Confidence set-membership state estimation for LPV systems with inexact scheduling variables

Pan, Zhichao; Luan, Xiaoli; Liu, Fei

doi:10.1016/j.isatra.2021.04.016

Cited by 10 publications

(20 citation statements)

References 35 publications

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“…In the last decades, state estimation for LPV systems has been widely studied and applied to feedback control 1,2 and diagnosis. 3,4 However, when the LPV system operates in a wide operating range and with parameter variations, a single LPV estimator often leads to conservative performance. Since the switched systems are able to describe a wide range of complex and nonlinear behaviours, a reasonable approach to avoid this kind of problem is to use Switched Linear Parameter Varying (SLPV) systems.…”

Section: Introductionmentioning

confidence: 99%

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Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

Zhang,

Puig,

Ifqir

2024

Intl J Robust & Nonlinear

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SummaryThis paper proposes a set‐membership state estimation method for Switched Linear Parameter Varying (SLPV) systems subject to unknown but bounded parametric uncertainties, disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed at every time iteration. The size of this zonotope is designed to be convergent and bounded by satisfying ‐radius‐based and Average Dwell Time (ADT) conditions that are formulated in the Linear Matrix Inequality (LMI) framework. An extension of the state estimation method is presented to address the fault/disturbance estimation problem for SLPV systems. By using the state augmentation technique, the fault/disturbance estimation problem is transformed into a state estimation problem of the generated augmented descriptor switched LPV system. An application to vehicle lateral dynamics fault estimation is used for assessment purposes. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods.

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Section: Introductionmentioning

confidence: 99%

“…In the last decades, state estimation for LPV systems has been widely studied and applied to feedback control 1,2 and diagnosis 3,4 . However, when the LPV system operates in a wide operating range and with parameter variations, a single LPV estimator often leads to conservative performance.…”

Section: Introductionmentioning

confidence: 99%

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

Zhang,

Puig,

Ifqir

2024

Intl J Robust & Nonlinear

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“…In 9,10 , the stochastic and set-based approaches are combined to improve the accuracy of the algorithms. Likewise, 11,12 merge stochastic and set-bounded uncertainties to design unified algorithms. Unlike the aforementioned approaches, there exist works as 13,14 that address robustness to stochastic filtering without assuming set-bounded noises.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the robustness of each method relies on the preset confidence level. Finally, the third field consists of merging different representations for uncertainties into a same estimator 3,12,22,23,24,25 . Since both stochastic and setbounded uncertainties are present in the third case, the state-estimation problem becomes even more challenging.…”

Section: Introductionmentioning

confidence: 99%

State Estimators for Discrete-Time Descriptor Linear Systems with Mixed Uncertainties and State Constraints

Paula

Raffo

Teixeira

2023

Preprint

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This paper presents two novel mixed-uncertainty state estimators for discrete-time descriptor linear systems, namely linear time-varying mixed-uncertainty filter (LTVMF) and linear time-invariant mixed-uncertainty filter (LTIMF). The former estimator is based on the minimum-variance approach, from which quadratic and explicit formulations are derived and addressed to LTI and LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The explicit version is developed to reduce the computational burden of quadratic solvers, which is based on a particularity of the state inequality constraints. The LTIMF algorithm is based on the mixed H 2 / H ∞ criterion motivated by performing low-cost computations. This speed benefit is originated from a reachability analysis involving constant design matrices. Both LTVMF and LTIMF algorithms solve state-estimation problems in which the uncertainties are combined to yield the so-called mixed-uncertainty vector, which is composed by set-bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed-uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto-optimal front. According to these arguments, LTVMF is introduced with a cost normalization, which enables the combination of beyond minimum-variance approaches. Likewise, the mixed H 2 / H ∞ criterion of LTIMF is introduced with slack variables to improve the quality of the state estimates. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples.

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“…Second, the approximation errors are modeled as random variables with specific distributions, which can reduce the conservativeness of the filter. To deal with two types of uncertainties, the merging SM and stochastic method 37,38 is improved to satisfy the finite-dimensional linearized system with arbitrarily distributed approximation errors. By using sample particles to describe the probability distributions of approximation errors, a kind of confidence state set whose level approaches 1 is constructed.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear set‐membership state estimation based on the Koopman operator

Pan

Liu

2022

Intl J Robust & Nonlinear

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In this study, the Koopman operator is applied to solve the challenging nonlinear set-membership (SM) state estimation problem. The basic idea is to lift the nonlinear system into a linear one with a higher dimension, and then linear SM estimation methods can be adopted. The Koopman operator is an infinite-dimensional linear decomposition of nonlinear dynamics. This linearized system can fully describe the state evolution of the nonlinear dynamics with input, output, and noises. To apply SM state estimation algorithms, a finite-dimensional approximation is obtained by using the data-driven method. Meanwhile, the statistical properties of the approximation errors are also utilized to reduce the conservativeness of the filter. The probability distributions of approximation errors are described by sample particles. Coupled with the unknown but bounded noises, the linearized system is associated with two types of uncertainties. To this end, the merging SM and stochastic strategy is adopted to construct a class of confidence state set whose level approaches 1. After that, the optimal filter gain is given to minimize the size of the confidence state set. Finally, three numerical examples are given to demonstrate the effectiveness of the proposed method.

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Confidence set-membership state estimation for LPV systems with inexact scheduling variables

Cited by 10 publications

References 35 publications

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

State Estimators for Discrete-Time Descriptor Linear Systems with Mixed Uncertainties and State Constraints

Nonlinear set‐membership state estimation based on the Koopman operator

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