Super twisting control of a parametrically excited overhead crane

The principal contribution of this note is to avoid the parametric resonance effect and attenuate the payload oscillations in an overhead-crane system subject to periodic variations in the base support. Considering an appropriate sliding output with relative degree one, we present the sliding mode control design based on the Super-Twisting Algorithm (STA), ensuring finite time convergence to the desired sliding surface for the linear periodic system with Lipschitz continuous matched and unmatched uncertainties bounded together by their gradients by known functions. The suggested approach also provides chattering phenomenon attenuation. Obtained results are verified experimentally.     

Attitude tracking control of a quadrotor UAV in the exponential coordinates

A new approach to control the attitude of a quadrotor UAV in terms of the exponential coordinates is developed in this paper. The exponential coordinate is a minimal representation of the rotation matrix, but it can avoid singularities. Since the quadrotor UAV can be considered as a rigid body aircraft, the analytic closed-form expressions of a rigid body's attitude kinematics are derived from differential of exponential on SO(3). Furthermore, based on the exponential expressions of attitude kinematics, the controller of a fully actuated rigid body is designed using trajectory linearization control method. The overall attitude controller contains two loops, which are designed according to the torque equation and the angular velocity equation respectively. In the numerical simulation, the proposed attitude controller is compared to a controller in the Euler angles, showing that singularities induced by Euler angles are avoided by using exponential coordinates. The robustness test of the attitude controller is also demonstrated in the simulation. The simulation results indicate that the proposed method can be applied to the attitude tracking control of an aerial robot especially when the robot needs to make aggressive maneuverings.     

Robust homography-based visual servo control for a quadrotor UAV tracking a moving target

In this study, a new robust homography-based visual tracking control approach for the quadrotor unmanned aerial vehicle (UAV) is developed. Specifically, employing the homography matrix as feedback, a hierarchical homography-based visual servoing (HBVS) scheme with a new command attitude extraction method to account for the underactuation of UAV is proposed. On this basis, a smooth hyperbolic tangent function is fulfilled as an augmented part of the backstepping control scheme, which guarantees the non-negative total thrust and avoid singularity. Additionally, a cascaded filter-based estimator and adaptive laws with integrable functions are embedded to counteract uncertainties including external perturbations, unknown acceleration of the moving target, and unknown image depth, and to facilitate the system’s asymptotic stability simultaneously. The theoretical analysis testifies that the whole close-loop system is asymptotically stable. Simulations further verify that the proposed HBVS controller can realize the visual tracking with a superior performance.     

Robust output feedback attitude tracking control for rigid-flexible coupling spacecraft

This paper investigates the robust attitude tracking control problem for a rigid-flexible coupling spacecraft. First, the dynamic model for a rigid-flexible coupling spacecraft is established based on the first-order approximation method to fully reveal the coupling effect between rigid movement and flexible displacement when the spacecraft is in rapid maneuver. In the condition that flexible vibration measurements are not available, an robust output feedback controller which is independent of model is presented using Lyapunov method with considering state-independent disturbances. To resolve the chattering problem caused by the discontinuous sign function, a modified continuous output feedback controller is proposed by introducing functions with continuous property. Rigorous proof is achieved showing that the proposed control law ensures asymptotic stability and guarantees the attitude of a rigid-flexible spacecraft to track a time-varying reference attitude based on angle and angular velocity measurements only. Finally, simulations are carried out to verify the simplicity and effectiveness of the proposed control scheme.     

Barrier function-based prescribed-performance adaptive attitude tracking control for spacecraft with uncertainties

This paper addresses the problem of robust adaptive attitude tracking control for spacecraft with mismatched and matched uncertainties. The idea of disturbance estimation and compensation is introduced into the control design. First, finite-time disturbance observers are developed for different channels of spacecraft based on barrier functions for achieving finite-time asymptotic estimates of unknown bounded uncertainties in the system. Second, a class of prescribed performance functions is considered in the design of the barrier function. The spacecraft attitude adaptive tracking control strategy with finite-time convergence capability and prescribed performance is proposed based on the designed finite-time disturbance observers and barrier function. Finally, the theoretical findings are verified by numerical simulations and compared with the simulation results of existing methods.     

Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping

In this paper, the trajectory tracking control problem of a six-degree of freedom (6-DOF) quadrotor unmanned aerial vehicle (UAV) with input saturation is studied. Applying a hierarchical control structure, a priori-bounded control thrust and the desired orientations are derived to stabilize the translational subsystem without singularities. By using a backstepping approach with a Nussbaum function, a priori-bounded control torque for the rotational subsystem is designed to track the desired orientations generated by the translational subsystem. With the proposed control scheme, the latent singularities in the attitude extraction process caused by saturation nonlinearities are avoided, and globally uniformly ultimately bounded (UUB) stability of the closed-loop system is achieved. The tracking error bound is further determined which can be made arbitrarily small by tuning certain control gains. Numerical simulation results are provided to show the effectiveness of the proposed control scheme.     

