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.     

Passivity-based resilient adaptive control for fuzzy stochastic delay systems with Markovian switching

The resilient adaptive controller design problem of a class of Itô-type Takagi–Sugeno (T–S) fuzzy stochastic systems with time-varying delay and Markovian switching is investigated. By utilizing improved matrix decoupling technique, passivity theory and stochastic Lyapunov–Krasovskii functional, LMIs-based sufficient conditions for the existence of resilient adaptive controller are provided such that the corresponding closed-loop system is almost surely asymptotically stable and robustly passive in the sense of expectation. The derived conditions can be easily solved with the help of LMI toolbox in Matlab. A simulation example is presented to illustrate the effectiveness of the proposed resilient adaptive control schemes.     

Barrier Lyapunov function based adaptive region tracking control for underwater vehicles with thruster saturation and dead zone

This paper proposes a new adaptive region tacking control scheme with nonlinear error transformation for underwater vehicles based on barrier Lyapunov functions. In the new scheme, a redefinition of the tracking error is given by introducing nonlinear error transformation in prescribed performance control. Although the results created by the new scheme indicate a slight decrease in the tracking precision, the real tracking error will be still kept within the prescribed performance functions, while the control signals also become smoother, compared with the original prescribed performance control scheme. Then an approximation form of the control input with constraints, together with an improved Nussbaum function, is designed to derive the control law for underwater vehicles with thruster saturation and dead zone. Furthermore, a new velocity error variable is given by introducing an auxiliary variable to compensate the effect from thruster saturation. Finally, it is proved that the nonlinear system is semi-global practical finite-time stable and the tracking error is always kept within the prescribed boundaries. The effectiveness of the proposed region tracking control scheme is validated through simulation-based case studies on an underwater vehicle with measurement noise.     

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.     

Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances

In this paper, a flatness-based adaptive sliding mode control strategy is presented to solve the trajectory tracking problem of a quadrotor. According to the differential flatness theory, the typical under-actuated quadrotor dynamics is transformed into a fully-actuated one. Based on this model, backstepping sliding mode controllers are designed to solve the trajectory tracking problem. To improve the robustness to disturbances, extended state observers are applied as a feedforward compensation of disturbances. Moreover, considering the high-order dynamics and possible instability caused by large observer gains, the adaptive method is applied to compensate for the estimation error. The effectiveness of the proposed control scheme is verified in simulations.     

Quantized adaptive tracking control for nonlinear systems with actuator backlash compensation

In this paper, the problem of adaptive tracking control is investigated for nonlinear systems with asymmetric actuator backlash. We assume that the nonlinearities of the systems are unknown and the external disturbances are bounded. First, the control input will be quantized by a hysteresis-type quantizer, which can reduce the communication rate of the control signal. Then, the asymmetric actuator backlash is approximated to a new model, and a novel adaptive controller with the quantizer is designed via an adaptive backstepping technique to guarantee all the signals of the closed-loop tracking error system are uniform ultimate boundedness. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.     

Distributed adaptive output-feedback tracking control of non-affine multi-agent systems with prescribed performance

This paper addresses the distributed adaptive output-feedback tracking control problem of uncertain multi-agent systems in non-affine pure-feedback form under a directed communication topology. Since the control input is implicit for each non-affine agent, we introduce an auxiliary first-order dynamics to circumvent the difficulty in control protocol design and avoid the algebraic loop problem in control inputs and the unknown control gain problem. A decentralized input-driven observer is applied to reconstruct state information of each agent, which makes the design and synthesis extremely simplified. Based on the dynamic surface control technique and neural network approximators, a distributed output-feedback control protocol with prescribed tracking performance is derived. Compared with the existing results, the restrictive assumptions on the partial derivative of non-affine functions are removed. Moreover, it is proved that the output tracking errors always stay in a prescribed performance bound. The simulation results are provided to demonstrate the effectiveness of the proposed method.     

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.     

Double-channel event-triggered adaptive tracking control of nonstrict-feedback nonlinear systems

This paper develops a novel way to control nonstrict-feedback nonlinear systems by using only one approximator, namely a neural network (NN) or a fuzzy logic system (FLS), in the first step of backstepping, such that the computational simplicity is ensured. The bounded property of basis functions solves the “algebraic loop” problem. The double-channel event-triggered control (ETC) is completed both in sensor-to-controller (SC) and controller-to-actuator (CA) channels, where the separate triggering conditions are fabricated. To solve the “jumps of virtual control laws (JVCL)” problem bedeviling the backstepping combined with ETC, this paper opens an avenue while guaranteeing the closed-loop stability with the aid of undetermined virtual control laws.     

