Optimal sliding mode tracking control of spacecraft formation flying with limited data communication

A Gauss pseudospectral method is proposed in this study to solve the optimal trajectory-planning problem for satellite rapid large-angle maneuvers. In order to meet the requirement of rapid maneuver capability of agile small satellites, Single Gimbal Control Moment Gyros (SGCMGs) are adopted as the actuators for the attitude control systems (ACS). Because the singularity problem always exists for SGCMGs during the large-angle maneuvering of the satellites, a trajectory optimization method for the gimbal rates is developed based on the Gauss pseudospectral method. This method satisfies the control requirement of satellite rapid maneuvers and evades the singularity problem of SGCMGs. The method treats the large-angle maneuver problem as an optimization problem, which meets the boundary condition and a series of the physical constraints including the gimbal angle constraint, the gimbal rates constraint, the singularity index constraint, and some other performance criteria. This optimization problem is discretized as a nonlinear programming problem by the Gauss pseudospectral method. The optimal nonsingularity gimbal angle trajectory is obtained by the sequence of quadratic programming (SQP). This approach avoids the difficulties in solving the boundary value problem. The simulations reveal that the Gauss pseudospectral method effectively plans an optimal trajectory and satisfies all the constraints within a short time.

This study investigates the neural adaptive integral sliding mode control for attitude tracking of flexible spacecraft, where unknown actuator nonlinearity, input quantisation and external disturbances are considered simultaneously. In this design, the hysteresis encoder–decoder scheme is employed between the controller and actuator side for signal quantisation. A quantised adaptive integral sliding mode control strategy is developed, where the neural network scheme is applied to approximate the unmeasurable rigid-flexible coupled nonlinear dynamics. The proposed control strategy can compensate for quantisation error, actuator faults, actuator dead-zone as well as external disturbances effectively, and guarantee the trajectory of the attitude tracking error converge to the equilibrium point along the designed sliding surface. Finally, a simulation example is conducted to demonstrate the validness of the developed quantised control strategy for flexible spacecraft attitude tracking problem.

6-DOF fixed-time adaptive tracking control for spacecraft formation flying with input quantization

O PTIMAL control problems are often solved numerically via direct methods [1]. In recent years, considerable attention has been focused on a class of direct transcription methods called pseudospectral [2–4] or orthogonal collocation [5,6] methods. In a pseudospectral method, a finite basis of global interpolating polynomials is used to approximate the state at a set of discretization points. The time derivative of the state is approximated by differentiating the interpolating polynomial and constraining the derivative to be equal to the vector field at a finite set of collocation points. Although any set of unique collocation points can be chosen, generally speaking, an orthogonal collocation is chosen, i.e., the collocation points are the roots of an orthogonal polynomial (or linear combinations of such polynomials and their derivatives). Because pseudospectral methods are commonly implemented via orthogonal collocation, the terms pseudospectral and orthogonal collocation are interchangeable (thus researchers in onefieldmay use the term pseudospectral [3], whereas others may use the term orthogonal collocation [5]). One advantage to pseudospectral methods is that for smooth problems, pseudospectral methods typically have faster convergence rates than other methods, exhibiting “spectral accuracy” [4]. Pseudospectral methods were traditionally used to solve fluid dynamics problems [3], whereas orthogonal collocation methods were first established in the chemical engineering community [6]. Seminal work in the mathematics of orthogonal collocation methods for optimal control dates back to 1979 [7] and, in recent years, the following orthogonal collocationmethods have risen to prominence: the Legendre pseudospectral method [8], the Chebyshev pseudospectral method [9], the Radau orthogonal collocation method [10,11], and the Gauss pseudospectral method [12]. Within the class of pseudospectral methods, there are two very different and widely used implementation strategies that can be best described as local and global approaches. In a local approach, the time interval is divided into a large number of subintervals called segments or finite elements [6] and a small number of collocation points are usedwithin each segment. The segments are then linked via continuity conditions on the state, the independent variable, and possibly the control. The rationale for using local collocation is that a local method provides so-called local support [13] (i.e., the discretization points are located so that they support the local behavior of the dynamics) and is both computationally simple and efficient. Although local methods have a long history in solving optimal control problems, much of the recent work has shown great success in the application of global collocation [14,15] (i.e., collocation using a global polynomial across the entire time interval). Researchers are also looking into higher-order local methods [16,17], which lie in between global and local methods. In light of the recent results that promote global orthogonal collocation and the long history of the use local collocation, it is important to gain a better understanding as to how these two different philosophies compare in practice. This Note provides a comparison between global and local orthogonal collocation solutions for two optimal control problems.A recently developed orthogonal collocation method called the Gauss pseudospectral method (GPM) [12] is employed in both a global format and a local format. In the global approach, the GPM is implemented on a single segment and the number of collocation points is varied. As a local approach, the GPM is implemented such that a number of equal width segments are varied, while a small fixed number of collocation points are used in each segment. We note that the local application of the GPM is similar to the approaches of [6,10,18]. The results obtained in this research suggest that, except in special circumstances, global orthogonal collocation is preferable to local orthogonal collocation. For the smooth example in this study, the global GPM is much more accurate than the local GPM for a given number of total collocation points. Furthermore, for a desired accuracy, the global approach is computationally more efficient than the local approach in smooth problems. For nonsmooth problems, as in the second example, the local and global approach are quite similar in terms of accuracy.

