Design of a robust model predictive controller with reduced computational complexity

Razi, Maryam; Haeri, ءMohammad

doi:10.1016/j.isatra.2014.09.008

Cited by 10 publications

(7 citation statements)

References 18 publications

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“…The Lipschitz weighing matrix N has a significant impact on calculation of the feedback gain F i , such that larger value of N results in conservative response of feedback gains and then smaller polyhedral sets. In an analytical method has been introduced, which calculates the optimal value of matrix N by solving an SOS optimization problem instead of a trial and error procedure. In addition, the number of polyhedral invariant sets S i , i ∈ {1, 2, …, N } affects control performance such that increasing the number of polyhedral invariant sets improve the control performance and decrease discontinuity in the system responses, even though increasing the number of polyhedral invariant sets is encouraging but the computational time increases somewhat.…”

Section: Off‐line Constrained Mpc Using Polyhedral Invariant Setsmentioning

confidence: 99%

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Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

Shokrollahi

Shamaghdari

2018

Asian Journal of Control

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In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non-linear systems composed of a linear constant part followed by a non-linear term. We characterize the maximal admissible set for the non-linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state-feedback RMPC law is derived off-line for Lipschitz non-linear systems. The state-feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed-loop robust stability. Most of the computational burdens are moved off-line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on-line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.

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Section: Off‐line Constrained Mpc Using Polyhedral Invariant Setsmentioning

confidence: 99%

“…For fast processing, this concern is more stringent. There are some works that have tried to reduce the on‐line computation demand . An off‐line strategy based on a look‐up table is used in to reduce the on‐line computational burden.…”

Section: Introductionmentioning

confidence: 99%

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

Shokrollahi

Shamaghdari

2018

Asian Journal of Control

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“…Meanwhile, model predictive controller is widely used to control industrial systems [4][5][6][7][8] due to its unique features. Given the fact that most operational systems are nonlinear and bounded systems, the predictive controllers are used on the basis of linear or non-linear models with uncertainty [9][10][11][12][13][14]. One reason for this is that non-linear predictive control algorithms lead to nonconvex, non-linear optimization problems, the solution requires reiterative methods along with extended calculation times [8].…”

Section: Introductionmentioning

confidence: 99%

“…However, in many systems, the non-linear effects cannot be ignored. In these conditions, the system can be approximated by a linear model and considered on the scope approximation error [12][13][14]. Predictive control has a strong advantage: it can consider constraints explicitly in the problem, but it cannot calculate the model uncertainty explicitly in the formulation.…”

Section: Introductionmentioning

confidence: 99%

A new robust LMI-based model predictive control for continuous-time uncertain nonlinear systems

Huofa

Marrani

2020

Automatika

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This paper presents a new robust predictive controller for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound as well as constraints on input states. The controller is designed in the form of an optimization problem of the 'worst-case' objective function over an infinite moving horizon. Through this objective function, constraints and uncertainties can be applied explicitly on the controller design, which guarantees the system stability. Next, LMI tool is used to improve the calculation time and complexity. To do this, in order to find the optimum gain for state-feedback, the optimization problem is solved using LMI method in each time step. Finally, to show the efficiency and effectiveness of the proposed algorithm, a surge phenomenon avoidance problem in centrifugal compressors is solved.

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“…However, in many systems, the nonlinear effects cannot be ignored. In these conditions, the system can be approximated by a linear model and be considered on the scope approximation error [15,16,17]. Predictive control has a strong advantage: it can consider constraints explicitly in the problem, but it cannot explicitly calculate the model uncertainty in the formulation.…”

Section: Introductionmentioning

confidence: 99%

Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem

Ziabari¹,

Jahed‐Motlagh²,

Salahshoor³

et al. 2017

Kybernetika

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Design of a robust model predictive controller with reduced computational complexity

Cited by 10 publications

References 18 publications

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

A new robust LMI-based model predictive control for continuous-time uncertain nonlinear systems

Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem

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