Model predictive control design for linear parameter varying systems: A survey

Morato, Marcelo Menezes; Normey‐Rico, Julio E.; Sename, Olivier

doi:10.1016/j.arcontrol.2020.04.016

Cited by 140 publications

(103 citation statements)

References 159 publications

(183 reference statements)

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“…which was used previously. In the setting of this paper, this stricter condition is necessary to guarantee consistency between the transition constraints (X i , Θ i |K i ) ⊆ X i+1 and the dynamics (4).…”

Section: Definitionmentioning

confidence: 99%

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Hanema

Tóth

Lazăr

2021

IET Control Theory & Appl

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This paper proposes a model predictive control (MPC) approach for non-linear systems where the non-linear dynamics are embedded inside a linear parameter-varying (LPV) representation. The non-linear MPC problem is therefore replaced by an LPV MPC problem, without using linearization. Compared to general non-linear MPC, advantages of this approach are that it allows for the tractable construction of a terminal set and cost, and that only a single convex program must be solved online. The key idea that enables proving recursive feasibility and stability, is to restrict the state evolution of the non-linear system to a time-varying sequence of state constraint sets. Because in LPV embeddings, there exists a relationship between the scheduling and state variables, these state constraints are used to construct a corresponding future scheduling tube. Compared to non-time-varying state constraints, tighter bounds on the future scheduling trajectories are obtained. Computing a scheduling tube in this setting requires applying a non-linear function to the sequence of constraint sets. Outer approximations of this non-linear projection-based scheduling tube can be found, e.g., via interval analysis. The computational properties of the approach are demonstrated on numerical examples.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Definitionmentioning

confidence: 99%

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Hanema

Tóth

Lazăr

2021

IET Control Theory & Appl

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“…The control action u к-1 is known. Then for the step k it is fair u к = u к-1 + Du к ; from here 7), constraints (6) can be represented as the system of linear ine qualities:…”

Section: Mpc With Quadratic Cost Function With Constraints On Input and Output Variablesmentioning

confidence: 99%

“…The general set of MPC strategy components consists of a process model, a performance index, constraints and an optimization method. Process models can be both linear and nonlinear or even a set of model combination [5][6][7] with input and/or output constraints as an explicit part of the models. P. Tatjewski, M. Ławryńczuk in [8] assume that such processes exist under influence of external disturbances and their models are not precise.…”

Section: Introductionmentioning

confidence: 99%

Model Predictive Control Toolbox Design for Nonstationary Process

Stepanets

Mariiash

2021

KPI SN

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Background. Model predictive control (MPC) approach is the basic feedback scheme, combined with high adaptive properties, which determines its successful use in the practice of design and operation of control systems. These advantages allow managing multidimensional objects with a complex structure, including nonlinearity, optimizing processes in real time within the constraints on controlled and managed variables, taking into account uncertainties in the task of objects and perturbations. Objective. The purpose of the paper is to design and analyse control system of carbon monoxide oxidation in the convector cavity based on MPC with linear-quadratic cost functional with constraint. Methods. The design of MPC is based on mathematical model of an object (relatively simple). At the current step, the prediction of object dynamic response on some final period of time (prediction horizon) is carried out; control optimization is performed, the purpose of which is to approximate the control variables of the prediction model to the corresponding setpoint on the predict horizon. The found optimal control is applied and measurement of an actual state of object at the end of a step is carried out. The prediction horizon is shifted one step further, and this algorithm are repeated. Results. The results of modeling the automatic control system show that the MPC approach provides maintenance of carbon dioxide content when changing oxygen consumption and overshoot caused by introduction bulk does not exceed 0.6 % that meets the technological requirements of the process. Conclusions. A fuse of the MPC and the quadratic functional given the constraints on the input signals is proposed. The problems of control degree of carbon oxidation in the convector cavity include non-stationarity, so the use of classical control methods is difficult. The MPC approach minimizes the cost function that characterizes the quality of the process. The predicted behaviour of a dynamic system will usually differ from its actual motion. The obtained quadratic functional is optimized to find the optimal control of degree of CO oxidation to CO2.

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“…In this perspective, Model Predictive Control (MPC) is a control technique including both feedback control and optimization that allows to take into account the deviations of the predictive model from the real progress of the disease Bussell, Dangerfield, Gilligan, and Cunniffe (2019) , Morato, Normey-Rico, and Sename (2020) . Although implementing the MPC controller typically requires a large amount of computational resources, which can lead to long computation time Carli, Cavone, Dotoli, Epicoco, and Scarabaggio (2019) , this is not a concern when the optimization is performed at a strategic level, as is the case of the decision-making process for the definition of the proper strategies to tackle epidemiological diseases.…”

Section: Introduction and Paper Positioningmentioning

confidence: 99%

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

Carli

Cavone

Epicoco

et al. 2020

Annual Reviews in Control

100

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The COVID-19 outbreak is deeply influencing the global social and economic framework, due to restrictive measures adopted worldwide by governments to counteract the pandemic contagion. In multi-region areas such as Italy, where the contagion peak has been reached, it is crucial to find targeted and coordinated optimal exit and restarting strategies on a regional basis to effectively cope with possible onset of further epidemic waves, while efficiently returning the economic activities to their standard level of intensity. Differently from the related literature, where modeling and controlling the pandemic contagion is typically addressed on a national basis, this paper proposes an optimal control approach that supports governments in defining the most effective strategies to be adopted during post-lockdown mitigation phases in a multi-region scenario. Based on the joint use of a non-linear Model Predictive Control scheme and a modified Susceptible-Infected-Recovered (SIR)-based epidemiological model, the approach is aimed at minimizing the cost of the so-called non-pharmaceutical interventions (that is, mitigation strategies), while ensuring that the capacity of the network of regional healthcare systems is not violated. In addition, the proposed approach supports policy makers in taking targeted intervention decisions on different regions by an integrated and structured model, thus both respecting the specific regional health systems characteristics and improving the system-wide performance by avoiding uncoordinated actions of the regions. The methodology is tested on the COVID-19 outbreak data related to the network of Italian regions, showing its effectiveness in properly supporting the definition of effective regional strategies for managing the COVID-19 diffusion.

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Model predictive control design for linear parameter varying systems: A survey

Cited by 140 publications

References 159 publications

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Model Predictive Control Toolbox Design for Nonstationary Process

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

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