Real-time control of aircraft take-off in windshear. Part I: Aircraft model and control schemes

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

doi:10.1109/med.2017.7984131

Cited by 8 publications

(7 citation statements)

References 19 publications

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“…The repulsive tubes are constructed with the uniform time sampling t i+1 − t i = 10 −3 s. To play against the repulsive disturbance, a quasi-optimal feedback control strategy u(t, x) based on parallelotope approximations of solvability tubes (see [7]) is used. Such a strategy has already been successfully applied to problems of aircraft control (see [9]). Simulation results show that the repulsive disturbance provides evasion from the target set, whereas constant disturbances whose values coincide with the vertices of the rectangle given by (26) cannot solve this problem.…”

Section: Generation Of Disturbancesmentioning

confidence: 99%

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: Generation Of Disturbancesmentioning

confidence: 99%

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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“…Recent investigations [15] and [16] utilize a method (see [17]) for the fast computation of rough approximations of solvability sets in linear conflict control problems. Using techniques of sequential linearization, this method is applied to nonlinear aircraft dynamics to design an appropriate control for take-off in the presence of downbursts.…”

Section: Introductionmentioning

confidence: 99%

Computation of Viability Kernels on Grid Computers for Aircraft Control in Windshear

Botkin¹,

Turova²,

Diepolder³

et al. 2018

Adv. sci. technol. eng. syst. j.

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This paper is devoted to the analysis of aircraft dynamics in the cruise flight phase under windshear conditions. The study is conducted with reference to a point-mass aircraft model restricted to move in a vertical plane. We formulate the problem as a differential game against the wind disturbances: The first player, autopilot, manages, via additional smoothing filters, the aircraft's angle of attack and power setting. The second player, wind, produces disturbances that are transferred, also via smoothing filters, into most dangerous wind gusts. The state variables of the game are subject to state constraints representing aircraft safety conditions related, for example, to the altitude, path inclination and velocity. Viability theory is used to compute the so-called viability kernels, the maximal subsets of state constraints where an appropriate feedback strategy of the first player can keep aircraft trajectories arbitrary long for all admissible disturbances generated by the second player. A grid method is utilized, and challenging computations in seven dimensions are conducted on a supercomputer system.

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“…As for solving the feedback target control problems for differential and discretetime systems, constructive computation schemes using ellipsoidal techniques were proposed [8,24,25,26,35] and then expanded to the polyhedral techniques that use polyhedral (parallelotope-valued) solvability tubes [15,17,19,20,21,22] (this had required the development of a quite different techniques). In [30,31], the polyhedral technique from [19,Sec. 3] was applied for constructing a real-time control of aircraft take-off in windshear using a sequential linearization of highly nonlinear point mass aircraft model equations around appropriate ascending paths.…”

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confidence: 99%

“…3] was applied for constructing a real-time control of aircraft take-off in windshear using a sequential linearization of highly nonlinear point mass aircraft model equations around appropriate ascending paths. Also in [30], the example with the linear differential game known as "Boy and Crocodile" is considered, where the mentioned parallelotope technique is compared with a grid method which computes the maximal solvability tube almost exactly if the grid is sufficiently fine.…”

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confidence: 99%

“…Convergence questions are not considered in this paper; in this connection the paper[9] may be mentioned which analyzes the Euler approximations in a set-valued framework.2 Some considerations of efficiency of calculating parallelotope-valued reachable rubes are given in[16, Sec. 9]; see also[30] about efficiency of the method for the case without SC on short time intervals.…”

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confidence: 99%

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On polyhedral control synthesis for dynamical discrete-time systems under uncertainties and state constraints

Kostousova¹

2018

Discrete &Amp; Continuous Dynamical Systems - A

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We deal with a problem of target control synthesis for dynamical bilinear discrete-time systems under uncertainties (which describe disturbances, perturbations or unmodelled dynamics) and state constraints. Namely we consider systems with controls that appear not only additively in the right hand sides of the system equations but also in the coefficients of the system. We assume that there are uncertainties of a set-membership kind when we know only the bounding sets of the unknown terms. We presume that we have uncertain terms of two kinds, namely, a parallelotope-bounded additive uncertain term and interval-bounded uncertainties in the coefficients. Moreover the systems are considered under constraints on the state ("under viability constraints"). We continue to develop the method of control synthesis using polyhedral (parallelotope-valued) solvability tubes. The technique for calculation of the mentioned polyhedral tubes by the recurrent relations is presented. Control strategies, which can be constructed on the base of the polyhedral solvability tubes, are proposed. Illustrative examples are considered.2010 Mathematics Subject Classification. Primary: 93C41, 93C55, 93B52, 93C05, 93C10; Secondary: 93B40, 52B12.

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Real-time control of aircraft take-off in windshear. Part I: Aircraft model and control schemes

Cited by 8 publications

References 19 publications

Quick Construction of Dangerous Disturbances in Conflict Control Problems

Quick Construction of Dangerous Disturbances in Conflict Control Problems

Computation of Viability Kernels on Grid Computers for Aircraft Control in Windshear

On polyhedral control synthesis for dynamical discrete-time systems under uncertainties and state constraints

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