An improved robust model predictive control for linear parameter‐varying input‐output models

Abbas, Hms Hossam; Hanema, Jurre; Tóth, Roland; Mohammadpour, Javad; Meskin, Nader

doi:10.1002/rnc.3906

Cited by 34 publications

(29 citation statements)

References 37 publications

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“…The nominal states z i|k are computed according to the nominal model in (19) given p 0|k = p(k) (for computing the corresponding system matrix), where z 0|k = x(k). The tightened state and input constraint sets Z and V are computed offline from (17a) and (17b), respectively.…”

Section: Optimization Problemmentioning

confidence: 99%

“…Such a control problem has been rarely investigated in the context of LPVMPC, where most of the developed methods have focused on regulating the state of the controlled system to the origin or to a set point. Robust tracking MPC approaches for LPV systems have been developed recently in [19], which have achieved offset-free tracking for piecewise constant references. In [20]- [22] LPVMPC algorithms have been proposed for tracking time-varying reference trajectories, e.g., command trajectories in robotics applications.…”

Section: Introductionmentioning

confidence: 99%

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Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

et al. 2021

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In this paper, a practical model predictive control (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the linear parameter-varying (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single quadratic programming (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of admissible reference, the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality.INDEX TERMS Constrained systems, Linear parameter-varying systems, Model predictive control, Robust stability, Robotic manipulators.

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Section: Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

et al. 2021

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“…when G [1] = G [2] and G [3] = −G [4] . In other cases, one can look for state transformations such that z(t) depends only on measurable/observable states, the (past) input and output (Abbas et al, 2017).…”

Section: Remarksmentioning

confidence: 99%

From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

Schoukens

Tóth

2018

IFAC-PapersOnLine

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Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples.

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“…In this context, MPC for LPV systems with exogenous scheduling variables has received a fair degree of attention in recent years. Most of these approaches are based on a worst‐case objective function that minimizes maximum values of an objective function for different values of the scheduling variables, which results in conservatism, this conservatism can be partially addressed by relaxation techniques . MPC for a certain class of quasi‐LPV systems, specifically those derived from output nonlinear systems, was studied in Chisci et al, where stability guarantees for set point tracking were obtained by partitioning the state space and deriving the terminal ingredients for each partition.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear model predictive control for models in quasi‐linear parameter varying form

Cisneros

Werner

2020

Intl J Robust & Nonlinear

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This article presents a nonlinear model predictive control (NMPC) approach based on quasi-linear parameter varying (quasi-LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi-LPV representations of the system using velocity-based linearization is presented in two examples. K E Y W O R D S efficient algorithms, linear matrix inequality, nonlinear model predictive control, quasi-linear parameter varying systems 1 Int J Robust Nonlinear Control. 2020;30:3945-3959.wileyonlinelibrary.com/journal/rnc

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An improved robust model predictive control for linear parameter‐varying input‐output models

Cited by 34 publications

References 37 publications

Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

Nonlinear model predictive control for models in quasi‐linear parameter varying form

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