Computing Funnels Using Numerical Optimization Based Falsifiers

Fejlek, Jiří; Ratschan, Stefan

doi:10.1109/icra46639.2022.9811730

Cited by 3 publications

(2 citation statements)

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“…The studies in funnel synthesis can be separated into two categories depending on whether they aim to maximize [3], [4], [5] or minimize the size of the funnel [2], [6], [7]. The funnel computation inherently aims to maximize the size of the funnel to have a larger controlled invariant set in the state space.…”

Section: Introductionmentioning

confidence: 99%

“…When employing the Lyapunov condition, the resulting optimization problem has a differential inequality of the Lyapunov function in continuous-time for a finite-time interval. Since it is intractable to satisfy the inequality for all time in the given interval, many approaches focus on checking the differential inequality at a finite number of node points [2], [4], [5]. When a quadratic Lyapunov function with a timevarying positive definite (PD) matrix is employed, the resulting differential inequality ends up with a differential linear matrix inequality (DLMI).…”

Section: Introductionmentioning

confidence: 99%

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Optimization-based Constrained Funnel Synthesis for Systems with Lipschitz Nonlinearities via Numerical Optimal Control

Kim¹,

Elango²,

Reynolds³

et al. 2023

Preprint

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This paper presents a funnel synthesis algorithm for computing controlled invariant sets and feedback control gains around a given nominal trajectory for dynamical systems with locally Lipschitz nonlinearities and bounded disturbances. The resulting funnel synthesis problem involves a differential linear matrix inequality (DLMI) whose solution satisfies a Lyapunov condition that implies invariance and attractivity properties. Due to these properties, the proposed method can balance maximization of initial invariant funnel size, i.e., size of the funnel entry, and minimization of the size of the attractive funnel for disturbance attenuation. To solve the resulting funnel synthesis problem with the DLMI as one of the problem constraints, we employ a numerical optimal control approach that uses a multiple shooting method to convert the problem into a finite dimensional semidefinite programming problem. This framework avoids the need for piecewise linear system matrices and funnel parameters, which are typically assumed in recent related work. We illustrate the proposed funnel synthesis method with a numerical example.

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