An adaptive fast super-twisting disturbance observer-based dual closed-loop attitude control with fixed-time convergence for UAV

In this paper, a fixed-time dual closed-loop attitude control method is investigated for a quadrotor unmanned aerial vehicle. Firstly, a fixed-time adaptive fast super-twisting disturbance observer is presented for estimating the unknown external disturbance. A modified adaptive law is employed based on an equivalent control method to obtain proper observer gains. Secondly, a fixed-time controller is designed by using a universal barrier Lyapunov function to satisfy asymmetric tracking error constraints. Then, a tracking differentiator is utilised to arrange the transition process. Finally, the implementation of the developed method in a quadrotor unmanned aerial vehicle is performed. Through stability analysis and simulation results, the effectiveness and superiority of the proposed fixed-time control method are validated.     

On novel trajectory tracking control of quadrotor UAV: A finite-time guaranteed performance approach

In this work, aiming at the trajectory tracking control of the quadrotor UAV subject to external disturbances and model uncertainties, a finite-time approach with preassigned performance guaranteed is proposed. First, the control system is decoupled into translational and rotational subsystems. Then, in both two subsystems, the performance bounds constructed by the newly established appointed-time performance functions are devised for guaranteeing the tracking performance, and the controllers are designed via applying the dynamic surface control technique with integral barrier Lyapunov functions involved. Moreover, finite-time tracking differentiators and finite-time multivariable disturbance observers are exploited to estimate the target signals and the lumped disturbances, respectively. Finally, two examples of simulation are carried out to validate the effectiveness and superiority of the proposed control method.     

Barrier Lyapunov function-based adaptive fuzzy attitude tracking control for rigid satellite with input delay and output constraint

This paper investigates the adaptive attitude tracking problem for the rigid satellite involving output constraint, input saturation, input time delay, and external disturbance by integrating barrier Lyapunov function (BLF) and prescribed performance control (PPC). In contrast to the existing approaches, the input delay is addressed by Pade approximation, and the actual control input concerning saturation is obtained by utilizing an auxiliary variable that simplifies the controller design with respect to mean value methods or Nussbaum function-based strategies. Due to the implementation of the BLF control, together with an interval notion-based PPC strategy, not only the system output but also the transformed error produced by PPC are constrained. An adaptive fuzzy controller is then constructed and the predesigned constraints for system output and the transformed error will not be violated. In addition, a smooth switch term is imported into the controller such that the finite time convergence for all error variables is guaranteed for a certain case while the singularity problem is avoided. Finally, simulations are provided to show the effectiveness and potential of the proposed new design techniques.     

Fault tolerant flight control system for the tilt-rotor UAV

A fault tolerant control scheme for actuator and sensor faults is proposed for a tilt-rotor unmanned aerial vehicle (UAV) system. The tilt-rotor UAV has a vertically take-off and landing (VTOL) capability like a helicopter during the take-off & landing while it could cruise with a high speed as a conventional airplane flight mode. A dual system in the flight control computer (FCC) and the sensor is proposed in this study. To achieve a high reliability, a fault tolerant flight control system is required for the case of actuator or sensor fault. For the actuator fault, the fault tolerant control scheme based on model error control synthesis is presented. A designed fault tolerant control scheme does not require system identification process and it provides an effective reconfigurability without fault detection and isolation (FDI) process. For the sensor fault, the fault tolerant federated Kalman filter is designed for the tilt-rotor UAV system. An FDI algorithm is applied to the federated Kalman filter in order to improve the accuracy of the state estimation even when the sensor fails. For a linearized six-degree-of-freedom linear model and nonlinear model of the tilt-rotor UAV, numerical simulation and process-in-the-loop simulation (PILS) are performed to demonstrate the performance of the proposed fault tolerant control scheme.     

Fault-tolerant control for the linearized spacecraft attitude control system with Markovian switching

In this article, the fault-tolerant control is investigated for the spacecraft attitude control system described by a linearized model with Markovian switching. First, the evolution of sudden failures of the spacecraft’s actuators is described by a Markov process. Then, the mathematical model of the spacecraft attitude control system with the Markov jump characteristic fault is established. Taking the uncertainty of the system model and external interference into consideration, a fault-tolerant control scheme is proposed for the established spacecraft attitude control system with the Markov jump characteristic fault by using the sliding mode control technique. Compared with some existing sliding mode controller design methods, the proposed method requires a less total number of LMIs to be solved. The stability and reachability of the resulting closed-loop system under the presented sliding mode control scheme are proven by applying the Lyapunov stability theory. Finally, some simulation results are provided to show the effectiveness and advantages of the proposed control method for spacecraft attitude control.     

