An improved method for nonlinear model reduction using balancing of empirical gramians

Hahn, Juergen; Edgar, Thomas F.

doi:10.1016/s0098-1354(02)00120-5

Cited by 200 publications

(181 citation statements)

References 24 publications

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“…The calculation of such policies, e.g. in the form Rivotti et al [296] A model order reduction via empirical gramians [149] is combined with a mp-MPC algorithm…”

Section: Multi-parametric Programmingmentioning

confidence: 99%

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Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Diangelakis

Pistikopoulos

2017

Computer Aided Chemical Engineering

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“…The calculation of such policies, e.g. in the form Rivotti et al [296] A model order reduction via empirical gramians [149] is combined with a mp-MPC algorithm…”

Section: Multi-parametric Programmingmentioning

confidence: 99%

“…The transformation matrix is based on empirical Grammians or covariance matrices which are computed via system simulation data [149,150]. The transformed system of eq.…”

Section: Model Approximationmentioning

confidence: 99%

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Diangelakis

Pistikopoulos

2017

Computer Aided Chemical Engineering

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“…Such situations can also be addressed by including the cost function of the system when solving the projection matrices, e.g. (Hahn and Edgar, 2002). More details about BT can be referred in a recent survey (Gugercin and Antoulas, 2004).…”

Section: ) Balanced Truncationmentioning

confidence: 99%

“…For example, the Galerkin projections is also applied to the balanced truncation by Hahn and Edgar (2002). The balanced truncation can also be applied to the multi-parametric programming based MPC to decrease the number of parameters stored in the memory, e.g.…”

Section: ) Balanced Truncationmentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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“…For nonlinear systems, the first step toward extension of the linear balancing methods has been set in [45], where a balancing formalism is developed for stable nonlinear continuous-time state-space systems based on the idea that state components that correspond to low control costs and high output energy generation (in the sense of L2 energy in a signal) are important for the description of the dynamics of the input-output behavior of the system, while state components with high control costs and low output energy generation can be left out of the description. Since then, many results on state-space balancing, modifications based on sliding time windows, and modifications based on proper orthogonal decomposition (POD), and computational issues for model reduction and related minimality considerations for nonlinear systems have appeared in the literature; for example, [18,20,28,37,38,58,59,64]. The relations of the original nonlinear balancing method of [45] with minimality are later explored in [47], and a more constructive approach that includes a strong relation with the nonlinear input-output operators, the nonlinear Hankel operator, and the Hankel norm of the system is presented in [10,12,48].…”

Section: Introductionmentioning

confidence: 99%

Balanced Realizations, Model Order Reduction, and the Hankel Operator

Scherpen¹

2010

The Control Systems Handbook, Second Edition

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An improved method for nonlinear model reduction using balancing of empirical gramians

Cited by 200 publications

References 24 publications

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

1-Bit processing based model predictive control for fractionated satellite missions

Balanced Realizations, Model Order Reduction, and the Hankel Operator

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