Krishna Dev Kumar

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

Quaternion-Based Adaptive Output Feedback Attitude Control of Spacecraft Using Chebyshev Neural Networks

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

Distributed Attitude Coordination Control for Spacecraft Formation Flying

A distributed attitude coordination control scheme using terminal sliding mode (TSM) is proposed for a group of spacecraft in the presence of external disturbances. A novel fast terminal sliding manifold is presented, and a robust control term based on the hyperbolic tangent function is employed to suppress bounded external disturbances. The finite-time stability of the overall closed-loop system is guaranteed by a Lyapunov-based approach, and numerical simulations are presented to demonstrate the performance of the proposed controller.

Decentralized Fault-Tolerant Control for Satellite Attitude Synchronization

This paper presents a decentralized adaptive fuzzy approximation design to achieve attitude tracking control for formation flying in the presence of external disturbances and actuator faults. A nonsingular fast terminal sliding mode controller that is based on consensus theory is designed for distributed cooperative attitude synchronization. It solves synchronization issues between multiple satellites by information topology. In the proposed control scheme, a fuzzy logic system (FLS) is introduced to approximate unknown individual satellite attitude dynamics due to actuator faults. In order to achieve fault management without the involvement of ground-station operators, the proposed control laws do not require an explicit fault detection and isolation mechanism. Numerical simulation results including actuator dynamics and initial condition uncertainties show that the proposed strategy with FLS can compensate for a fault. The system continues to operate after wheel faults, and the closed-loop distributed tracking control system is stochastically stable.

Attitude Coordination Control for a Group of Spacecraft Without Velocity Measurements

This paper investigates the problem of velocity-free attitude coordination control for a group of spacecraft with attitude represented by modified Rodrigues parameters. The communication flow among neighbor spacecraft is described by an undirected connected graph. Two velocity-free attitude coordination control schemes are proposed. By employing linear reduced-order observers, robust control and Chebyshev neural networks, the first velocity-free control scheme allows a group of spacecraft to simultaneously align their attitude and track a time-varying reference attitude even in the presence of unknown mass moment of inertia matrix and external disturbances, where all spacecraft have access to the common reference attitude. The second control law guarantees a group of spacecraft to track a time-varying reference attitude without requiring velocity measurements even when the common reference attitude is available only to a subset of the group members. Furthermore, the stability of the overall closed-loop system for both control laws is guaranteed by a Lyapunov-based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controllers.

Fault Tolerant Reconfigurable Satellite Formations Using Adaptive Variable Structure Techniques

This paper proposes two adaptive nonlinear control algorithms based on a variable-structure control design for multiple spacecraft formation flying. The nonlinear dynamics describing the motion of the follower spacecraft relative to the leader spacecraft are considered for the case in which the leader spacecraft is in an elliptical reference orbit, and the stability of such a formation in the presence of external perturbations is investigated. This paper presents fault-tolerant control schemes to account for accidental or degradation faults in spacecraft sensors and thrusters. The nonlinear analytical model describing the system is used to develop two adaptive fault-tolerant control laws (continuous sliding mode control and nonsingular terminal sliding mode control) that guarantee global asymptotic convergence of the position tracking error in the presence of unknown follower spacecraft mass and external disturbances. Several numerical examples are presented to demonstrate the efficacy of the proposed controllers to maintain the relative motion by correcting for initial offsets and external perturbation effects that tend to disperse the formation. Simulation results confirm that the suggested methodologies yield submillimeter formation, keeping precision and effectiveness in ensuring formation maneuvering. In addition, an abrupt blockage of the relative position sensors, thruster failure for a period of time, and thruster degradation (amidst formation keeping and reconfiguration maneuvers) are simulated to demonstrate the fault recovery capability of the controllers. The numerical results clearly establish the robustness of the proposed reconfigurable adaptive control scheme for precise formation keeping in the event of sensor and thruster faults.

