Command Filtered Backstepping Technique Research Articles

Command filter‐based adaptive finite‐time control of fractional‐order nonlinear constrained systems with input saturation

AbstractIn this article, the command filter‐based finite‐time tracking control issue is explored for fractional‐order nonlinear constrained systems (FONCSs) with saturated input. Firstly, a novel fractional‐order Lyapunov stability lemma is put forward, thereby offering a reliable strategy for finite‐time convergence of FONCSs. By employing an improved error compensation system and introducing auxiliary signal, a new finite‐time command filtered backstepping technique is developed. The proposed control strategy guarantees the finite‐time convergence characteristic of filtering signals, in addition to alleviate the impacts produced by saturated input. After that, a modified nonlinear state‐dependent function (NSDF) is developed to solve the state constraint problem while fulfilling the concavity condition. In comparison to the existing constrained control techniques in FONCSs, this approach not only ensures finite‐time convergence of the tracking error but also gets rid of feasibility demands. Ultimately, two simulation scenarios are supplied to illustrate the feasibility and usefulness of the suggested strategy.

Observer-Based Adaptive Control for Trajectory Tracking of AUVs with Input Saturation

In this paper, an observer-based adaptive control method is investigated for the horizontal trajectory tracking of autonomous underwater vehicles (AUV) with input saturation and system disturbances. Firstly, the desired surge speed and trajectory angle are established, which could decouple the tracking error subsystem and avoid the complex form. Secondly, the input saturation is approximated by a smooth function, and a nonlinear extended states observer (NESO) is designed for estimating system disturbances. Based on the command filtered backstepping technique, which can avoid the explosion caused by the derivative of the virtual control, an observer-based adaptive output feedback control method is developed, and an auxiliary system is applied to compensate for filtered tracking errors, input saturation bias, and observer errors. Finally, simulation results show the proposed method has good robustness in the face of system uncertainties, and the error is nearly 33.3% smaller than that of other control methods when meeting sudden trajectory changes. A good control performance is guaranteed.

Finite-time output feedback trans-media tracking control of a slender body trans-media vehicle via neural network extended state observer

The emerging trans-media vehicle is significant due to its amphibious ability. A finite-time output feedback trans-media tracking control scheme is proposed for a slender body trans-media vehicle with unknown time-varying hydrodynamics and external disturbances. First, a novel neural network extended state observer is developed to observe the vehicle’s velocities and handle the time-varying hydrodynamics and total disturbances simultaneously. Then, combined with the proposed observer, the finite-time command filtered backstepping technique is carefully constructed to yield the finite-time output feedback tracking control. The strength of the proposed approach to the existing methods is that it ensures the trans-media tracking errors converge to the small region of origin within a finite time, even in the absence of velocity measurements. The simulations are given to illustrate the superiority of the proposed scheme.

Adaptive finite-time anti-disturbance fuzzy control for uncertain time-delay nonlinear systems and its application to SVC

The adaptive finite-time anti-disturbance fuzzy control method for n-dimensional uncertain nonlinear systems with input delay is proposed in this paper. For unknown nonlinear terms of the controlled system, the fuzzy logic systems (FLSs) are utilized to approximate them. To further improve the robustness of the controlled system, the disturbance observer is established to estimate external disturbances, facilitating the designed controller to compensate for the influence of external disturbances. Moreover, the Pade approximation method is used to transform the time-delay system model, which is convenient for controller design. With the aid of the finite-time command filtered backstepping technique, the adaptive finite-time disturbance rejection controller with low computational complexity is designed, which can compensate for the errors caused by the filters and assure that system state variables are stable and bounded in a finite time. In the end, the simulation for the single-machine infinite bus (SMIB) system with static var compensator (SVC) is presented to illustrate the effectiveness of the proposed control approach.

