Embedding of Nonlinear Systems in a Linear Parameter-Varying Representation

Abbas, Hossam S.; Tóth, Roland; Petreczky, Mihály; Meskin, Nader; Mohammadpour, Javad

doi:10.3182/20140824-6-za-1003.02506

Cited by 28 publications

(30 citation statements)

References 14 publications

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“…Many nonlinear processes can be described under an LPV formalism, as long as Linear Differential Inclusion (LDI) is respected, see (Boyd et al, 1994;Abbas et al, 2014). Consider the generic nonlinear system below, with states x ∈ R nx , measured outputs y ∈ R ny and control signal u ∈ R nu :…”

Section: Linear Parameter Varying Systemsmentioning

confidence: 99%

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

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

108

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Motivated by the fact that many nonlinear plants can be represented through Linear Parameter Varying (LPV) embedding, and being this framework very popular for control design, this paper investigates the available Model Predictive Control (MPC) policies that can be applied for such systems. This paper reviews the available works considering LPV MPC design, ranging from the sub-optimal, simplified, yet Quadratic Programming (QP) algorithms, the tube-based tools, the set-constrained procedures, the Nonlinear Programming procedures and the robust ones; the main features of the recent research body on this topic are examined. A simulation example is given comparing some of the important techniques. Finally, some suggestions are given for future investigation threads, seeking further applicability of these methods.

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Section: Linear Parameter Varying Systemsmentioning

confidence: 99%

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

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

108

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“…Due to the inclusion of these scheduling parameters, LPV systems are linear in the state space, but nonlinear in the parameter space 2 . Due to this property (linear differential inclusion 25 ), LPV systems are represented with a much simpler framework than full nonlinear models, being very similar to LTI models (and, thus, possessing many of the LTI advantages) -one can say that LPV embedding is somewhere in between the nonlinear and the LTI formalisms.…”

Section: Linear Parameter Varying Systemsmentioning

confidence: 99%

“…• Step (3): Solve LMIs (24) and (75), verifying that inequality (25) holds for the Lipschitz constant Γ. Compute the terminal set according to and Theorem 1;…”

Section: Loopmentioning

confidence: 99%

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Morato

Normey-Rico

Sename

2020

Intl J Robust & Nonlinear

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This paper develops a state-feedback Model Predictive Control (MPC) framework for Nonlinear Parameter Varying (NLPV) systems with explicit Lipschitz nonlinearities along the input trajectory. Considering a guess for the evolution of the scheduling parameters along the prediction horizon, the proposed optimization procedure for the MPC design includes a terminal stage cost, a contracting terminal region constraint and nominal predictions scheduled with respect to this guess. The terminal region is taken so that it is monotonically decreasing to a predetermined set, which guarantees recursive feasibility of the algorithm with respect to a bound on the admissible uncertainties (introduced from the scheduling parameter guess). The terminal set is a scheduled robust control invariant set for Lipschitz nonlinear systems, computed through some proposed LMIs. The inclusion of the terminal ingredient also serves to demonstrate Input-to-State Quadratic Stability. This paper ends with a successful numerical simulation example of the technique applied to the control of a Semi-Active automotive suspension system equipped with Electro-Rheological dampers.

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“…In [2], inspired by the feedback linearization theory, a systematic procedure is proposed to convert control affine nonlinear SS representation into state minimal LPV SS representations in an observable canonical form, where the scheduling parameter depends on the derivatives of the inputs and outputs of the system. In addition, if the states of the nonlinear model can be measured or estimated, then the procedure can be modified to provide LPV models scheduled by these states.…”

Section: Other Approaches and Current Directions Of Researchmentioning

confidence: 99%

Advances in Gain-Scheduling and Fault Tolerant Control Techniques

Rotondo¹

2018

Springer Theses

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This thesis presents some contributions to the state-of-the-art of the fields of gainscheduling and fault tolerant control (FTC).In the area of gain-scheduling, the connections between the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms are analyzed, showing that the methods for the automated generation of models by nonlinear embedding and by sector nonlinearity, developed for one class of systems, can be easily extended to deal with the other class. Then, two measures, based on the notions of overboundedness and region of attraction estimates, are proposed in order to compare different models and choose which one can be considered the best one. Later, the problem of designing state-feedback controllers for LPV systems has been considered, providing two main contributions. First, robust LPV controllers that can guarantee some desired performances when applied to uncertain LPV systems are designed, by using a double-layer polytopic description that takes into account both the variability due to the varying parameter vector and the uncertainty. Then, the idea of designing the controller in such a way that the required performances are scheduled by the varying parameters is explored, which provides an elegant way to vary online the behavior of the closed-loop system. In both cases, the problem reduces to finding a solution to a finite number of linear matrix inequalities (LMIs), which can be done efficiently using the available solvers.In the area of fault tolerant control, the thesis first shows that the aforementioned double-layer polytopic framework can be used for FTC, in such a way that different strategies (passive, active and hybrid) are obtained depending on the amount of available information. Later, an FTC strategy for LPV systems that involves a reconfigured reference model and virtual actuators is developed. It is shown that by including the saturations in the reference model equations, it is possible to design a model reference FTC system that automatically retunes the reference states whenever the system is affected by saturation nonlinearities. In this way, a graceful performance degradation in presence of actuator saturations is incorporated in an elegant way. Finally, the problem of FTC of unstable LPV systems subject to actuator saturations is considered. In this case, the design of the virtual actuator is performed in such a way that the convergence of the state trajectory to zero is assured despite the saturations and the appearance of faults. Also, it is shown that it is possible to obtain some guarantees about the tolerated delay between the fault occurrence and its isolation, and that the nominal controller can be designed so as to maximize the tolerated delay.i Resum Aquesta tesi presenta diverses contribucions a l'estat de l'art del control per planificació del guany i del control tolerant a fallades (FTC).Pel que fa al control per planificació del guany, s'analitzen les connexions entre els paradigmes dels sistemes lineals a paràmetres variants en el temps (LPV) i d...

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Embedding of Nonlinear Systems in a Linear Parameter-Varying Representation

Cited by 28 publications

References 14 publications

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

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

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Advances in Gain-Scheduling and Fault Tolerant Control Techniques

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