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.     

Analyzing noise-induced tracking errors in control systems with saturation: A stochastic linearization approach

Noise Induced Tracking Error (NITE) refers to the tracking error of the mean of the output in feedback control systems with nonlinear instrumentation subject to zero-mean measurement noise. Most of the previous work rely on the stochastic averaging for NITE analysis, the validity of which requires that the bandwidth of the zero mean measurement noise is much higher than that of the system. This is because the results obtained by stochastic averaging are asymptotic with respect to the noise bandwidth. Due to the asymptotic nature of the analysis tool, it is not straightforward to provide a quantitative argument for high bandwidth. An alternative method in the literature that can analyze NITE is stochastic linearization for random input, which is analogous to the well known describing function approach for sinusoidal input. Unlike stochastic averaging, stochastic linearization is not an asymptotic approximation. Therefore, analysis can be carried out for any given noise bandwidth. We carry out NITE analysis using stochastic linearization for a class of LPNI systems that are prone to NITE; identify the system conditions under which the averaging analysis of NITE may yield inaccurate results for a finite noise bandwidth; and prove that the results from the two methods agree as the noise bandwidth approaches infinity. In addition, an existing NITE mitigation strategy is extended based on the proposed method. Numerical examples are given to illustrate the results.     

Distributed finite-time adaptive consensus tracking control for multiple AUVs with state constraints

Aiming at the consensus tracking control problem of multiple autonomous underwater vehicles (AUVs) with state constraints, a new neural network (NN) and barrier Lyapunov function based finite-time command filtered backstepping control scheme is proposed. The finite-time command filter is utilized to filtering the virtual control signal, the error compensation signal is constructed to eliminate filtering error due to the use of filter, and the NN approximation technology is used to deal with the unknown nonlinear dynamics. The control scheme can guarantee that the consensus tracking errors of position states converge into the desired neighborhood of the origin in finite-time while not exceeding the predefined constraints. Finally, simulation studies prove the feasibility of proposed control algorithm.     

Predefined performance adaptive control of robotic manipulators with dynamic uncertainties and input saturation constraints

In this paper, a novel adaptive control is investigated for robotic manipulators to unify the study of predefined performance control, input saturation and dynamic uncertainties. The focus is to achieve three user-defined performance indices of the closed-loop system with simultaneous existence of input constraints and model uncertainties, that is overshoot, precision within prescribed finite time and predefined steady-state error. To ensure the performance constraints, an error transformation is constructed for the manipulators by two auxiliary functions and embedded into the barrier Lyapunov function (BLF) in the backstepping analysis. Furthermore, the adaptive control strategies and the adaptive anti-saturation compensator are, respectively, developed to address the dynamics uncertainties and the actuator saturation. The Lyapunov analysis is employed to show that all the closed-loop signals are bounded. Finally, simulation studies and experiments on Baxter robot demonstrate the effectiveness of the proposed method.     

Asymptotic adaptive tracking control and application to mechatronic systems

This article develops an asymptotic tracking control strategy for uncertain nonlinear systems subject to additive disturbances and parametric uncertainties. To fulfill this work, an adaptive-gain disturbance observer (AGDO) is first designed to estimate additive disturbances and compensate them in a feedforward way, which eliminates the impact of additive disturbances on tracking performance. Meanwhile, an updated observer gain law driven by observer estimation errors is adopted in AGDO, which reduces the conservatism of observer gain selection and is beneficial to practical implementation. Also, the parametric uncertainties existing in systems are addressed via an integrated parametric adaptive law, which further decreases the learning burden of AGDO. Based on the parametric adaption technique and the proposed AGDO approach, a composite controller is employed. The stability analysis uncovers the system asymptotic tracking performance can be attained even when facing time-variant additive disturbances and parametric uncertainties. In the end, comparative experimental results of an actual mechatronic system driven by a dc motor uncover the validity of the developed approach.     