Optimal aeroassisted symmetric transfer between coplanar elliptical orbits

Backstepping method is a successful approach to deal with the systems in strict-feedback form. However, for networked control systems, the discontinuous virtual law caused by state quantization introduces huge challenges for its applicability. In this article, a quantized adaptive robust control approach in backsetpping framework is developed in this article for networked strict-feedback nonlinear systems with both state and input quantization. In order to prove the efficiency of the designed control scheme, a novel form of Lyapunov candidate function was constructed in the process of analyzing the stability, which is applicable for the systems with nondifferentiable virtual control law. In particular, the state and input quantizers can be in any form as long as they meet the sector-bound condition. The theoretic result shows that the tracking error is determined by the pregiven constants and quantization errors, which are also verified by the simulation results.

In the present paper, a composite formation strategy for multiple missiles is proposed, which is composed of the optimal formation configuration trajectory and a robust controller for trajectory tracking and formation keeping. Motion models describing multiple missiles formation configuration and keeping are established. Many constraints such as initial position, terminal position and collision avoidance are taken into account. Based on the Gauss Pseudospectral method, an optimal trajectory is designed which makes multiple missiles configurate the designated shape in the shortest time with less control energy. With the consideration of practical situations such as missiles' position error, measurement error of information between missiles and their limited control input, a robust controller is designed to track the optimal formation configuration trajectory and then keep the designated formation shape by adopting dynamic surface control. Simulation results demonstrate that by adopting the composite formation strategy, multiple missiles can configurate the designated shape in the shortest time with less control energy and then keep the formation shape in spite of much disturbance.

Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

In the last decade, research studies on parking planning mainly focused on path planning rather than trajectory planning. The results of trajectory planning are more instructive for a practical parking process. Therefore, this paper proposes a trajectory planning method in which the optimal autonomous valet parking (AVP) trajectory is obtained by solving an optimal control problem. Additionally, a vehicle kinematics model is established with the consideration of dynamic obstacle avoidance and terminal constraints. Then the parking trajectory planning problem is modeled as an optimal control problem, while the parking time and driving distance are set as the cost function. The homotopic method is used for the expansion of obstacle boundaries, and the Gauss pseudospectral method (GPM) is utilized to discretize this optimal control problem into a nonlinear programming (NLP) problem. In order to solve this NLP problem, sequential quadratic programming is applied. Considering that the GPM is insensitive to the initial guess, an online calculation method of vertical parking trajectory is proposed. In this approach, the offline vertical parking trajectory, which is calculated and stored in advance, is taken as the initial guess of the online calculation. The selection of an appropriate initial guess is based on the actual starting position of parking. A small parking lot is selected as the verification scenario of the AVP. In the validation of the algorithm, the parking trajectory planning is divided into two phases, which are simulated and analyzed. Simulation results show that the proposed algorithm is efficient in solving a parking trajectory planning problem. The online calculation time of the vertical parking trajectory is less than 2 s, which meets the real-time requirement.

