Optimal Synthesis of LTI Koopman Models for Nonlinear Systems with Inputs

Iacob, Lucian Cristian; Tóth, Roland; Schoukens, Maarten

doi:10.1016/j.ifacol.2022.11.289

Cited by 2 publications

(1 citation statement)

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“…The matrix

H\left(\theta \right)\in {\mathbb{R}}^{2\times 2}

is chosen such that

H\left(\theta \right)\theta =G\left(\theta \right)

for all

\theta \in {\mathbb{R}}^2

. Note that such

H

always exists as

G

is continuously differentiable and

G(0)=0

46 . System (35a) only hides the nonlinear terms

M\left(\theta \right)\ddot{\theta}

of (34) into the linear embedding

M\left(\theta \right)\ddot{\phi}

while keeping the rest unchanged.…”

Section: Nonlinear Stabilization Via Vccmmentioning

confidence: 99%

Virtual control contraction metrics: Convex nonlinear feedback design via behavioral embedding

Wang,

Tóth,

Koelewijn

et al. 2024

Intl J Robust & Nonlinear

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This article presents a systematic approach to nonlinear state‐feedback control design that has three main advantages: (i) it ensures exponential stability and ‐gain performance with respect to a user‐defined set of reference trajectories, (ii) it provides constructive conditions based on convex optimization and a path‐integral‐based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter‐varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and ‐gain performance for all trajectories of the targeted reference behavior. We show that the proposed methodology is a unified generalization of the two distinct categories of linear‐parameter‐varying (LPV) state‐feedback control approaches: global and local methods. Moreover, it provides rigorous stability and performance guarantees as a method for nonlinear tracking control, while such properties are not guaranteed for tracking control using standard LPV approaches. Code is available at https://github.com/ruigangwang7/VCCM.

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“…The matrix