An offset-free MPC formulation for nonlinear systems using adaptive integral controller

Hermansson, Ayman William; Syafiie, S.

doi:10.1016/j.isatra.2019.01.037

Cited by 20 publications

(18 citation statements)

References 86 publications

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“…In Definition 5, symmetric input constraints have been assigned as this permits straightforward transformation of constraint satisfaction conditions to linear matrix inequality (LMI) form, which are incorporable in many optimization solvers. 41…”

Section: Remark 8 (Symmetric and Nonsymmetric Constraints)mentioning

confidence: 99%

Model predictive tracking control of uncertain moving structures with nonaffine saturated actuation: Rotating control force

Yaqubi

Homaeinezhad

2021

Proceedings of the Institution of Mechanical Engineers, Part G:

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This article presents a novel scheme for model-based control of multi-input–multi-output (MIMO) systems considering input nonaffinity, nonlinear dynamical effects, and bounded modeling uncertainty. Commonly, model-based control of a nonaffine system is conducted based on an equivalent pseudo-affine expression. However, validity of this approximation necessitates boundedness of inputs and states. Furthermore, existence of truncation errors is inevitable when obtaining the pseudo-affine model. Therefore, robustness to bounded uncertainty should be ensured even in cases where the original system is deterministic. To address the expressed issues, in this study the boundedness assumptions are incorporated in a constrained robust model predictive control (MPC) algorithm. The corresponding MPC scheme is based on construction of cost according to predicted sliding functions over a finite prediction horizon. It should be noted that for the considered class of uncertain nonlinear nonaffine system, obtaining the perquisite robust stability and feasibility conditions is non-trivial. To attain the aforementioned qualities, it is proposed that sliding functions can be expressed as the sum of input-based terms (using pseudo-affine approximation of input gains based on Taylor expansion) and dynamical variation terms. Subsequently, robust stability is ensured by constructing a Lyapunov-based terminal cost. Constraints satisfaction conditions are determined based on calculation of the corresponding feasible region. Numerical simulations for a nonlinear nonaffine mechanical system indicate efficiency of the presented control model. Comparisons with other applicable schemes highlight significant features of the presented algorithm and the attained improvements regarding stability and control feasibility are discussed.

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Section: Remark 8 (Symmetric and Nonsymmetric Constraints)mentioning

confidence: 99%

Model predictive tracking control of uncertain moving structures with nonaffine saturated actuation: Rotating control force

Yaqubi

Homaeinezhad

2021

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…The tube-based MPC has better steady-state performance but a worse transient performance than the DOBMPC, and they have almost the same computational complexities. It is possible to achieve offset-free tracking in the case of constant or known dynamic disturbance [18][19][20][21][22][23][24]. In [24] an economic robust tube-based MPC for offset-free tracking of discrete-time linear systems was presented.…”

Section: Introductionmentioning

confidence: 99%

Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

Zamani

Bolandi

2022

IET Control Theory & Appl

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This paper develops a novel observer-based robust tracking predictive controller for discrete-time nonlinear affine systems capable of dealing with changing setpoints and nonadditive non-slowly varying unknown disturbance with bounded variations. The existence of disturbance and/or sudden changes in a setpoint may lead to feasibility and stability issues in the stabilizing terminal constraint-based MPC. Since robust tracking MPCs usually consider additive disturbance, the recursive feasibility of these methods may be lost in the presence of non-additive non-slowly varying disturbance. The robust tracking MPC presented here extends the artificial reference-based MPC to deal with both changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state constraints as new system constraints. The authors also guarantee the boundedness of disturbance observation error and closed-loop tracking error. In this method, the optimal tracking error converges asymptotically to the terminal region, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. It is shown that the proposed controller can achieve offset-free tracking in the presence of constant disturbance. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

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“…Also, economic MPC formulations including the offset-free feature to account for model uncertainties can be found in [25]- [27]. A different approach for discrete-time systems was developed in [28] using a multiple linear MPC that can handle some amount of plant-model uncertainty, and it was improved with an adaptive integral action to guarantee offset-free tracking while avoiding the use of an observer.…”

Section: Introductionmentioning

confidence: 99%

Offset-Free Nonzero Tracking for Nonlinear Impulsive Systems With Application to Biomedical Processes

et al. 2022

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Impulsive control systems have shown strong potential to represent and address challenging problems, especially in the biomedical field. In recent research, these problems have been tackled with advances in linear impulsive control systems. However, many biomedical applications are better described by nonlinear impulsive models, and therefore, it is necessary to develop analysis tools and control strategies in this context. In the literature, the main properties of nonlinear impulsive control systems have been fully understood, but there is no major development of control strategies. Particularly, there is no substantiation of model predictive control (MPC) strategies maintaining convexity of the optimization problem and closedloop stability, and there is no control strategy to reduce the offset problem when there are parameter variations, which is a common situation in biological processes. Therefore, the main novelties of this paper are: (i) an MPC formulation extended to nonlinear impulsive systems that addresses non-zero tracking, (ii) the sufficient and necessary conditions to guarantee the stability of the closed-loop system at an equilibrium target, (iii) a comprehensive description of an offset-free MPC to handle low to moderate plant-model mismatches, (iv) the conditions to guarantee offset-free control. Finally, the MPC and offset-free MPC are tested to address the drug administration problem in two biomedical applications: oncolytic virus therapy, to regulate tumor dynamics using doses of oncolytic, and type 1 diabetes treatment, to regulate glycemia using insulin injections. Satisfactory results were obtained in simulation scenarios including parameter variations in nonlinear models that represent the corresponding dynamics.

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An offset-free MPC formulation for nonlinear systems using adaptive integral controller

Cited by 20 publications

References 86 publications

Model predictive tracking control of uncertain moving structures with nonaffine saturated actuation: Rotating control force

Model predictive tracking control of uncertain moving structures with nonaffine saturated actuation: Rotating control force

Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

Offset-Free Nonzero Tracking for Nonlinear Impulsive Systems With Application to Biomedical Processes

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