Longitudinal Anisotropy-Based Flight Control in a Wind Shear

Kurdyukov, Alexander P.; Pavlov, B. V.; Timin, Victor N.; Vladimirov, Igor G.

doi:10.1016/s1474-6670(17)32211-5

Cited by 3 publications

(8 citation statements)

References 3 publications

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“…2) each anisotropic characteristic value φ i is a monotonically increasing function of the parameter α; 3) if the anisotropic characteristic values φ i are different, then dφi dα 0; 4) each anisotropic characteristic value φ i is a continuous function of the parameter α. Proof: Applying the results of [11], [12] to equations (14), (23) and (8), (24), we obtain that T T 2 and S S 2 . It follows that [10]…”

Section: Controller Order Reduction By Anisotropic Balanced Trunmentioning

confidence: 98%

“…Definition 2: When the stabilizing solutions T and S of respective control and filtering Riccati equations (14) and (8) are in form (17), (18), the system is said to be in anisotropic balanced coordinates, and the realization…”

Section: Controller Order Reduction By Anisotropic Balanced Trunmentioning

confidence: 99%

“…Writing control and filtering algebraic Riccati equations (14) and (8) in the anisotropic balanced state-space representation ( A, B 2 , C 2 ) yields, respectively,…”

Section: Controller Order Reduction By Anisotropic Balanced Trunmentioning

confidence: 99%

“…More detailed problem statement and aircraft model can be found in [14]. The obtained control law minimizes the influence of actuator and measurement noises, as well as wind disturbance on deviations of airspeed ∆V and altitude ∆h from prescribed values (controlled variables).…”

Section: Application Example: Flight Controlmentioning

confidence: 99%

“…Nonlinear equations describing an aircraft longitudinal motion [14] were linearized in the trajectory point with airspeed V 0 = 71.375 m/sec and altitude h 0 = 600 m. The resulted standard plant model (1) has order n = 6.…”

Section: Application Example: Flight Controlmentioning

confidence: 99%

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Stochastic robust controller reduction by anisotropic balanced truncation

Tchaikovsky

Kurdyukov

2009

2009 IEEE International Conference on Control Applications

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Section: Controller Order Reduction By Anisotropic Balanced Trunmentioning

confidence: 98%

Section: Controller Order Reduction By Anisotropic Balanced Trunmentioning

confidence: 99%

“…Writing control and filtering algebraic Riccati equations (14) and (8) in the anisotropic balanced state-space representation ( A, B 2 , C 2 ) yields, respectively,…”

Section: Controller Order Reduction By Anisotropic Balanced Trunmentioning

confidence: 99%

Section: Application Example: Flight Controlmentioning

confidence: 99%

Section: Application Example: Flight Controlmentioning

confidence: 99%

See 3 more Smart Citations

Stochastic robust controller reduction by anisotropic balanced truncation

Tchaikovsky

Kurdyukov

2009

2009 IEEE International Conference on Control Applications

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In Between the $$LQG/H_{2}$$- and $$H_{\infty } $$-Control Theories

Kurdyukov

Andrianova

Belov

et al. 2021

Autom Remote Control

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Synthesis of anisotropic suboptimal controllers by convex optimization

Tchaikovsky,

Kurdyukov,

Timin

2011

Preprint

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This paper considers a disturbance attenuation problem for a linear discrete time invariant system under random disturbances with imprecisely known distributions. The statistical uncertainty is measured in terms of the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the H ∞ norm. The designed anisotropic suboptimal controller generally is a dynamic fixed-order output-feedback compensator which is required to stabilize the closed-loop system and keep its anisotropic norm below a prescribed threshold value. Rather than resulting in a unique controller, the suboptimal design procedure yields a family of controllers, thus providing freedom to impose some additional performance specifications on the closed-loop system. The general fixed-order synthesis procedure employs solving a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities in reciprocal matrices which make the general optimization problem nonconvex. By applying the known standard convexification procedures it is shown that the resulting optimization problem is convex for the full-information state-feedback, output-feedback full-order controllers, and static outputfeedback controller for some specific classes of plants defined by certain structural properties. In the convex cases, the anisotropic γ-optimal controllers are obtained by minimizing the squared norm threshold value subject to convex constraints. In a sense, the anisotropic controller seems to offer a promising and flexible trade-off between H 2 and H ∞ controllers which are its limiting cases. In comparison with the state-space solution to the anisotropic optimal controller synthesis problem presented before which results in a unique full-order estimator-based controller defined by a complex system of cross-coupled nonlinear matrix algebraic equations, the proposed optimization-based approach is novel and does not require developing specific homotopy-like computational algorithms.

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Longitudinal Anisotropy-Based Flight Control in a Wind Shear

Cited by 3 publications

References 3 publications

Stochastic robust controller reduction by anisotropic balanced truncation

Stochastic robust controller reduction by anisotropic balanced truncation

In Between the $$LQG/H_{2}$$- and $$H_{\infty } $$-Control Theories

Synthesis of anisotropic suboptimal controllers by convex optimization

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