An adaptive time‐varying barrier Lyapunov function‐based attitude tracking control for spacecrafts without angular velocity measurement

The cooperative tracking control problem for the multiagent systems with unknown dynamic models, state constraints, control input constraints, optimal performance index, and convergence rate constraints is investigated in this article. A novel design framework is proposed to cope with these constraints and requirements. More specifically, the mean value theorem is utilized to transform the control input constraint to the unconstrained form. The performance function combined with a barrier Lyapunov function is leveraged to achieve the guaranteed transient tracking performance, finite-time convergence, and state constraints. To satisfy the optimal performance index, while considering the unknown dynamics of agents, we employ the actor-critic neural network architecture to get the near-optimal solution. Our control scheme is completely model-free. The rigorous Lyapunov stability analyses show that the full-state constraints and control input constraints are always satisfied, and the cooperative tracking errors can be made as small as possible in a finite time at a desired decay rate by appropriately setting the parameters in the performance function and barrier Lyapunov function. Finally, the simulation and hardware tests are conducted to clarify the effectiveness of the proposed control strategy.

This paper examines the problem of fixed-time attitude tracking fault-tolerant for rigid spacecraft without angular velocity measurement, in the presence of uncertainties, external disturbances, and actuator faults. First, a fixed-time observer is established to obtain accurate estimates of the unmeasurable angular velocities, by applying a fixed-time observer, a fixed-time tracking control method is addressed to enable the tracking spacecraft to track the target spacecraft with time-varying attitude in a fixed time. A fixed-time output feedback attitude tracking controller is designed and the fixed time stability of the system is proved. In addition, the simulation results verify the effectiveness of the proposed control strategy.

S INCE some catastrophic faults or failures may be induced due to the aging or damage of actuators and sensors during the mission of a spacecraft, those faults would lead to performance degradation of the spacecraft attitude control system or even result in the specified aerospacemission failure. Therefore, fault tolerance of the spacecraft attitude control system is one of the key issues that needs to be addressed. With a view to tackle such a challenge, fault-tolerant control (FTC) has received considerable attention in order to enhance the spacecraft reliability and to guarantee the attitude control performance [1–5]. In [5], an adaptive FTC is developed for the flexible spacecraft attitude tracking system where the persistent bounded disturbances, unknown inertia parameter, and even two types of reaction wheel faults are successfully accommodated. Indeed, the aforementioned approaches offer many attractive conceptual features, but at the same time they are derived based on the availability of direct and exact measurements of both the angular velocity and the attitude orientation. It is important to note, however, that when it comes to practical implementation, the angular velocity measurements are not always available because of either cost limitations or implementation constraints. Motivated from such a practical consideration, it is therefore highly desirable to develop partial state feedback attitude control strategies with spacecraft angular velocity measurements eliminated. The issue has been addressed in the literature by using observer-based control [6,7], Lyapunov-based control [8,9], and variable structure control [10] under normal operation of spacecraft. In this work, we provide solutions to two different problems of the flexible spacecraft attitude control system. The first problem consists of developing a control law to perform a attitude stabilization maneuver without angular velocity magnitude. In contrast with the velocity-free control schemes available in the literature, the presented approach can guarantee the attitude control performance be greatly robust to external disturbances and unknown inertia parameters. The second problem solved is the casewhere both loss of control effectiveness and additive fault occur in actuators simultaneously, but the attitude still requires stabilization with high resolution. To the best knowledge of the authors, this study is the first attempt to deal with fault-tolerant attitude stabilization control for flexible spacecraft with the angular velocity magnitude eliminated. The Note is organized as follows. Section II presents the mathematical model and attitude control problems formation of a flexible spacecraft under normal and faulty actuator conditions. Section III presents the proposed fault-tolerant attitude stabilization controller without velocity magnitude in the presence of two types of actuator faults. Simulation results to demonstrate various features of the proposed scheme are given in Sec. IV followed by conclusions in Sec. V.

