Observability of Uncertain Nonlinear Systems Using Interval Analysis

Paradowski, Thomas; Lerch, Sabine; Damaszek, Michelle; Dehnert, Robert; Tibken, Bernd

doi:10.3390/a13030066

Cited by 11 publications

(7 citation statements)

References 23 publications

(49 reference statements)

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“…Bounded enclosures can be obtained only if the condition of full detectability/identifiability of states and parameters is verified. See Paradowski et al (2020) for observability analysis in the presence of uncertainty.…”

Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

Joint state and parameter estimation based on constrained zonotopes

Rego¹,

Locatelli²,

Raimondo³

et al. 2022

Preprint

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This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples.

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Section: Nonlinear Systems With Linear Output Equationmentioning

confidence: 99%

Joint state and parameter estimation based on constrained zonotopes

Rego¹,

Locatelli²,

Raimondo³

et al. 2022

Preprint

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show abstract

“…] are guaranteed to be real-valued. According to Rohn [46,47], interval bounds for the range of each eigenvalue are given by the enclosures…”

Section: Remarkmentioning

confidence: 99%

“…is determined as in Equation (47). The remaining degree of freedom η * k can be found according to the work of John [50].…”

Section: General Solution Proceduresmentioning

confidence: 99%

Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design

2021

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Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft.

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“…However, this only holds for local observability, while for global observability analysis, the Lie derivatives have to be investigated [36,38]. Due to the non-linear nature of the governing equations, alternative methods need to be implemented to perform observability analysis, such as the ones in [15] or [16]. This work proposes to combine the observability matrices of different timesteps into a large observability matrix.…”

Section: Observability Analysis Of the Extended Kalman Filtermentioning

confidence: 99%

“…For example, in tire force estimation applications, vehicle position states are typically unobservable when no GPS measurement is present, although these measurements do not contribute significantly to the tire force estimation performance [1,14]. Furthermore, the non-linear governing equations create additional challenges to evaluate observability globally and/or locally [15,16]. Additionally, some virtual sensing applications feature models with lots of states (e.g., for meteorology or oceanography typically > 10 6 [6]), of which only a few significantly contribute to the estimator performance.…”

Section: Introductionmentioning

confidence: 99%

Sensor Selection and State Estimation for Unobservable and Non-Linear System Models

Devos

Kirchner

Croes

et al. 2021

Sensors

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To comply with the increasing complexity of new mechatronic systems and stricter safety regulations, advanced estimation algorithms are currently undergoing a transformation towards higher model complexity. However, more complex models often face issues regarding the observability and computational effort needed. Moreover, sensor selection is often still conducted pragmatically based on experience and convenience, whereas a more cost-effective approach would be to evaluate the sensor performance based on its effective estimation performance. In this work, a novel estimation and sensor selection approach is presented that is able to stabilise the estimator Riccati equation for unobservable and non-linear system models. This is possible when estimators only target some specific quantities of interest that do not necessarily depend on all system states. An Extended Kalman Filter-based estimation framework is proposed where the Riccati equation is projected onto an observable subspace based on a Singular Value Decomposition (SVD) of the Kalman observability matrix. Furthermore, a sensor selection methodology is proposed, which ranks the possible sensors according to their estimation performance, as evaluated by the error covariance of the quantities of interest. This allows evaluating the performance of a sensor set without the need for costly test campaigns. Finally, the proposed methods are evaluated on a numerical example, as well as an automotive experimental validation case.

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Observability of Uncertain Nonlinear Systems Using Interval Analysis

Cited by 11 publications

References 23 publications

Joint state and parameter estimation based on constrained zonotopes

Joint state and parameter estimation based on constrained zonotopes

Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design

Sensor Selection and State Estimation for Unobservable and Non-Linear System Models

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