economic MPC of the Absorption Column in Post-Combustion Carbon Capture through Zone Tracking

Decardi‐Nelson

Liu

2022

Energies

View full text Add to dashboard Cite

Several studies have reported the importance of optimally operating the absorption column in a post-combustion CO2 capture (PCC) plant. It has been demonstrated in our previous work how economic model predictive control (EMPC) has a great potential to improve the operation of the PCC plant. However, the use of a general economic objective such as maximizing the absorption efficiency of the column can cause EMPC to drive the state of the system close to the constraints. This may lead to solvent overcirculation and flooding, which are undesirable. In this work, we present an EMPC with zone tracking algorithm as an effective means to address this problem. The proposed control algorithm incorporates a zone tracking objective and an economic objective to form a multi-objective optimal control problem. To ensure that the zone tracking objective is achieved in the presence of model uncertainties and time-varying flue gas flow rate, we propose a method to modify the original target zone with a control invariant set. The zone modification method combines both ellipsoidal control invariant set techniques and a back-off strategy. The use of ellipsoidal control invariant sets ensure that the method is applicable to large scale systems such as the absorption column. We present several simulation case studies that demonstrate the effectiveness and applicability of the proposed control algorithm to the absorption column in a post-combustion CO2 capture plant.

show abstract

Ellipsoidal approximations to attraction domains of linear systems with bounded control

Cited by 14 publications

References 11 publications

A tractable ellipsoidal approximation for voltage regulation problems

A tractable ellipsoidal approximation for voltage regulation problems

Robust economic MPC of the absorption column in post-combustion carbon capture through zone tracking

Robust Economic MPC of the Absorption Column in Post-Combustion Carbon Capture through Zone Tracking

Contact Info

Product

Resources

About