The global adaptive set stabilization problem of the attitude of a rigid spacecraft is addressed in this paper. Two different cases are considered. First, by using adaptive backstepping method, the authors design a global adaptive control law for the attitude control system with unknown inertia matrix such that the attitude and the angular velocities can be globally asymptotically stabilized to a set consisting of two equilibria. And then, based on the obtained backstepping adaptive law, the authors consider the case that the angular velocities are not measurable. By introducing an auxiliary state, a semi-global adaptive set stabilization law without angular velocity measurements is also designed. It is rigorously proved that, for the two cases, both of the closed loop systems satisfy the set stability. The effectiveness of the proposed methods is verified by simulation results.

Finite-time output feedback attitude control for rigid spacecraft under control input saturation

This paper investigates a novel robust adaptive dynamic surface control scheme based on the barrier Lyapunov function (BLF), online composite learning, disturbance observer, and improved saturation function. It is mainly designed for a class of skid-to-turn (STT) interceptor integrated guidance and control (IGC) design problems under multi-source uncertainties, state constraints, and input saturation. The serial-parallel estimation model used in this study estimates the system states and provides “critic” information for the neural network and disturbance observer; then, these three are combined to realize online composite learning of the multiple uncertainties of the system and improve the interception accuracy. In addition, the state and input constraints are resolved by adopting the BLF and the improved saturation function, while the design of the auxiliary system ensures stability. Finally, a series of simulation results show that the proposed IGC scheme with a direct-hit intercept strategy achieves a satisfactory effect, demonstrating the validity and robustness of the scheme.

In this paper, for the six-degree-of-freedom (six-DOF) model of hypersonic flight vehicle (HFV) subject to actuator faults, state constraints, parametric uncertainties, and external disturbances, an adaptive fault tolerant control (FTC) scheme is proposed based on barrier Lyapunov functions (BLFs). The study is begun with a series of control-oriented manipulations: at first, due to the high complexity of the six-DOF model, the corresponding simplified model is proposed under reasonable assumptions; then, through the stability analysis of the internal dynamics, we can conclude that the vehicle model is a non-minimum phase system, namely, having unacceptable zero-dynamics. In order to solve the non-minimum phase problem, the elevator-to-lift coupling term is regarded as uncertainty of the model. Subsequently, in consideration of the insufficient control torque caused by the fault of the rudder or elevators, an adaptive fault-tolerant controller is designed based on BLFs, backstepping method, and Nussbaum gains. In the control law, the uncertain parameters are replaced by their estimates updated by adaptive laws. And the angle of attack and the roll angle of the aircraft are constrained in the preset range. Additionally, the convergence of the proposed FTC algorithm and the boundedness of all the signals of the closed system is proved by Lyapunov stability theory. At last, the numerical simulation results of the six-DOF model are carried out to manifest the effective tracking performance of the proposed FTC scheme.

The challenging problem on the design of a large-angle attitude tracking controller for rigid satellites without angular velocity measurements is investigated in this article. An efficient and practical angular velocity-free control strategy with a simple, yet efficient structure is proposed. The attitude tracking maneuver is accomplished with the desired attitude pointing accuracy ensured despite disturbances. Compared with the existing observer-based velocity-free schemes, no observer is embedded into the control scheme. The developed approach can be implemented online and in real time. It does not require expensive online computation, enabling its convenient application to practical large-angle attitude tracking maneuvers. The presented control solution is numerically and experimentally validated on a rigid satellite testbed.

Investigations of an integrated angular velocity measurement and attitude control system for spacecraft using magnetically suspended double-gimbal CMGs

In this paper, an adaptive neural network (NN) constraint control method is studied for a class of uncertain nonlinear nonstrict feedback systems with state constraints. The restrictive assumption that the unknown internal dynamics must possess the monotonically increasing characteristics in previous results is removed. The property of radial basis function (RBF)NNs is used to solve the algebraic loop problem based on the approximation structure. In order to achieve full state constraint satisfactions, the barrier Lyapunov functions (BLFs) are employed in each design procedure. Based on the backstepping and less adjustable parameters techniques, the controllers and the adaptive laws are obtained. By using the Lyapunov stability theory, the boundedness of all signals in the closed-loop system is proved. Therefore, the scheme not only solves the stability problem of the nonstrict feedback system but also overcomes the influence of the state constraint on the control performance. Finally, the effectiveness of the control method is verified by two simulation examples.

