This paper deals with the problem of position and attitude tracking control for a rigid spacecraft. A fully actuated system (FAS) model for the six degree-of-freedom (6DOF) spacecraft motion is derived first from the state-space model by variable elimination. Considering the uncertainties from external disturbance, unknown motion information, and uncertain inertia properties, an extended state observer (ESO) is designed to estimate the total disturbance. Then, a tracking controller based on FAS approach is designed, and this makes the closed-loop system a constant linear one with an arbitrarily assignable eigenstructure. The solution to the parameter matrices of the observer and controller is given subsequently. It is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the origin. Finally, numerical simulation demonstrates the effectiveness of the proposed controller.

This paper proposes a scheme of trajectory tracking control for the hovercraft. Since the model of the hovercraft is under-actuated, nonlinear, and strongly coupled, it is a great challenge for the controller design. To solve this problem, the control scheme is divided into two parts. Firstly, we employ differential flatness method to find a set of flat outputs and consider part of the nonlinear terms as uncertainties. Consequently, we convert the under-actuated system into a full-actuated one. Secondly, a reinforcement learning-based active disturbance rejection controller (RL-ADRC) is designed. In this method, an extended state observer (ESO) is designed to estimate the uncertainties of the system, and an actorcritic-based reinforcement learning (RL) algorithm is used to approximate the optimal control strategy. Based on the output of the ESO, the RL-ADRC compensates for the total uncertainties in real-time, and simultaneously, generates the optimal control strategy by RL algorithm. Simulation results show that, compared with the traditional ADRC method, RL-ADRC does not need to manually tune the controller parameters, and the control strategy is more robust.

In this note, the well-known Brockett’s first example system is treated with the fully actuated system (FAS) approach. Firstly, it is shown that the system can be exponentially substabilized by a smooth controller in the sense that, except those starting from initial values on the z₀-axis of the initial value space, all trajectories of the designed system as well as the control signals decay to zero exponentially. Secondly, global stabilization is realized through a way of enabling the trajectories starting from initial values on the z₀-axis also to go to the origin. The idea is to firstly move an initial point on the z₀-axis away from the axis using a pre-controller, and then to take over by the designed exponentially sub-stabilizing controller.

In this paper, the problem of stabilization is considered for discrete-time multiple-input nonlinear systems with distinct input delays law based on the fully actuated system approach. In order to compensate the input delays, a prediction scheme is presented to predict future states based on the closed-loop linear system. Then, a stabilizing law is constructed for nonlinear delayed systems by replacing the future states in the control law for the corresponding delay-free systems with their prediction. Finally, numerical examples are given to verify the effectiveness of the proposed approach.

This paper focuses on the problem of adaptive control for a class of time-delay systems. First, the strict feedback nonlinear time-delay system is transformed into a fully actuated system by utilizing the fully actuated system theory. Then, the uncertain time-delay terms of the system are bounded by the product of the absolute value of the system state and the non-linear function with the unknown parameters. By following the high order fully actuated system approaches, a continuous adaptive controller is designed for the system. It is proved that the controller can render the system achieve asymptotically stability. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical results.

This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain. To make the compensation for time-varying delays concise, active and universal, a novel nonlinear predictive control method is proposed. The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays. At the same time, the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived. Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.

This paper investigates the attitude and orbit control for the combined spacecraft formed after a target spacecraft without the autonomous control ability is captured by a service spacecraft. The optimal controller of fully-actuated system is proposed to realize the attitude and orbit stabilization control of combined spacecraft. The stability of the system is proved by introducing Lyapunov function. Numerical simulation of the combined spacecraft and physical experiment based on the combined spacecraft simulator (CSS) are completed. Both simulation and experiment results demonstrate the effectiveness and practicability of the optimal controller of fully-actuated system.

The multi-degree of freedom (muti-DOF) manipulator system is a complex control system with the strong coupling feature and high nonlinearity. In this paper, trajectory tracking control of a six-degree of freedom (6-DOF) manipulator based on fully-actuated system models and a direct parametric method is investigated. The fully-actuated system model of the 6-DOF manipulator is established by using the Denavit Hartenberg (DH) notation and Euler-Lagrange dynamics. A disturbance observer is constructed to solve the nonlinear uncertainties such as unmodeled dynamics and external disturbances. Then, a controller is designed using the direct parametric method to make the 6-DOF manipulator reach the desired position with high accuracy. After that, a switching control strategy is developed to suppress the peak value belonging to the controller. Simulation results reveal the effect of the proposed control approach.

The article is devoted to the almost disturbance decoupling problem for high-order fully actuated (HOFA) nonlinear systems with strict-feedback form. Using the full-actuation feature of high-order fully actuated systems and Lyapunov stability theory, a state feedback control law and virtual control laws are designed. The unknown disturbances are handled by almost disturbance decoupling (ADD) method. Finally, the effectiveness of the control strategy is verified by stability analysis and simulation.

