Finite Horizon Worst Case Analysis of Linear Time-Varying Systems Applied to Launch Vehicle

Biertümpfel, Felix; Pholdee, Nantiwat; Bennani, Samir; Pfifer, Harald

doi:10.1109/tcst.2023.3260728

Cited by 2 publications

(3 citation statements)

References 35 publications

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“…This article develops theoretical and computational methods to analyze the robustness of uncertain nonlinear systems over finite time horizons. Motivating applications include robotic systems, 1 space launch vehicles, 2,3 and aircraft during the landing phase 4 . The analysis in this article considers an uncertain system modeled by an interconnection of a (nominal) nonlinear, time‐varying system and an uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Trajectory‐based robustness analysis for nonlinear systems

Seiler,

Venkataraman

2023

Intl J Robust & Nonlinear

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This article considers the robustness of an uncertain nonlinear system along a finite‐horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients. First, the nonlinear system is approximated by a linear time‐varying (LTV) system via linearization along a trajectory. This linearization introduces an additional forcing input due to the nominal trajectory. Second, the input/output behavior of the perturbation is described by time‐domain, integral quadratic constraints (IQCs). Third, a dissipation inequality is formulated to bound the worst‐case deviation of an output signal due to the uncertainty. These steps yield a differential linear matrix inequality (DLMI) condition to bound the worst‐case performance. The robustness condition is then converted to an equivalent condition in terms of a Riccati differential equation. This yields a computational method that avoids heuristics often used to solve DLMIs, for example, time gridding. The approach is demonstrated by a two‐link robotic arm example.

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Section: Introductionmentioning

confidence: 99%

“…Finite‐horizon robustness of continuous‐time LTV systems has also been considered in References 22 and 23 and more recently in References 3,9‐11. There is also related work in discrete‐time, for example, References 25‐27.…”

Section: Introductionmentioning

confidence: 99%

Trajectory‐based robustness analysis for nonlinear systems

Seiler,

Venkataraman

2023

Intl J Robust & Nonlinear

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“…There has also been considerable work recently on developing IQC-based robustness analysis tools for time-varying systems using dissipativity-based arguments. 10,11 For instance, dissipativity-based robustness analysis results have been developed for discrete-time LTV systems, 12,31 continuous-time finite horizon LTV systems, 32,33 and interconnected discrete-time LTV systems. 34 This work falls under the class of papers that use dissipativity-based arguments for IQC-based robust stability and performance analysis and deals with discrete-time eventually periodic nominal systems, which include both finite horizon and periodic systems as special cases, subject to structured uncertainties (which could include static and dynamic, time-invariant and time-varying, linear perturbations) and potentially multiple constraints on the initial values of the state variables.…”

Section: Introductionmentioning

confidence: 99%

Robustness analysis of uncertain time‐varying systems with unknown initial conditions

Farhood

2023

Intl J Robust & Nonlinear

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SummaryThis paper focuses on the robustness analysis of discrete‐time, linear time‐varying (LTV) systems subject to various uncertainties, such as static and dynamic, time‐invariant and time‐varying, linear perturbations, and unknown initial conditions. The proposed approach is based on integral quadratic constraint theory and allows for a potentially more accurate characterization of the set in which the initial state resides by imposing separate constraints on the initial values of the state variables as opposed to simply requiring the initial state to lie in some ellipsoid. The adopted problem formulation facilitates the analysis of uncertain LTV systems subject to disturbance inputs that are bounded pointwise in time, and the developed results enable determining useful pointwise bounds on the performance outputs given such inputs. The main analysis result is given for eventually periodic nominal systems, which include linear time‐invariant, finite horizon, and periodic systems as special cases. The analysis conditions are expressed as linear matrix inequalities. Two additional results stemming from the main analysis theorem are provided that can be used to determine overapproximated ellipsoidal reachable sets. Finally, the utility of the proposed approach is demonstrated in an illustrative example.

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Finite Horizon Worst Case Analysis of Linear Time-Varying Systems Applied to Launch Vehicle

Cited by 2 publications

References 35 publications

Trajectory‐based robustness analysis for nonlinear systems

Trajectory‐based robustness analysis for nonlinear systems

Robustness analysis of uncertain time‐varying systems with unknown initial conditions

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