Command-filtered Backstepping Control Research Articles

Fuzzy wavelet neural adaptive finite-time self-triggered fault-tolerant control for a quadrotor unmanned aerial vehicle with scheduled performance

This paper focuses on fuzzy wavelet neural networks-based adaptive finite-time self-triggered fault-tolerant control design with assured tracking performance for a quadrotor unmanned aerial vehicle subject to unknown actuator faults. First, an improved finite-time performance function is integrated with the command-filtered backstepping control framework to assure the scheduled tracking performance, which can effectively constrain the transient fluctuations of the tracking error at fault occurrence. Then, two compensation mechanisms are developed to weaken the adverse impact induced by actuator faults and filter errors. Further, a fuzzy wavelet neural adaptive self-triggered fault-tolerant controller with guaranteed performance is designed to improve the fault insensitivity and tracking accuracy of the controlled vehicle, where the fuzzy wavelet neural networks are employed to approximate the unknown nonlinearities and the control signals are allowed to achieve irregular updating only when the pre-specified trigger protocol is violated. Stability analysis proves that the designed controller guarantees the attitude and position subsystems are practical finite-time stable, and the tracking errors are strictly confined to a preassigned region and never cross its allowed bounds. Finally, the validity of the developed control scheme is confirmed by the simulation results.

Rotation matrix-based finite-time trajectory tracking control of AUV with output constraints and input quantization

This study investigated a rotation-matrix-based finite-time trajectory tracking problem for autonomous underwater vehicles (AUVs) in the presence of output constraints, input quantization, and uncertainties. First, a rotation matrix-based attitude representation is introduced, which allow attitude dynamics to be globally and uniquely represented without unwinding. To satisfy the finite-time stability of AUV tracking control and the output constraints imposed by introducing the new attitude error vector, a novel finite-time command-filtered backstepping controller (FTCFBC) is proposed based on the asymmetrical time-varying barrier Lyapunov function (TVBLF). Subsequently, a second-order auxiliary dynamic system (ADS) is proposed to estimate the negative effects that of input quantization errors. Because the quantized control inputs can be switched at an appropriate earlier or later switching timing depending on the output of the ADS, the negative impact of quantization errors on the control accuracy is reduced. Moreover, an adaptive finite-time disturbance observer (AFTDO) is developed to estimate the lumped uncertainties without prior information on the bounds of the uncertainties. Finally, the results of the theoretical analysis verified that the tracking errors can converge within a finite time. Numerical simulations confirmed the effectiveness of the proposed control scheme.

Adaptive fuzzy extended state observer for a class of nonlinear systems with output constraint

Abstract In this study, an adaptive fuzzy extended state observer (AFESO) for single-input–single-output nonlinear affine systems in the presence of external disturbances and output constraints is proposed. In this regard, an extended state observer (ESO) was employed to estimate the unmeasured states and external disturbances simultaneously. To improve the estimation accuracy, the observer gains were adjusted using an adaptation law. To obtain a more comprehensive mathematical analysis and an accurate model for the ESO and to increase the degree of freedom, a Takagi–Sugeno fuzzy system was employed. The proposed AFESO relaxes the limitations of the ESO and improves the system performance as compared with the classical methods in the presence of time-varying disturbances. Next, a command-filtered backstepping controller is designed based on the barrier Lyapunov function method, which guarantees fast convergence of the tracking error as well as satisfying the output constraints of the system. The stability analysis showed that both the estimation error of the AFESO and the tracking error of the controller are bounded, and the tracking error converges to a small neighborhood of the origin. A simulating example of a flexible-joint manipulator shows the effectiveness of the proposed method as compared with the recently proposed method in the literature.