Robust Attitude Coordination Control for Spacecraft Formation Flying Under Actuator Failures

This paper examines attitude coordination control for spacecraft formation flying. A class of distributed adaptive fault-tolerant attitude coordination control laws is proposed. The proposed control laws do not require online identification of failures. Using the Lyapunov approach and graph theory, it is shown that the control laws guarantee a group of spacecraft that simultaneously track a common time-varying reference attitude, even when the reference attitude is available only to a subset of the members of a group. Finally, numerical simulation is presented to show that the distributed controller is successful in achieving high-attitude tracking and synchronization performance, even in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, actuator failures, and control saturation limits.

Neural Network-Based Distributed Attitude Coordination Control for Spacecraft Formation Flying With Input Saturation

This brief considers the attitude coordination control problem for spacecraft formation flying when only a subset of the group members has access to the common reference attitude. A quaternion-based distributed attitude coordination control scheme is proposed with consideration of the input saturation and with the aid of the sliding-mode observer, separation principle theorem, Chebyshev neural networks, smooth projection algorithm, and robust control technique. Using graph theory and a Lyapunov-based approach, it is shown that the distributed controller can guarantee the attitude of all spacecraft to converge to a common time-varying reference attitude when the reference attitude is available only to a portion of the group of spacecraft. Numerical simulations are presented to demonstrate the performance of the proposed distributed controller.

Particle Swarm Optimization Applied to Spacecraft Reentry Trajectory

THE numerical solution of optimal control problems that are nonlinear and, therefore, generally without analytical solutions, can be categorized into different classes with their own advantages and characteristics. In the direct approach, the model equations of the considered system are discretized, and the control trajectories are parametrized to obtain a finite-dimensional parameter optimization problem [1]. Among these direct methods, global optimization methods (also known as evolutionary algorithms), have become of interest in recent years and various research has been done in this area [1–4]. Some well-known methods in this category are genetic algorithms (GAs), which model the evolution of species based on Darwin’s principle of survival of the fittest; simulated annealing (SA), which mimics the equilibrium of large numbers of atoms during an annealing process; and ant-colony optimization, which is inspired by the behavior of the ants. Among all global optimization techniques, the swarm intelligence (SI)-based methods are becoming more popular due to their speed and accuracy qualities. They are inspired by natural phenomena such as the behavior of groups of birds, ant colonies, herds of animals, and even social connections between human beings [3]. The idea of particle swarm optimization (PSO) that is addressed in this Note was first introduced in 1995 by Eberhart and Kennedy [5] and was then followed and modified by other researchers [6]. The most important factor that stands out in SI methods is that because they use the whole experience of the group of individuals, rather than only the experience of each individual particle (i.e., one potential solution), their convergence speed is faster than other methods. The scope of this Note is to present a new method for solving an optimal control problem using a PSO method and avoiding the calculations needed in the common analytical approaches. This is accomplished by using an existing solution for a specific problem and then trying to find other possible trajectories for other objectives of interest. This Note is organized as follows: in Sec. II, the system of equations ofmotion for a reentry spacecraft is presented based on [7]. In Sec. III the PSO optimization method and mapping procedure are described. In Sec. IV the results are presented for two different objective functions. The first objective is for validating the proposed method in terms of accuracy and the other objective isminimizing the integral of the heat applied to the spacecraft.

Distributed finite-time velocity-free attitude coordination control for spacecraft formations

In this paper, the finite-time velocity-free attitude coordination control for spacecraft formation flying under an undirected communication graph is addressed. A finite-time observer is introduced to obtain an accurate estimation of unmeasurable angular velocity and a decentralized finite-time observer is employed to estimate the angular acceleration of the virtual leader. With the application of the finite-time observer, the decentralized finite-time observer, and the homogeneous method, a continuous distributed finite-time attitude coordination control law is designed for a group of spacecraft without requiring angular velocity measurements. A rigorous proof shows that semi-global finite-time stability of the overall closed-loop system can be achieved and the proposed velocity-free control law guarantees a group of spacecraft to simultaneously track a common time-varying reference attitude in finite time even when the reference attitude is available only to a subset of the group members. The performance of the control scheme derived here is illustrated through numerical simulations.