Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

Ahbe, Eva; Listov, Petr; Iannelli, Andrea; Smith, Roy S.

doi:10.1016/j.ifacol.2020.12.550

Cited by 1 publication

(2 citation statements)

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“…Indeed, R obtained from VSS-∂ lin is significantly smaller than all other estimates as its only flexibility consists of the uniform scaling of the Lyapunov sublevel set obtained for the linearized system. Allowing the shape of this sublevel set to vary results in significantly larger estimates, as the sets R obtained for VSS-∂ (2) show. This option still only considers quadratic Lyapunov functions and the cost function is equal to the one in VSS-∂ lin while the computational complexity is significantly increased due to the constraints on Q and added decision variables.…”

Section: 1mentioning

confidence: 78%

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A novel moving orthonormal coordinate-based approach for region of attraction analysis of limit cycles

Ahbe

Iannelli

Smith

2023

JCD

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The paper proposes a Lyapunov theory-based method to compute inner estimates of the region of attraction (ROA) of stable limit cycles. The approach is based on a transformation of the system to transverse coordinates, defined on a moving orthonormal coordinate system (MOC) for which a novel construction is presented. The proposed center point MOC (cp-MOC) is associated with a user-defined center point and provides flexibility to the construction of the transverse coordinates. In particular, compared to the standard approach based on hyperplanes orthogonal to the flow, the new construction allows the analyst to obtain larger regions of the state space where the well-definedness property of the transformation is satisfied. This has important benefits when using transverse coordinates to compute inner estimates of the ROA. To demonstrate these improvements, a sum-of-squares optimization-based formulation is proposed for computing inner estimates of the ROA of limit cycles for polynomial dynamics described in transverse coordinates. Different algorithmic options are explored, taking into account computational and accuracy aspects. Results are shown for three different systems exhibiting increasing complexity. The presented algorithms are extensively compared, and the newly cp-MOC is shown to markedly outperform existing approaches.

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Section: 1mentioning

confidence: 78%

“…Scaling the ellipsoid inside a variable-degree-V sublevel set (referred to as SE-∂(r)). It is well-known that higher degree Lyapunov functions have the potential to verify larger ROA estimates [40,44,2]. In this algorithmic option, the Lyapunov function is thus parametrized as…”

Section: 21mentioning

confidence: 99%