Practical finite-/fixed-time improved command-filtered backstepping control for nonlinear systems via immersion and invariance

This paper presents a practical finite-/fixed-time adaptive tracking control scheme based on improved command filtered backstepping (ICFBS) and immersion and invariance (I&I) for a class of single-input single-output (SISO) strict-feedback nonlinear systems with uncertainty parameterization. The conventional command-filtered backstepping method (CFBS) is improved by introducing any bounded function such that ICFBS relaxes the boundedness assumption of the control direction function and elevates the tunable space of the design scheme, with almost no increase in computational complexity. The higher-power composite term of a parameter estimation is designed in the parameter update law based on I&I and the inequality constructed by us proves that this form of the adaptive update law can be augmented to suit for not only uniform ultimate bounded (UUB) and practical finite-time stability but also practical fixed-time stability of the whole closed-loop system. The error compensation system is also extended to realize the practical finite-/fixed-time convergence of the error compensation signals. The proposed controller guarantees practical finite-/fixed-time stability of the closed-loop system. Therefore, our work solves two unsolved problems: both practical fixed-time and practical finite-/fixed-time ICFBS and I&I adaptive tracking control. Finally, the proposed control scheme is validated by a practical electromechanical system and a nonlinear system with unbounded control direction functions.

Disturbance Observer-Based Event-Triggered Adaptive Command Filtered Backstepping Control for Fractional-Order Nonlinear Systems and Its Application

This paper considers the disturbance observer-based event-triggered adaptive fuzzy tracking control issue for a class of fractional-order nonlinear systems (FONSs) with quantized signals and unknown disturbances. To improve the disturbance rejection ability, a fractional-order nonlinear disturbance observer (FONDO) is designed to estimate the unknown composite disturbances. Furthermore, by combining an improved fractional-order command-filtered backstepping control technique and an event-triggered control mechanism, an event-triggered adaptive fuzzy quantized control scheme is established, which guarantees the desired tracking performance can be achieved even in the presence of network constraint. Finally, the validity and superiority of the theoretic results are verified by a fractional-order horizontal platform system.

Command-Filtered Backstepping Repetitive Control for a Class of Uncertain Nonlinear Systems Based on Additive State Decomposition

This paper presents a command-filtered backstepping repetitive control (RC) method for a class of uncertain nonlinear systems with multiple disturbances, which is based on additive state decomposition (ASD) technique and active disturbance rejection approach. First, the original nonlinear system is decomposed into a linear time-invariant (LTI) primary system with periodic inputs and a nonlinear secondary system with multiple, aperiodic disturbances. The original nonlinear tracking problem is accordingly decomposed into two subproblems: RC problem for an LTI periodic system and a robust stabilization problem for a nonlinear system. By making using of the known information of the model, a linear extended state observer is constructed to estimate the matched total disturbance together with the system states and then a command-filtered backstepping control law incorporating with the estimate of the equivalent input disturbance is developed for the secondary system that ensures the robust stability and compensates for the effects of the multiple disturbances and residual nonlinearity. Stability criterion for each subsystem is established. Moreover, a particle-swarm-optimization algorithm is adopted to simultaneously optimize the controller parameters of the system. Finally, simulations and comparative experiments demonstrate the validity and superiorities of this method.

Finite-time command-filtered backstepping control for nonlinear systems with input delay and time-varying full-state constraints

This paper examines a finite-time command-filtered backstepping control proposed for a class of strict-feedback nonlinear systems with input delay and time-varying asymmetric full-state constraints. The existing control method either ignores the effect of input delay or converges asymptotically in infinite time. A command-filtered backstepping design is used to decrease computational burden. A first-order Levant differentiator is employed to replace the command filter for estimating the virtual control signals in finite time. The time-varying asymmetric barrier Lyapunov function (TVABLF) and command-filtered backstepping design are applied to alleviate the significant challenges caused by the backstepping approach and full-state constraints. A novel finite-time delay compensation mechanism is proposed to remove the impact of input delay. The closed-loop signals are proved to be practical bounded. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Finite-Time Distributed Attitude Synchronization for Multiple Spacecraft With Angular Velocity and Input Constraints

The attitude synchronization problem for multiple spacecraft with angular velocity and input constraints is investigated in this article, under the mild assumptions that the leader’s states can reach each follower through a path and the communications between followers are bidirectional. An adaptive finite-time distributed observer is designed to estimate the leader’s states for each follower spacecraft, which has the superiority in the fully distributed that the communication topology or some other global information is not required, and the finite-time convergence can be guaranteed. Furthermore, the novel auxiliary systems are first proposed to avoid the angular velocity and input constraints being violated, while the finite-time command filtered backstepping controller is designed to track the leader’s attitude motion. The remarkable features of the developed algorithm are the global finite-time attitude consensus of multiple spacecraft, with the constraints satisfied. Moreover, the efficiency of the proposed method is illustrated by numerical simulations and real-time platform verification.

