LPV modeling of nonlinear systems: A multi‐path feedback linearization approach

Abbas, Hossam S.; Tóth, Roland; Petreczky, Mihály; Meskin, Nader; Velni, Javad Mohammadpour; Koelewijn, Patrick J. W.

doi:10.1002/rnc.5799

Cited by 10 publications

(6 citation statements)

References 50 publications

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“…Nonlinear MPC is computationally expensive [46], so a linear MPC is adopted for the control of the quadcopter attitude. The nonlinear rotational dynamic model is reformulated to Linear Parameter varying (LPV) and treated as the linear time invariant system (LTI) [47].…”

Section: Linear Mpc Formulationmentioning

confidence: 99%

An optimal hybrid quadcopter control technique with MPC-based backstepping

Nwafor,

Eneh,

Ndefo

et al. 2024

Archives of Control Sciences

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Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.

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Section: Linear Mpc Formulationmentioning

confidence: 99%

An optimal hybrid quadcopter control technique with MPC-based backstepping

Nwafor,

Eneh,

Ndefo

et al. 2024

Archives of Control Sciences

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Section: Lpv Modelmentioning

confidence: 99%

“…To estimate the LPV model, as a first step, we select the type of basis functions and the expansion order 𝑁 𝑝 in (17). To guarantee the zero curl of the LPV model coefficients, condition ( 15) is applied to the parametrization (17). Note that applying (15) to the LPV parametrization can change the expansion order 𝑁 𝑝 for some coefficients (as shown in 25 ).…”

Section: Lpv Modelmentioning

confidence: 99%

Nonlinear Continuous-time System Identification by Linearization around a Time-varying setpoint

Sadegh

Sharabiany

Lataire

2023

Preprint

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This paper handles the identification of nonlinear systems through linear time-varying (LTV) approximation. The mathematical form of the nonlinear system is unknown and regenerated through an experiment followed by LTV and linear parameter-varying (LPV) estimation and integration. By employing a well-designed experiment the linearized model of the nonlinear system around a time-varying trajectory is obtained. The result is an LTV approximation of the nonlinear system around that trajectory. Having estimated the LTV model, an LPV model is identified. It is shown that the parameter-varying (PV) coefficients of this LPV model are partial derivatives of the nonlinear system evaluated at the trajectory. In this paper, we will show that there exists a relation between the LPV coefficients. This structural relation in the LPV model ensures the integrability of PV coefficients for nonlinear reconstruction. Indeed, the vector of the LPV coefficients is the gradient of the nonlinear system evaluated at the trajectory. Then, the nonlinear system is reconstructed through symbolic integration of the coefficients. The proposed method is a data-driven scheme that can reconstruct an estimate of the nonlinear system and its mathematical form using input-output measurements. Finally, the use of the proposed method is illustrated via a simulation example.

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“…where 𝜙(⋅) is Lipschitz continuous and bounded on a compact set 𝕏 ⊂ ℝ n x . Sufficient conditions under which an embedding of the form (4) can be constructed for an arbitrary continuous-time non-linear system can be found in [3,32]. The discrete-time case is still a topic of ongoing research.…”

Section: Problem Settingmentioning

confidence: 99%

“…A class of systems that can always be embedded in the required form of (4) are, for instance, Lur'e systems of the form

x false(k + 1 false) = A x + ϕ (x) + B u

where

ϕ (\cdot)

is Lipschitz continuous and bounded on a compact set

X \subset {double-struckR}^{n_{x}}

. Sufficient conditions under which an embedding of the form (4) can be constructed for an arbitrary continuous‐time non‐linear system can be found in [3, 32]. The discrete‐time case is still a topic of ongoing research.…”

Section: Preliminariesmentioning

confidence: 99%

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

Hanema

Tóth

Lazăr

2021

IET Control Theory & Appl

Self Cite

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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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LPV modeling of nonlinear systems: A multi‐path feedback linearization approach

Cited by 10 publications

References 50 publications

An optimal hybrid quadcopter control technique with MPC-based backstepping

An optimal hybrid quadcopter control technique with MPC-based backstepping

Nonlinear Continuous-time System Identification by Linearization around a Time-varying setpoint

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

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