Control Lyapunov function optimal sliding mode controllers for attitude tracking of spacecraft

The attitude tracking control problem for a rigid spacecraft using two optimal sliding mode control laws is addressed. Integral sliding mode (ISM) control is applied to combine the first-order sliding mode with optimal control and is applied to quaternion-based spacecraft attitude tracking maneuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the control Lyapunov function (CLF) approach is used to solve the infinite-time nonlinear optimal control problem, whereas the Lyapunov optimizing control (LOC) method is applied to solve the finite-time nonlinear optimal control problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking maneuvres is presented and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

Event-triggered backstepping control for attitude stabilization of spacecraft

To decrease the communication frequency between the controller and the actuator, this paper addresses the spacecraft attitude control problem by adopting the event-triggered strategy. First of all, a backstepping-based inverse optimal attitude control law is proposed, where both the virtual control law and the actual control law are respectively optimal with respect to certain cost functionals. Then, an event-triggered scheme is proposed to realize the obtained inverse optimal attitude control law. By designing the event triggering mechanism elaborately, it is guaranteed that the trivial solution of the closed-loop system is globally exponentially stable and there is no Zeno phenomenon in the closed-loop system. Further, the obtained event-triggered attitude control law is modified and extended to the more general case when the disturbance torque cannot be ignored. It is proved that all states of the closed-loop system are bounded, the attitude error can be made arbitrarily small ultimately by choosing appropriate design parameters and the Zeno phenomenon is excluded in the closed-loop system. In the proposed event-triggered attitude control approaches, the control signal transmitted from the controller to the actuator is only updated at the triggered time instant when the accumulated error exceeds the threshold defined elaborately. Simulation results show that by using the proposed event-triggered attitude control approach, the communication burden can be significantly reduced compared with the traditional spacecraft control schemes realized in the time-triggered way.     

Sliding mode attitude tracking of rigid spacecraft with disturbances

The attitude tracking control problem of a spacecraft nonlinear model with external disturbances and inertia uncertainties is addressed in this paper. First, a new sliding mode controller is designed to ensure the asymptotic convergence of the attitude and angular velocity tracking errors against external disturbances and inertia uncertainties by using a modified differentiator to estimate the total disturbances. Second, an adaptive algorithm is applied to compensating the disturbances, by which another sliding mode controller is successfully designed to achieve a high performance on the attitude tracking in the presence of the inertia uncertainties, external disturbances and actuator saturations. Finally, simulation results are presented to illustrate effectiveness of the control strategies.     

Probability-constrained tracking control for a class of time-varying nonlinear stochastic systems

This paper is concerned with the probability-constrained tracking control problem for a class of time-varying systems with stochastic nonlinearities, stochastic noises and successively packet loss. The main purpose of this paper is to design a time-varying observer and tracking controller such that (1) the probabilities of both the estimation error and tracking error confined to given ellipsoidal sets are larger than prescribed constants, and (2) the ellipsoids are minimized in the sense of matrix norm at each time point. By using a stochastic analysis method, the probability constrained tracking control problem is solved and sufficient conditions are obtained in terms of recursive linear matrix inequalities. A recursive optimization algorithm is developed to design the observer and tracking controller such that not only the addressed probability constrained aim is satisfied, but also the ellipsoidal sets are minimized. At last, a simulation example is given to illustrate the effectiveness and applicability of the developed approach.     

Online adaptive policy iteration based fault-tolerant control algorithm for continuous-time nonlinear tracking systems with actuator failures

In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.     

Fuzzy-logic adaptive variable structure multiple-model algorithm for tracking a high maneuvering target

The conventional interacting multiple model (IMM) algorithm will increase the computational load when applying a large number of models, meanwhile, it cannot yield accurate estimation results with a small number of models. Furthermore, the unknown target acceleration is regarded as an additional process noise to the target model, and its time-varying variance is hard to be approximated. The paper proposes a fuzzy-logic adaptive variable structure multiple model (FAVSMM) algorithm for tracking a high maneuvering target. The algorithm can optimize the model parameters using the model probability and construct an optimal model set quickly, and the fuzzy-logic IMM algorithm included in the FAVSMM algorithm is adopted for states estimation. The simulation results show that the proposed algorithm can match well with the actual target trajectory with less computational complexity and better accuracy.     

Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle

This paper is concerned with the adaptive sliding mode control (ASMC) design problem for a flexible air-breathing hypersonic vehicle (FAHV). This problem is challenging because of the inherent couplings between the propulsion system, the airframe dynamics and the presence of strong flexibility effects. Due to the enormous complexity of the vehicle dynamics, only the longitudinal model is adopted for control design in the present paper. A linearized model is established around a trim point for a nonlinear, dynamically coupled simulation model of the FAHV, then a reference model is designed and a tracking error model is proposed with the aim of the ASMC problem. There exist the parameter uncertainties and external disturbance in the model, which are not necessary to satisfy the so-called matched condition. A robust sliding surface is designed, and then an adaptive sliding mode controller is designed based on the tracking error model. The proposed controller can drive the error dynamics onto the predefined sliding surface in a finite time, and guarantees the property of asymptotical stability without the information of upper bound of uncertainties as well as perturbations. Finally, simulations are given to show the effectiveness of the proposed control methods.