Optimal Design and Command Filtered Backstepping Control of Exoskeleton With Series Elastic Actuator

Abstract The lower limb exoskeleton can improve mobility and safety during rehabilitation for human. However, most current exoskeleton systems are not capable of providing variable joint stiffness in response to changing external demands. In this paper, a knee exoskeleton based on the series elastic actuator (SEA) is designed for safe human-computer interaction. The structural dimensions of the exoskeleton actuation mechanism were optimized based on gait biomechanics to ensure stability and compactness. While maintaining the mechanism range of motion (ROM), this optimization ensures that less peak force is required during the gait cycle. However, the insertion of series elastic actuators inevitably brings new challenges for high precision control of the exoskeleton, such as the problems of modeling errors, compliance, friction, and external disturbances in the exoskeleton joint. To achieve high precision control of the exoskeleton, an extended disturbance observer (EDO) based command filtered backstepping control (CFBC) of the knee exoskeleton is developed. The effective observation of friction, external disturbances, and modeling errors in the system is obtained by the EDO. Compared with conventional backstepping control, the CFBC can not only solve the “explosion of complexity” problem through a command filter but also reduce filter errors by an error compensation mechanism. Based on the Lyapunov stability, all signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, comparison simulation results demonstrate the effectiveness of the proposed control approach.

Adaptive fuzzy command filtered backstepping control for uncertain pure-feedback systems

This paper considers tracking control of non-affine pure-feedback systems with uncertain disturbances; a new adaptive fuzzy command filtered backstepping controller is presented. First, the non-affine difficulty of pure-feedback systems is solved with the help of the mean-value theorem, and the fuzzy logic systems (FLSs) are adopted to estimate the system uncertainties which contain external disturbances. Next, a novel command-filtered technology is proposed to avoid the so-called “explosion of complexity” in the backstepping design process. The compensation mechanism is employed to eliminate the shortcoming of the traditional dynamic surface control. The presented control scheme ensures that all closed-loop signals are bounded, and the system output can track the given reference signal. The main contribution of this paper is that the developed approach is not only generalized to uncertain non-affine pure-feedback systems, which extends the practical applications of classical command filtered schemes, but also has an error compensation system, which improves tracking performance in comparison with existing dynamic surface control proposals. Finally, several simulation experiments validate the effectiveness and superiority of the proposed control scheme.

Command-Filtered Backstepping Control for a Class of Chaotic Systems

The problem of command-filtered backstepping control for a class of chaotic systems was studied in this paper. At each step of the backstepping design, a command filtering backstepping method is introduced to use a new virtual control signal, in which the derivative of the virtual control was approximated by using the output of filter. Then, the asymptotic stability conditions for synchronization errors are obtained by using the Lyapunov stability criterion and this control method. The design technique has the advantages of the conventional command-filtered backstepping control. An example shows the proposed method was feasible.

Adaptive fuzzy command filtering control for nonlinear MIMO systems with full state constraints and unknown control direction

In this paper, the command-filter-based adaptive control strategy is proposed for a class of unknown nonlinear multiple input multiple output (MIMO) systems with full state constraints and unknown control direction, whose unknown nonlinear function is approximated by the fuzzy logic system (FLS). First, the fuzzy logic system (FLS) act as the universal approximator of the unknown nonlinear function and the command-filtered backstepping control method is utilized to handle the difficulty induced by the explosion of differentiation, as well as the compensating signals are designed to make up for the command filter error. Besides, the appropriate barrier Lyapunov function and the Nussbaum-type functions are employed to deal with the constraints violation and the unknown direction control gains, respectively. It is proved that the practical tracking performance of the system can be achieved with the designed protocols and all signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, the simulation example is performed to verify the effectiveness of the proposed control strategy.