Prescribed performance tracking control of a free-flying flexible-joint space robot with disturbances under input saturation

Aiming at the trajectory tracking of a free-flying flexible-joint space robot (FFSR) with unknown time-varying disturbances and input saturation, we develop a robust control law with prescribed performance constraints via backstepping technique. A disturbance observer is employed to estimate the unknown time-varying disturbances and two auxiliary systems are introduced to handle input saturation. Moreover, we use the dynamic surface control (DSC) technique to deal with the complexity explosion caused by multiple derivatives of the virtual control signals. The performance function and transformation function are utilized to improve the tracking performance. It is proved that the designed control law can maintain the tracking error of the FFSR within a predefined region, while guaranteeing the uniform ultimate boundedness of all signals in the FFSR closed-loop control system. Finally, simulations are carried out to demonstrate the effectiveness of the developed prescribed performance tracking control.     

Precise robust motion tracking of a piezoactuated micropuncture mechanism with sliding mode control

This paper proposes a novel model-based control scheme to achieve the precise robust motion control of a piezoactuated micropuncture mechanism for cell injection. Using the Bouc–Wen model, the hysteretic dynamic model of the micropuncture mechanism is constructed, and its local optimization is conducted to facilitate engineering applications. On the basis of this model, a controller that synthesizes a fast nonsingular terminal sliding mode (FNTSM) control and time-delay estimation (TDE) is constructed. The control law for FNTSM has the advantages of continuous output, absence of chatter, and finite-time convergence of tracking error. The unknown quantity for TDE technology can be estimated and compensated online to reduce the FNTSM gain. Experiments on the micropuncture mechanism demonstrate that the developed control scheme provides smaller tracking error than the delay-control strategy based on the linear-error dynamic model or the model-free control scheme (e.g., Jin and Hsia’s controller). Micropuncture experiments on zebrafish embryo are successfully completed. Moreover, from the practical aspects, the control scheme developed herein can be effectively implemented in other types of micro-operation mechanisms driven by piezoelectric actuators.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.     

Global fuzzy adaptive asymptotic tracking control for nonlinear reaction-diffusion equations with time-varying coefficients

This study focuses on the research of the globally asymptotic tracking problem of unknown nonlinear reaction-diffusion equations with time-varying coefficients and uncertain external disturbance. Firstly, fuzzy logic systems and adaptive bounding technique are used to deal with nonlinear reaction-diffusion equations with time-varying coefficients and uncertain external disturbance. Secondly, a novel global state feedback adaptive fuzzy control algorithm is proposed to make the nonlinear reaction-diffusion equations track the target systems globally and asymptotically. In addition, the globally asymptotic tracking condition can be obtained, which overcomes the semi-global results in the existing literatures. Finally, three simulation examples are given to illustrate the feasibility and effectiveness of the proposed control protocols.     

Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs

This paper is concerned with the image-based visual servoing (IBVS) control for uncalibrated camera-robot system with unknown dead-zone constraint, where the uncertain kinematics and dynamics are also considered. The control implementation is achieved by constructing a smooth inverse model for dead-zone-input to eliminate the nonlinear effect resulting from the actuator constraint. A novel adaptive algorithm, which does not require a priori knowledge of the parameter intervals of dead-zone model, is proposed to update the parameter values online, and the dead-zone slopes are not required the same. Furthermore, to accommodate the uncertainties of uncalibrated camera-robot system, adaptation laws are developed to estimate the uncertain parameters, simultaneously avoiding singularity of the image Jacobian matrix. With the full consideration of unknown dead-zone constraint and system uncertainties, an adaptive robust visual tracking control scheme together with dead-zone compensation is subsequently established such that the image tracking error converges to the origin. Based on a 3-DOF manipulator, simulations are conducted to verify the tracking performance of the proposed controller.     

Optimal adaptive reset control with guaranteed transient and steady state tracking error bounds

In this paper, a solution for improvement of transient performance in adaptive control of nonlinear systems is proposed. An optimal adaptive controller based on a reset mechanism and a prescribed performance bound is devised. The suggested controller has the structure of adaptive backstepping controller in which the estimated parameters are reset to an optimal value. The designed controller ensures both the transient bound and the asymptotical convergence of the states. It is shown that the tracking error satisfies the prescribed performance bound all the time, besides the speed of the convergence rate is increased by resetting the estimated parameters. The results have been proved through both the analytical and simulation studies. The proposed method is applied to an Augmented Quarter Car Model as a case study. Simulation results verify the established theoretical consequences that the prescribed performance bound based optimal adaptive reset controller can enhance the transient performance of the adaptive controller.