Systems with Multiple Nonlinear Feedback Controls

This paper is concerned with the linear/nonlinear aeroelastic control of 2-D supersonic lifting surfaces. Its goal is to provide the feedback control mechanism enabling one to enlarge the flight envelope by increasing the flutter speed, and also to control the character, benign/catastrophic of the flutter instability boundary. Structural and aerodynamic nonlinearities are included in the aeroelastic governing equations, and linear and nonlinear feedback controls in both plunging and pitching are employed in conjunction with proportional velocity feedback controls. The attention of the paper is focused on multiple Hopf bifurcations. In particular, the jumping phenomenon found in our previous work will be further investigated to reveal the physical implications. It is found that such a jumping occurs when the system has multiple families of limit cycles bifurcating from a same set of parameter values with multiple solutions for frequencies. The case investigated in this paper is restricted to zero structure damping. Center manifold reduction and normal form theory are applied to consider the stability of post-flutter solutions and the associated jumping phenomenon. Numerical simulations are presented to show the implications of time delay in the considered controls.

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Optimal nonlinear feedback controls for a class of linear systems

Journal of the Franklin Institute ◽

10.1016/0016-0032(75)90059-9 ◽

1975 ◽

Vol 298 (5-6) ◽

pp. 463-466 ◽

Cited By ~ 1

Author(s):

M. Sobral,

Keyword(s):

Linear Systems ◽

Nonlinear Feedback ◽

Feedback Controls

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Analysis on nonlinear feedback controls for differential mobile robots and its application to multi-robot formation control - part two

2008 10th International Conference on Control, Automation, Robotics and Vision ◽

10.1109/icarcv.2008.4795835 ◽

2008 ◽

Author(s):

Jie Wan ◽

Peter Chen

Keyword(s):

Mobile Robots ◽

Formation Control ◽

Nonlinear Feedback ◽

Feedback Controls ◽

Control Part ◽

Multi Robot

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ON THE COMPUTATION OF OPTIMAL NONLINEAR FEEDBACK CONTROLS

Control Applications of Nonlinear Programming and Optimization ◽

10.1016/b978-0-08-031665-9.50009-2 ◽

1986 ◽

pp. 27-30 ◽

Cited By ~ 2

Author(s):

H. Bourdache-Siguerdidjane ◽

M. Fliess

Keyword(s):

Nonlinear Feedback ◽

Feedback Controls

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On the computation of optimal nonlinear feedback controls

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)69243-7 ◽

1985 ◽

Vol 18 (2) ◽

pp. 245 ◽

Cited By ~ 1

Author(s):

H. Bourdache-Siguerdidjane ◽

M. Fliess ◽

M. Rouff

Keyword(s):

Nonlinear Feedback ◽

Feedback Controls

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On the Computation of Optimal Nonlinear Feedback Controls

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)60910-8 ◽

1985 ◽

Vol 18 (2) ◽

pp. 27-30

Author(s):

H. Bourdache-Siguerdidjane ◽

M. Fliess

Keyword(s):

Nonlinear Feedback ◽

Feedback Controls

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On the computation of optimal nonlinear feedback controls

Annual Review in Automatic Programming ◽

10.1016/0066-4138(85)90459-8 ◽

1985 ◽

Vol 13 ◽

pp. 27-30

Author(s):

H Bourdache-Siguerdidjane ◽

M Fliess

Keyword(s):

Nonlinear Feedback ◽

Feedback Controls

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Covariance Control of Nonlinear Dynamic Systems via Exact Stationary Probability Density Function

Journal of Vibration and Acoustics ◽

10.1115/1.1640355 ◽

2004 ◽

Vol 126 (1) ◽

pp. 71-76 ◽

Cited By ~ 8

Author(s):

O. Elbeyli ◽

J. Q. Sun

Keyword(s):

Present Method ◽

Stochastic Systems ◽

Control Method ◽

Solution Process ◽

Maximum Entropy Principle ◽

Nonlinear Feedback ◽

Feedback Controls ◽

Approximate Methods ◽

Covariance Control ◽

Special Cases

This paper presents a method for designing covariance type controls of nonlinear stochastic systems. The method consists of two steps. The first step is to find a class of nonlinear feedback controls with undetermined gains such that the exact stationary PDF of the response is obtainable. The second step is to select the control gains in the context of the covariance control method by minimizing a performance index. The exact PDF makes the solution process of optimization very efficient, and the evaluation of expectations of nonlinear functions of the response very accurate. The theoretical results of various orders of response moments by the present method have been compared with Monte Carlo simulations. Special cases are studied when the approximate methods based on the maximum entropy principle or other closure schemes leads less accurate response estimates, while the present method still works fine.

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STUDY OF GLOBALLY EXPONENTIAL SYNCHRONIZATION FOR THE FAMILY OF RÖSSLER SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406016148 ◽

2006 ◽

Vol 16 (08) ◽

pp. 2395-2406 ◽

Cited By ~ 19

Author(s):

XIAOXIN LIAO ◽

PEI YU

Keyword(s):

Numerical Simulations ◽

Lyapunov Functions ◽

Chaos Control ◽

Chaotic Systems ◽

Exponential Synchronization ◽

Nonlinear Feedback ◽

Feedback Controls ◽

The Family ◽

Control And Synchronization ◽

Theoretical Results

This paper considers the globally exponential synchronization (GES) of the family of Rössler chaotic systems. One pair of the six transmitter-receiver systems is specifically studied, and algebraic criterion for the GES is obtained via proper nonlinear feedback controls. Based on the study of the systems' structures, appropriate Lyapunov functions are constructed for error systems. The method presented in this paper provides a convenient tool in the practical use of chaos control and synchronization. Numerical simulations are provided to demonstrate the theoretical results.

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