Steering a flexible spacecraft between equilibrium points

1992 ◽  
Author(s):  
Pasquale Lucibello
Keyword(s):  
Equilibrium Points ◽  
Flexible Spacecraft

Attitude stabilization of flexible spacecraft under limited communication with reinforced robustness

2019 ◽  
Vol 41 (16) ◽  
pp. 4475-4487 ◽  
Author(s):  
Syed Muhammad Amrr ◽  
M Nabi
Keyword(s):  
Attitude Control ◽  
Communication Channel ◽  
Equilibrium Points ◽  
Flexible Spacecraft ◽  
Sampled Data ◽  
External Disturbances ◽  
Attitude Stabilization ◽  
Potential Alternative ◽  
Bandwidth Constraint ◽  
Event Based

This paper proposes a robust event-driven control for attitude regulation in flexible spacecraft affected by inertial parametric uncertainties and external disturbances. The bandwidth constraint of the communication channel between controller and system requires an event-based control design. Under the action of proposed control law, the system trajectories are ensured to be uniformly ultimately bounded (UUB) in a small vicinity of their equilibrium points. Apart from the boundedness of states, the proposed event-triggered controller also satisfies bandwidth restrictions by achieving a substantially low control usage. The results obtained from numerical simulations are indeed encouraging. It demonstrates the proposed controller as a potential alternative to the periodically sampled data controllers. Moreover, the proposed control strategy successfully eludes the unwanted unwinding phenomenon encountered in quaternion based attitude control of the spacecraft.

Fuel optimal propulsive reboost of flexible spacecraft

1992 ◽  
Author(s):  
LARRY SILVERBERG ◽  
JIM REDMOND
Keyword(s):  
Flexible Spacecraft

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 876
Author(s):  
Wieslaw Marszalek ◽  
Jan Sadecki ◽  
Maciej Walczak
Keyword(s):  
Equilibrium Points ◽  
Autonomous Systems ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
Dynamical Model ◽  
Bifurcation Diagrams ◽  
Step Size ◽  
Oscillatory Systems ◽  
Two Parameter ◽  
Parameter Bifurcation

Two types of bifurcation diagrams of cytosolic calcium nonlinear oscillatory systems are presented in rectangular areas determined by two slowly varying parameters. Verification of the periodic dynamics in the two-parameter areas requires solving the underlying model a few hundred thousand or a few million times, depending on the assumed resolution of the desired diagrams (color bifurcation figures). One type of diagram shows period-n oscillations, that is, periodic oscillations having n maximum values in one period. The second type of diagram shows frequency distributions in the rectangular areas. Each of those types of diagrams gives different information regarding the analyzed autonomous systems and they complement each other. In some parts of the considered rectangular areas, the analyzed systems may exhibit non-periodic steady-state solutions, i.e., constant (equilibrium points), oscillatory chaotic or unstable solutions. The identification process distinguishes the later types from the former one (periodic). Our bifurcation diagrams complement other possible two-parameter diagrams one may create for the same autonomous systems, for example, the diagrams of Lyapunov exponents, Ls diagrams for mixed-mode oscillations or the 0–1 test for chaos and sample entropy diagrams. Computing our two-parameter bifurcation diagrams in practice and determining the areas of periodicity is based on using an appropriate numerical solver of the underlying mathematical model (system of differential equations) with an adaptive (or constant) step-size of integration, using parallel computations. The case presented in this paper is illustrated by the diagrams for an autonomous dynamical model for cytosolic calcium oscillations, an interesting nonlinear model with three dynamical variables, sixteen parameters and various nonlinear terms of polynomial and rational types. The identified frequency of oscillations may increase or decrease a few hundred times within the assumed range of parameters, which is a rather unusual property. Such a dynamical model of cytosolic calcium oscillations, with mitochondria included, is an important model in which control of the basic functions of cells is achieved through the Ca2+ signal regulation.

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