Fixed-time command-filtered backstepping control design for hydraulic turbine regulating systems

A novel practical fixed-time command-filtered backstepping strategy for a hydraulic turbine regulating system (HTRS) is developed in this paper. The developed controller is designed with the help of a combination of command-filtered backstepping and practical fixed-time stability theory. Based on this scheme, the obtained control strategy is utilized to ensure that the equilibrium point is practically fixed-time stable, and all signals of the closed-loop system are bounded within a fixed time. The main contributions of this paper are threefold: (i) The control scheme for frequency regulation of the HTRS is proposed to deal with the problem of the “explosion of terms” caused by conventional backstepping design. (ii) The proposed practical fixed-time control law can guarantee superior stabilization with a more precisely bounded convergence time, and (iii) The proposed controller performs well, simultaneously offers better transient performance, and overcomes three important drawbacks arising in the current results of fixed-time synergetic controllers. The strategy's effectiveness and feasibility are validated in a nonlinear model of the HTRS connected to a single-machine infinite bus power system. The numerical simulation indicates that the frequency regulation and improved transient performances in fixed time are achieved based on the proposed strategy. Further, the presented control reduces the oscillations rapidly and performs better than fixed-time synergetic control and modified fixed-time synergetic control approaches.

Decentralised adaptive tracking control for the interconnected nonlinear systems with asymmetric full state dynamic constraints

This paper studies the decentralised adaptive tracking control problem for the interconnected nonlinear systems with asymmetric full state dynamic constraints and input quantisation using dynamic event triggering mechanism. The broad learning system (BLS) is firstly utilised to identify the unstructured uncertainties, and a BLS-based nonlinear observer is established to estimate the unmeasurable states. Then, a unified barrier function (UBF) is constructed to address the asymmetric full state dynamic constraints. Next, both of command-filtered backstepping control technique and dynamic event triggering mechanism are adopted to design the control scheme in the asymmetric full state dynamic constraints case. The proposed control scheme could guarantee that all signals of the closed-loop systems are semi-globally ultimately uniformly bounded (SGUUB), the tracking errors converge to the bounded compact set and the full states dynamic constraints are not violated. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive neural tracking control for switched nonlinear systems with state quantization

In this study, an adaptive neural tracking control problem for uncertain switched nonlinear systems with state quantization under arbitrary switching is investigated. A command-filtered backstepping control design strategy is implemented to overcome the difficulty that the time derivate of common virtual control signals cannot be well defined. By deriving the closed-loop system quantized errors bounded, quantized states can be used to the control design and unquantized states can be applied to the stability analysis. And then, an adaptive neural tracking control approach for switched nonlinear systems with state quantization via common Lyapunov function is proposed, which guarantees that all the signals in the closed-loop system remain semiglobal uniform ultimate boundedness and the genuine output of system can well track the reference trajectory. Finally, the proposed method is demonstrated by two simulation results.

Adaptive Command-Filtered Fuzzy Nonsingular Terminal Sliding Mode Backstepping Control for Linear Induction Motor

This paper puts forward a projection-based adaptive command filtered fuzzy nonsingular terminal sliding mode backstepping (PACFTB) control method for the speed control of the linear induction motor (LIM) with unknown end effects. Firstly, the technique of fuzzy logic systems (FLS) is investigated to approximate the nonlinear components of the LIM’s mathematical model, which reduces the difficulty and cost of controller design. Then, a constrained command-filtered backstepping controller is designed with a filtering compensator compensating for the inherent error of constrained filter. Moreover, the nonsingular terminal sliding mode control method is combined in the controller design for its advantages of finite-time convergence of the system, and the projection-operator-based adaptive laws are established at the same time. Finally, the stability analysis proves that the boundedness and stability of all signals can be ensured with the proposed PACFTB controller, and the simulation results along with experiment results verify that the proposed control strategy has better control performance than the conventional command filter backstepping and PI controller.

