­­­Control and Anti-control of Chaos Based on the Moving Largest Lyapunov Exponent Using Reinforcement Learning

In this paper, the abundant nonlinear dynamical behaviors of a fractional-order time-delayed Duffing system under harmonic excitation are studied. By constructing Melnikov function, the necessary conditions of chaotic motion in horseshoe shape are detected, and the chaos threshold curve is obtained by comparing the results obtained through the Melnikov theory and numerical iterative algorithm. The results show that the trend of change is the same, which confirms the accuracy of the chaos threshold curve. It could be found that when the excitation frequency ω is larger than a certain value, the Melnikov theory is not valid for these values. Furthermore, by numerical simulation, some numerical results are obtained, including phase portraits, the largest Lyapunov exponents, and the bifurcation diagrams, Poincare maps, time histories, and frequency spectrograms at some typical points. These numerical simulation results show that the system exhibits some new complex dynamical behaviors, including entry into the state of chaotic motion from single period to period-doubling bifurcation and chaotic motion and periodic motion alternating under the necessary condition of chaotic occurrence. In addition, the effects of time delay, fractional-order coefficient, fractional order, linear viscous damping coefficient, and linear stiffness coefficient on the chaotic threshold curve are discussed, respectively. Those results reveal that there exist abundant nonlinear dynamic behaviors in this fractional-order system, and by adjusting these parameters reasonably, the system could be transformed from chaotic motion to non-chaotic motion. 

Bifurcation and Chaotic Behavior of Duffing System with Fractional-Order Derivative and Time Delay

TianQin is a proposed mission for space-based gravitational-wave detection that features a triangular constellation in circular high Earth orbits. The mission entails three drag-free controlled satellites and long-range laser interferometry with stringent beam pointing requirements at remote satellites. For the payload architecture and pointing control strategies, having two test masses per satellite, one for each laser arm, and rotating entire optomechanical assemblies (each consisting of a telescope, an optical bench, an inertial sensor, etc.) for constellation breathing angle compensation represent an important option for TianQin. In this paper, we examine its applicability from the perspectives of test mass and satellite control in the science mode, taking into account of perturbed orbits and orbital gravity gradients. First, based on the orbit-attitude coupling relationship, the required electrostatic forces and torques for the test mass suspension control are estimated and found to be sufficiently small for the acceleration noise budget. Further optimization favors configuring the centers of masses of the two test masses collinear and equidistant with the center of mass of the satellite, and slightly offsetting the assembly pivots from the electrode housing centers forward along the sensitive axes. Second, the required control forces and torques on the satellites are calculated, and thrust allocation solutions are found under the constraint of having a flat-top sunshield on the satellite with varying solar angles. The findings give a green light to adopting the two test masses and telescope pointing scheme for TianQin. 

Payload architecture and pointing control strategies for TianQin

The space gravitational wave detector uses the inter-satellite laser interferometer to measure a change in distance with ultra-high precision at the picometer level. Its special differential wavefront sensing technology based on laser interference is used to obtain the ultra-high-precision relative attitude between spacecrafts. In order to acquire the measurement, it is necessary to maintain high-precision attitude pointing and alignment for the optical path line-of-sight of the detector. This paper proposes a frequency division control method. More specifically, we chose the telescope attitude control loop frequency division as it is the faster response part, mainly relative to the high-frequency band within the measurement bandwidth. The spacecraft attitude frequency division is mainly in the low-frequency band within the measurement bandwidth. Finally, a high-precision simulation analysis is carried out. The results show that compared with traditional methods, the use of frequency division control design can significantly improve the attitude and pointing stability of the system and provide control support for systems requiring high pointing coordination accuracy, such as space gravity wave detectors.

/pdf/frequency-division-control-of-line-of-sight-tracking-for-12s91tl6.pdf

Frequency Division Control of Line-of-Sight Tracking for Space Gravitational Wave Detector

In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.

/pdf/control-scheme-for-a-fractional-order-chaotic-genesio-tesi-2ue404tunf.pdf

Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model

Chaotic motion and control of a tethered-sailcraft system orbiting an asteroid

Stacked Recurrent Neural Network Based High Precision Pointing Coupled Control of the Spacecraft and Telescopes

This paper aims to propose a switching rule to improve the efficiency and stability of the mode switching process for the drag-free satellite. The switching rules will ensure the stability of the different controllers during the switching process. Unlike traditional satellite switching control, the inner loop and the outer loop of the drag-free satellite are strongly coupled. The drag-free satellite not only needs to consider the controller design in the inner loop but also the controller design of the outer loop. In the outer loop, a Proportion Integration Differentiation control method is adopted to design the controller. In the inner loop, considering the release error effect of the test mass, a nonlinear sliding-mode control is employed as a controller before the mode switch. The H∞ mixed-sensitivity controller, to improve the robustness of the system and solve the problem of controller saturation, is designed after the mode switch. In the stability analysis of the switching system, the piecewise continuous Lyapunov function method is adopted. The region of attraction, which is used as the switching rule, is calculated based on the sum of squares. The obtained results demonstrate that the proposed switching rule satisfies the control accuracy and system stability. 

Mode Switching Control for Drag-free Satellite Based on Region of Attraction

Abstract The service robots of space station in-cabin have attracted more and more attention. The space in-cabin robot with a pneumatic continuum arm is studied in this paper. It could be safer, more efficient and more flexible than the space rigid robot. However, the coupling motion of the moving base and the pneumatic continuum continuous arm brings a new challenge for controlling the end-effector to track the desired path. In this paper, a new control method based on the zeroing neural network (ZNN) is developed to solve the high-precision kinematics trajectory tracking control problem of unknown models. The real-time Jacobian matrix of the in-cabin robots with a pneumatic continuum arm is estimated by the input–output information when the parameter and the structure of the kinematic model are unknown. Moreover, this paper also employs a modified activation function power-sigmoid activation function (PSAF) to improve the robustness. In addition, it is proved through the Lyapunov stability theory that the proposed control approach is convergent and stable. Finally, the simulation results are given to show the effectiveness and robustness of the proposed control method for space in-cabin robots with a pneumatic continuum arm. 

/pdf/robust-tracking-control-of-unknown-models-for-space-in-cabin-3t4yc7b9.pdf

Robust tracking control of unknown models for space in-cabin robots with a pneumatic continuum arm

GKYP-Based Finite Frequency Control for Relative Motion of Drag-Free Satellite

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