A new robust tracking control approach is proposed for strict-feedback nonlinear systems with state and input constraints. The constraints are tackled by extending the control input as an extended state and introducing an integral barrier Lyapunov function (IBLF) to each step in a backstepping procedure. This extends current research on barrier Lyapunov functions(BLFs)-based control for nonlinear systems with state constraints to IBLF-based control for strict-feedback nonlinear systems with state and input constraints. Since the IBLF allows the original constraints to be mixed with the error terms, the use of IBLF decreases conservatism in barrier Lyapunov functions-based control. In the backstepping procedure, neural networks (NNs) with projection modifications are applied to estimate system uncertainties, due to their ability in guaranteeing estimators in a given bounded area. To facilitate the use of the once-differentiable NNs estimators in the backstepping procedure, the virtual controllers are passed through command filters. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the proposed control.

Neuro-adaptive optimized control for full active suspension systems with full state constraints

In this article, the singularity-free adaptive fuzzy fixed-time control problem is studied for an uncertain n-link robotic system with the position tracking error constraint. The controlled robotic system can be described as a multiple-input-multiple-output system.To implement the user-defined performance, an improved error conversion mechanism based on performance functions is presented such that the converted error is limited to an interval greater than zero, and an appropriate barrier Lyapunov function (BLF) is constructed to avoid the breach of position tracking error constraint. The fuzzy approximator is utilized to estimate the unknown functions. The significance and challenges of this article are to establish a new error conversion mechanism and design corresponding BLF that can be integrated into fixed-time control design to present a singularity-free adaptive fuzzy fixed-time control scheme. Benefits of the proposed adaptive fixed-time controller in comparison to the current approaches are that it cannot cause the singularity issue appearing in backstepping-based fixed-time control design and ensures quick transient response. Combining with Lyapunov stability theory, the boundedness of the closed-loop signals is ensured, and the position tracking error can be constrained in the user-defined performance boundaries. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Adaptive fixed-time consensus control for a class of non-strict feedback multi-agent systems subject to input nonlinearities, state constraints, unknown control directions, and actuator faults

The disturbance rejection problem of aerial vehicles is a widely concerned issue. For attitude dynamics, we propose a method for directly designing a geometric observer (GOB) based on the special orthogonal group SO(3), thus reducing the impact of model mismatch and being unrestricted by the aircraft attitude. Considering the type of measurement available, we have developed two GOBs: GOB-I, which uses both attitude and angular velocity measurements, and GOB-II, which uses only attitude measurement. The stability of GOB is theoretically proved, with the GOB-I exhibiting almost global asymptotic stability and the GOB-II demonstrating local asymptotic stability. We have compared the estimation performance of our proposed GOB with four other disturbance observers (DOBs) for five types of disturbances. The simulation results show that, in the small attitude scenarios, our proposed GOB-I observer performs comparably with the compensation function observer (CFO) and the nonlinear disturbance observer (NDOB) that use both attitude and angular velocity measurements, while the GOB-II performs comparably with the extended state observer (ESO) that uses only attitude measurements. In the agile attitude scenarios, our proposed GOB-I observer significantly outperforms CFO and NDOB, and GOB-II also performs much better than ESO. Compared with the reduced-order observer, which uses only angular velocity measurement, the GOB-I can handle more complex disturbances and provides compensation for sensor errors. Flight experiments conducted with a lifting-wing quadcopter demonstrate the efficiency of our method in resisting unknown payload in hover flight and model uncertainty in agile maneuver.