MPC for Large-Scale Systems via Model Reduction and Multiparametric Quadratic Programming

Hovland, Svein; Willcox, Karen; Gravdahl, Jan Tommy

doi:10.1109/cdc.2006.377323

Cited by 25 publications

(12 citation statements)

References 26 publications

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“…Moreover, it is important to develop a model reduction method, which is compatible with MPC. Such topic has been studied in e.g., [11]. It is also important to apply the proposed method to practical large-scale systems.…”

Section: Resultsmentioning

confidence: 99%

Approximate MLD System Model of Switched Linear Systems for Model Predictive Control

Kanazawa

Kobayashi

Yamashita

2017

SICE Journal of Control, Measurement, and System Integration

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: In this paper, to reduce the computation time for solving the finite-time optimal control problem (i.e., the model predictive control (MPC) problem), an approximate model of switched linear systems is proposed. A switched linear system is one of the typical subclasses of hybrid systems, and has several applications such as networked control systems. First, an approximation of the state variable in switched linear systems is derived. Next, using auxiliary binary and continuous variables, an approximate model given by a mixed logical dynamical system model is derived. Using this approximate model, the dimension of the auxiliary continuous variable can be reduced. As a result, the online computation time in MPC can decrease. Finally, the effectiveness of the proposed method is presented by a numerical example.

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Section: Resultsmentioning

confidence: 99%

Approximate MLD System Model of Switched Linear Systems for Model Predictive Control

Kanazawa

Kobayashi

Yamashita

2017

SICE Journal of Control, Measurement, and System Integration

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“…Because of the uncertainty introduced by reducing the order of the model, it is common practice in MPC based on reduced-order models to impose only soft constraints on the state variables [11]. In other studies the dynamics of the actual high-dimensional system is completely disregarded, thus no guarantee is provided in regard to the satisfaction of constraints or the recursive feasibility of the control algorithm [12]. These shortcomings reflect on the fact that the vast majority of applications of reduced-order control does not take into account the physical borders of the underlying system [13].…”

Section: Introductionmentioning

confidence: 99%

Constrained model predictive control based on reduced-order models

Sopasakis

Bernardini

Bemporad

2013

52nd IEEE Conference on Decision and Control

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The need for reduced-order approximations of dynamical systems emerges naturally in model-based control of very large-scale systems, such as those arising from the discretisation of partial differential equation models. The controller based on the reduced-order model, when in closed-loop with the large-scale system, ought to endow certain properties, in primis stability, but also satisfaction of state constraints and recursive computability of the control law in the case of constrained control.In this paper we introduce a new approach to the design of model predictive controllers to meet the aforementioned requirements while the on-line complexity is essentially tantamount to the one that corresponds to the low-dimensional approximate model.

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“…Reduced order modeling [8] is also a well established field. While often used for simulation, reduced order models have also been applied to control problems [6], [12] using ROMPC [13]- [18]. In [16], guarantees on constraint satisfaction are given by considering the neglected dynamics as a bounded disturbance.…”

Section: Introductionmentioning

confidence: 99%

Reduced Order Model Predictive Control For Setpoint Tracking

Lorenzetti

Benoit

Singh

et al. 2019

2019 18th European Control Conference (ECC)

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Despite the success of model predictive control (MPC), its application to high-dimensional systems, such as flexible structures and coupled fluid/rigid-body systems, remains a largely open challenge due to excessive computational complexity. A promising solution approach is to leverage reduced order models for designing the model predictive controller. In this paper we present a reduced order MPC scheme that enables setpoint tracking while robustly guaranteeing constraint satisfaction for linear, discrete, time-invariant systems. Setpoint tracking is enabled by designing the MPC cost function to account for the steady-state error between the full and reduced order models. Robust constraint satisfaction is accomplished by solving (offline) a set of linear programs to provide bounds on the errors due to bounded disturbances, state estimation, and model approximation. The approach is validated on a synthetic system as well as a high-dimensional linear model of a flexible rod, obtained using finite element methods.

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MPC for Large-Scale Systems via Model Reduction and Multiparametric Quadratic Programming

Cited by 25 publications

References 26 publications

Approximate MLD System Model of Switched Linear Systems for Model Predictive Control

Approximate MLD System Model of Switched Linear Systems for Model Predictive Control

Constrained model predictive control based on reduced-order models

Reduced Order Model Predictive Control For Setpoint Tracking

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