Generation of Dangerous Disturbances for Flight Systems

Botkin, Nikolai D.; Martynov, Kirill; Turova, Varvara; Diepolder, Johannes

doi:10.1007/s13235-018-0259-5

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…Theorem 1 Let Eqs. ( 4)- (5), with relations ( 6)- (7), be solvable on [0, θ], and det P(t) = 0, t ∈ [0, θ], then the tube V P (•) and the disturbance strategy (8) provide a solution to Problem 1.…”

Section: Remarkmentioning

confidence: 99%

“…if formulas ( 1), ( 4), (5), and the definition of ξ are used. Note that every admissible control u satisfies the relation u − r = Rα at time t, where α is a vector such that α ∞ ≤ 1.…”

Section: Remarkmentioning

confidence: 99%

“…• grid methods, e.g., [3], that scale as O(N d ) per time step, where N is the grid resolution per dimension, • methods that represent repulsive tubes with arbitrary convex polygons, e.g., [5],…”

Section: Remarkmentioning

confidence: 99%

“…Nevertheless, such methods require large computation resources on multiprocessor computer platforms. More appropriate for linear conflict control problems are methods proposed in [5,12] where repulsive tubes are approximated by polyhedrons, which however involves solving a lot of linear programming problems. Therefore, such methods also require significant computer resources.…”

Section: Introductionmentioning

confidence: 99%

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Quick Construction of Dangerous Disturbances in Conflict Control Problems

Martynov

Botkin

Turova

et al. 2020

Annals of the International Society of Dynamic Games

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The paper is devoted to the construction of dangerous disturbances in linear conflict control problems. Using the technique of sequential linearization, dangerous disturbances can also be constructed for nonlinear systems such as aircraft dynamics equations, including filters, servomechanisms, etc. The procedure proposed is based on a dynamic programming method and consists in the backward integration of ordinary matrix differential equations defining centers, sizes, and orientations of time-dependent parallelotopes forming a repulsive tube in the time-space domain. A feedback disturbance strategy can keep the state vector of the conflict control system outside the repulsive tube for all admissible inputs of the control.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quick Construction of Dangerous Disturbances in Conflict Control Problems

Martynov

Botkin

Turova

et al. 2020

Annals of the International Society of Dynamic Games

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that the solutions to the evasion problems may be useful for construction of dangerous disturbances, for example, in problems of aircraft control [3,22].…”

Section: Introductionmentioning

confidence: 99%

On Solving an Enhanced Evasion Problem for Linear Discrete–time Systems

Kostousova

2022

UMJ

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We consider the problem of an enhanced evasion for linear discrete-time systems, where there are two conflicting bounded controls and the aim of one of them is to be guaranteed to avoid the trajectory hitting a given target set at a given final time and also at intermediate instants. First we outline a common solution scheme based on the construction of so called solvability tubes or repulsive tubes. Then a much more quick and simple for realization method based on the construction of the tubes with parallelepiped-valued cross-sections is presented under assumptions that the target set is a parallelepiped and parallelotope-valued constraints on controls are imposed. An example illustrating this method is considered.

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