Adaptive Fuzzy Finite-Time Command-Filtered Backstepping Control of Flexible-Joint Robots

SUMMARYThe problem of finite-time tracking control for n-link flexible-joint robot manipulators is addressed. An adaptive fuzzy finite-time command-filtered backstepping control scheme is presented to solve the following problems: “explosion of terms” problem, finite-time stabilization of the closed-loop system, and the reduction of computational cost. To this end, new virtual adaptive control signals and new finite-time error compensation mechanism are constructed using inherent properties of robot manipulator systems. Based on the Lyapunov theory, the finite-time stabilization of the closed-loop system is proved. Simulation studies show the effectiveness of the proposed method.

Novel anti-saturation robust controller for flexible air-breathing hypersonic vehicle with actuator constraints

A novel anti-saturation robust control algorithm (NARC) is presented for flexible air-breathing hypersonic vehicle (FAHV) with actuator saturation, including two controllers designed for velocity and height subsystem respectively. Firstly, an anti-saturation finite-time dynamic inversion controller is designed for velocity subsystem, in which an anti-saturation fixed-time compensator (ASFC) is proposed to ensure the stability of saturated system and make it exit saturated region faster. Compared with conventional anti-saturation compensator, the auxiliary variable of ASFC can converge with faster speed and higher precision when actuator is not saturated, which avoids the impact on original system. Secondly, an anti-saturation robust command filtered backstepping controller is designed for height subsystem, combining backstepping control, ASFC and a novel fixed-time filter (FTF). Compared with low pass filter, the FTF proposed can track input signal with faster response speed and higher precision without the need to select a smaller time constant, so as to avoid introducing high-frequency noise. Meanwhile, convergence domain of height subsystem can be reduced as well. Ultimately, simulations on FAHV with actuator constraints, parametric uncertainties and external disturbances are performed using the NARC and conventional anti-saturation controller respectively to demonstrate the superiority of NARC.

Path following of the autonomous airship with compensation of unknown wind and modeling uncertainties

The motion control of the airship has been an attractive topic in recent years. This paper investigates the problem of the path following of the autonomous airship. Due to the characteristics of the large volume, slow speed, and low-maneuverability, the airship is sensitive to the wind. Based on the design idea of the line-of-sight (LOS) guidance law, a parameter-observer-based LOS (POBLOS) guidance law is proposed. The unknown and time-varying influence from the wind is estimated by the parameter observer and then compensated in the design of the guidance loop. In order to overcome the disturbances of the modeling uncertainties and drift forces induced by the wind, the method of the command filtered backstepping control (CFBC) combined with the disturbance observer is employed in the control loop. The disturbance observer is constructed based on the formulation of the nonlinear disturbance observer (NDO) and improved by adding the status estimation error feedback, which results in a more robust performance when modeling uncertainties and time-varying disturbances exist. The stability analysis shows that the path following error is ultimately bounded. The results of the simulation indicate that the path following system has a good performance and is robust against the influence of the wind and modeling uncertainties.

Adaptive fuzzy sliding mode command-filtered backstepping control for islanded PV microgrid with energy storage system

This study focuses on the control of islanded photovoltaic (PV) microgrid and design of a controller for PV system. Because the system operates in islanded mode, the reference voltage and frequency of AC bus are provided by the energy storage system. We mainly designed the controller for PV system in this study, and the control objective is to control the DC bus voltage and output current of PV system. First, a mathematical model of the PV system was set up. In the design of PV system controller, command-filtered backstepping control method was used to construct the virtual controller, and the final controller was designed by using sliding mode control. Considering the uncertainty of circuit parameters in the mathematical model and the unmodeled part of PV system, we have integrated adaptive control in the controller to achieve the on-line identification of component parameters of PV system. Moreover, fuzzy control was used to approximate the unmodeled part of the system. In addition, the projection operator guarantees the boundedness of adaptive estimation. Finally, the control effect of designed controller was verified by MATLAB/Simulink software. By comparing with the control results of proportion-integral (PI) and other controllers, the advanced design of controller was verified.