Thermoacoustic instability phenomena often encounter in gas turbine combustors, especially for the premixed combustor design, with many possible detrimental results. As a classical experiment, the Rijke tube is the simplest and the most effective illustration to study the thermoacoustic instability. This paper investigates the active control approach of the thermoacoustic instability in a horizontal Rijke tube. What’s more, the radial basis function (RBF) neural network is adopted to estimate the complex unknown continuous nonlinear heat release rate in the Rijke tube. Then, based on the proposed second-order fully actuated system model, the authors present an adaptive neural network controller to guarantee the flow velocity fluctuation and pressure fluctuation to converge to a small region of the origin. Finally, simulation results demonstrate the feasibility of the design method.

This paper is concerned with formation control of fully-actuated underwater vehicles (FUVs), focusing on improving system convergence speed and overcoming velocity measurement limitation. By employing the fixed-time control theory and command filtering technique, a full state feedback formation algorithm is proposed, which makes the follower track the leader in a given time with all signals in the system globally practically stabilized in fixed time. To avoid degraded control performance due to inaccurate velocity measurement, a fixed-time convergent observer is designed to estimate the velocity of FUVs. Then the authors give an observer-based fixed-time control method, with which acceptable formation performance can be achieved in fixed time without velocity measurement. The effectiveness and performance of the proposed method are demonstrated by numerical simulations.

This paper utilizes the high-order fully actuated (HOFA) system approach to synthesize a class of nonlinear systems. First, the original nonlinear system can be rewritten in a quasi-linear form, which is more general than other nonlinear systems, such as strict-feedback systems. Based on a rank condition, the quasi-linear system can be transformed into a canonical form. Second, a simple transformation is adopted to convert the above canonical form into the HOFA model. Once an HOFA model is derived, the authors design a controller to make the closed-loop system a constant linear system with the desired eigenstructure. Finally, a numerical example illustrates the fitness and effectiveness of the proposed approach.

Safety is an essential requirement for control systems. Typically, controlled mobile robots are subject to safety constraints, to which control laws in typical forms may not be directly applicable. This paper employs barrier function to describe safety constraints, analyzes the interaction between the barrier function and the uncertain actuation dynamics by employing the ideas of interconnected systems, and proposes a quadratic-programming-based integration of the control algorithms subject to the safety constraint for a class of fully actuated systems.

In this paper, the prescribed error trajectory control is proposed for second-order fully actuated systems. At first, by taking advantage of the full-actuation property, an intermediate control law is designed such that the intermediate closed-loop system is in a very simple form. Then, by utilizing the initial conditions of system states and the prescribed error performance function, the intermediate control law is developed to force the tracking error of the system on the proposed sliding mode surface from the beginning. The overall control law is obtained by combining the aforementioned steps. It is revealed that under the designed control law, the tracking error of the closed-loop system converges to zero along the prescribed error trajectory. Finally, an example is provided to validate the effectiveness of the presented approach.

For a class of second-order sub-fully actuated systems (SOSFASs), this paper presents a preset-trajectory-based (PT-based) adaptive stabilising control method by integrating the function augmented sliding mode control (FASMC) technique and the flat-zone introduced Lyapunov function technique. The SOSFASs under study are subject to internal uncertainties and external disturbances. The proposed PT-based stabilising control method exhibits several attractive features: 1) The system states can converge to a predefined region close to zero in a preassigned time and can be confined in a preassigned ‘safe’ area, which can make the control coefficient matrix always full rank so as to preserve the realizability of the proposed controller; 2) the utilization of flat-zone introduced Lyapunov function technique not only eliminates the chatting phenomenon, but also avoids the potential persistent increase problem of the adaptive law; and 3) the control gain increases as the adaptive law increases only when necessary, that is, when the current control gain is not sufficient to suppress uncertainties or disturbances, therefore, the conservativeness of the control design due to unnecessarily high control gain can be effectively reduced. The effectiveness of the proposed control method is verified via a numerical example.

The attitude of spherical liquid-filled spacecraft is controlled based on the high-order fully actuated system approaches. The rigid-fluid coupling dynamic equation can be established in terms of the Euler angles of the spacecraft and the angular velocities of the liquid fuel. According to the dynamic equation, three kinds of input selections are presented. In the case of one control input, the dynamic equation is transformed into the third-order or the second-order differential equations of the Euler angle by the high-order fully actuated system approaches. Then a control law is designed to track the target. The effectiveness of the control law is demonstrated by numerical simulations.

In this paper, a fully-actuated system approach (FASA) based control method is proposed for rigid spacecraft attitude tracking with actuator saturation. First, a second-order fully-actuated form of spacecraft attitude error model is established by modified Rodrigues parameters (MRPs). The unknown total disturbance caused by inertial uncertainty and external disturbance is estimated by using extended state observer, then an FASA based controller is developed. Further, a control parameterization method is adopted to optimize the parameter matrices of FASA based controller with the actuator saturation. Finally, a numerical example is carried out to validate the effectiveness of the proposed scheme.

It is well known that for a linear system in state space form, controllability is equivalent to arbitrary pole assignment by state feedback. This brief points out that for a scalar high-order fully actuated linear system, the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account, that is, controllability cannot guarantee arbitrary pole assignment by state feedback.