Towards gain tuning for numerical KKL observers

Buisson-Fenet, Mona; Bahr, Lukas; Morgenthaler, Valery; Meglio, Florent Di

doi:10.48550/arxiv.2204.00318

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…The proposed approach can be used to determine empirically the class of (distributional) indistinguishability of any state for an arbitrary nonlinear system, and to observe the continuous increase in relative distinguishability as we get farther from that class. We illustrate this with an undamped, unforced Duffing oscillator, often used in nonlinear observer design [26,27]:…”

Section: B Analyzing Observability In the State Spacementioning

confidence: 99%

Data-Driven Observability Analysis for Nonlinear Stochastic Systems

Massiani¹,

Buisson-Fenet²,

Solowjow³

et al. 2023

Preprint

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Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from measurement data. The presence of noise further complicates this analysis, as standard notions of distinguishability are tailored to deterministic systems. We build on distributional distinguishability, which extends the deterministic notion by comparing distributions of outputs of stochastic systems. We first show that both concepts are equivalent for a class of systems that includes linear systems. We then present a method to assess and quantify distributional distinguishability from output data. Specifically, our quantification measures how much data is required to tell apart two initial states, inducing a continuous spectrum of distinguishability. We propose a statistical test to determine a threshold above which two states can be considered distinguishable with high confidence. We illustrate these tools by computing distinguishability maps over the state space in simulation, then leverage the test to compare sensor configurations on hardware.

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Section: B Analyzing Observability In the State Spacementioning

confidence: 99%

Data-Driven Observability Analysis for Nonlinear Stochastic Systems

Massiani¹,

Buisson-Fenet²,

Solowjow³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Yet solving this parametric PDE is still difficult and is further complicated by the differentiation. The neural network-based approaches proposed in existing works, [23][24][25] although built on the sound basis that neural networks act as universal approximators, theoretically are not exempt from the nonconvexity of training problems and local solutions.…”

Section: Kkl Observer and Its Existencementioning

confidence: 99%

“…To avoid solving the PDEs, Ramos et al 23 proposed to train a neural network that represents the inverse transformation from immersed states to the actual states. Buisson-Fenet et al 24 further considered the tuning of poles in the embedded linear dynamics along with the neural network training. A more sophisticated approach by Niazi et al 25 adopted the idea of physics-informed neural networks and used two neural networks-one for the immersion and one for its inverse; the loss metric for their training includes a state reconstruction error and a prediction error of the embedding.…”

Section: Introductionmentioning

confidence: 99%

Data‐driven state observation for nonlinear systems based on online learning

Tang

2023

AIChE Journal

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For controlling nonlinear processes represented by state‐space models, a state observer is needed to estimate the states from the trajectories of measured variables. While model‐based observer synthesis is traditionally challenging due to the difficulty of solving pertinent partial differential equations, this article proposes an efficient model‐free, data‐driven approach for state observation, which is suitable for data‐driven nonlinear control without accurate nonlinear models. Specifically, by using a Chen–Fliess series representation of the observer dynamics, state observation is endowed with an online least squares regression formulation that can be solved by gradient flow with performance guarantees. When the target state trajectories for regression are unavailable, by exploiting the Kazantzis–Kravaris/Luenberger observer structure, state observation is reduced to a dimensionality reduction problem amenable to an online implementation of kernel principal component analysis. The proposed approach is demonstrated by a limit cycle dynamics and a chaotic system.

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Towards gain tuning for numerical KKL observers

Cited by 2 publications

References 17 publications

Data-Driven Observability Analysis for Nonlinear Stochastic Systems

Data-Driven Observability Analysis for Nonlinear Stochastic Systems

Data‐driven state observation for nonlinear systems based on online learning

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