Consensus tracking and vibration control for multiple single-link flexible manipulators with input signal quantization

In this paper, an improved predefined-time scheme is constructed to solve the tracking control problem of switched nonlinear systems with input quantization (IQ) and hysteresis nonlinearity. First, we introduce quantized control to address the communication resource wastage caused by the time-sampling mechanisms. The unexpected high-frequency components introduced by IQ affect system performance seriously. To overcome this case, a new approach is proposed to remedy this, wherein a novel quantization-filtering auxiliary system is conceived via the utilization of a band-pass filter. Subsequently, an improved PTL is developed, combining the filter parameters and quantization parameters, which has two main characteristics: (1) it has a coupled relationship between filter and quantizer, further reducing the minimum upper bound of settle time and the complexity of tuning simulation parameters and (2) compared to traditional predefined-time lemmas, it has faster convergence rates. Furthermore, a predefined-time filter is devised to address the issue of “explosion of complexity.” Finally, the effectiveness of the developed control strategy is validated through numerical and practical examples.

A safe and rapid formation generation is of great importance for the cooperation performance of the multiple unmanned helicopters. The trajectory optimization and control is the key problem in the process of the formation generation. To achieve this goal, a novel safe formation generation strategy is proposed through trajectory optimization and tracking control. First, the rapidly-exploring random tree (RRT) algorithm is applied to obtain the initial guess to satisfy the requirement of rapid solution. Then, the Gauss pseudospectral method is used to transform the optimal control problem to the nonlinear programming (NLP) problem and the sequence quadratic programming (SQP) method is utilized to gain the optimal trajectory combined with the initial guess. Second, a finite-time sliding mode controller is proposed to ensure the finite time trajectory tracking in the presence of model parameter uncertainties and unknown external disturbances. Finally, the numerical simulation is provided to show the effectiveness of the proposed formation generation strategy for unmanned helicopters formation.

This paper investigates the tracking control problem of multiagent systems with Lipschitz nonlinearities and external disturbances that track a target with states that are not available to any of the agents. For this purpose, a distributed estimation and control algorithm (DECA) is firstly designed for each agent to estimate and track the target’s states. Then, the proposed DECA is extended based on a finite time disturbance estimator for tracking control in the presence of external disturbances. The stability analysis of suggested algorithms is also considered. Simulation examples illustrate the promising performance of the proposed algorithms.

The objective of this paper is to investigate a reliable method to generate optimal ascent trajectory for hypersonic air-breathing vehicles. When solving optimal trajectories in endo-atmospheric flight, most of traditional indirect methods suffer from difficulties in finding an appropriate initial guess and getting a convergent solution for the two point boundary value problem (TPBVP). With improvements on on-board computer performance, direct methods such as pseudospectral method show promising potential for real-time optimal guidance. It removes the need for computing analytical gradients of aerodynamic coefficients, and remains high accurate solution similar to indirect methods. In this work, optimal ascent trajectory generation problem was formulated as a fuel-optimal control problem. Gauss pseudospectral method (GPM) was presented to generate the optimal ascent trajectories. Optimal solutions from GPM were compared with an indirect method based on finite difference method (FDM). Numerical simulations were studied with various initial conditions to investigate the optimal trajectory characteristics for hypersonic air-breathing vehicles. The results verified the validity and accuracy of GPM for ascent trajectory optimization.

Distributed RISE control for spacecraft formation reconfiguration with collision avoidance