Distributed adaptive cooperative control via command filters for multi-agent systems including input unmodeled dynamics and sensor faults

This study focuses on the topic of distributed adaptive cooperative tracking control (CTC) for non-strict feedback multi-agent systems (MASs) including input unmodeled dynamics, prescribed performance, sensor faults and unknown control directions. An adaptive neural CTC tactic is raised via command filtered backstepping technique. With the help of the property of Gaussian function, the barriers produced by the non-strict feedback terms and partial sensor faults are handled. Moreover, the prescribed performance on measured synchronization error is considered by designing a finite-time performance function. By introducing normalization signals and adjusting parameters, the problems caused by input unmodeled dynamics are resolved. The compensation signals and normalization signals are integrated into the whole Lyapunov function in the stability analysis. All the variables in the controlled system are turned out to be semi-globally uniformly ultimately bounded (SGUUB). Meanwhile, the synchronization errors never exceed to predefined boundary. A simulation example is employed to confirm the viability of the constructed control method.

Event-based adaptive fuzzy tracking control for nonlinear systems with guaranteed performance

This article is concerned with the problem of event-based adaptive prescribed time tracking control for a class of uncertain strict-feedback nonlinear systems. To ensure that the considered system possesses the user-specified tracking performance, an improved error transformation is constructed and incorporated with a novel fixed-time performance function with an infinite initial value, completely removing the restriction that the tracking error is less than the pre-assigned performance boundary in the initial interval. Then, the utilization of command filtered technique and two single parameter estimators severally related to the upper bounds of fuzzy logic systems-based unknown constant parameters and external disturbances not only obviates the “explosion of complexity” issue but also simplifies the control design procedure. On this basis, by skillfully synthesizing adaptive technology and event-triggered mechanism within the framework of command filtered backstepping technique, a novel adaptive fuzzy event-triggered control solution is presented to save the limited network resources. Under the developed controller, the tracking error is steered to converge to an adjustable asymmetric region within a pre-specified time, and the boundedness of all closed-loop signals is ensured. Finally, simulation studies are performed to demonstrate the effectiveness and practicability of the developed control solution.

Path Following With Prescribed Performance for Under-Actuated Autonomous Underwater Vehicles Subjects to Unknown Actuator Dead-Zone

This paper investigates the problem of path following with prescribed performance for autonomous underwater vehicles subjects to unknown actuator dead-zone nonlinearity. To cope with this practical problem abstracted from hydrodynamic noise measurement, an adaptive command filtered backstepping method with actuator dead-zone compensation is proposed. By introducing a damped exponential barrier functions, new tracking errors are defined to satisfy the prescribed performance requirements. The path following control method is theoretically based on the command filtered backstepping technique for handling the complexity explosion problem attribute to the repeating derivations. Moreover, the filter compensation mechanism is designed to eliminate the negative effect of the filter errors. To deal with the actuator dead-zone nonlinearity, a fuzzy logic system based dead-zone compensation method is developed that dose not need the inverse of the dead-zones. Numerical simulations are conducted to demonstrate the theoretical analysis, and the usefulness and potential of the new design scheme is revealed.

Adaptive Finite-Time Command Filtered Controller Design for Nonlinear Systems With Output Constraints and Input Nonlinearities.

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

Event-based adaptive neural network asymptotic tracking control for a class of nonlinear systems

In this work, an event-triggered adaptive neural network asymptotic tracking control scheme is developed for non-lower-triangular nonlinear systems by using the command-filtered backstepping technique. To reduce the communication burden and unnecessary waste of communication resources, an event-triggered control signal based on a relative threshold is designed. In the design process, neural networks are used to approximate the nonlinear function existing in the system, and the upper bounds for the approximation error and the external disturbance together form an adaptive law with one parameter to achieve the asymptotic tracking performance. Additionally, the problem of “explosion of complexity” is avoided by utilizing the command-filtered technique in the backstepping framework. Based on the Lyapunov stability theory and Barbalat’s lemma, this developed scheme guarantees that the tracking error asymptotically converges to zero. At the end, two simulation examples are shown to verify the effectiveness of the control method.

Command-Filter-Based Fixed-Time Bipartite Containment Control for a Class of Stochastic Multiagent Systems

This article studies the command-filter-based fixed-time bipartite containment control problem for a class of nonlinear stochastic multiagent systems (MASs). The considered stochastic MASs in nonstrict feedback form is subject to unknown nonlinear functions and stochastic disturbances, which can be solved by exploiting the universal approximation property of radial basis function neural networks. In addition, the event-triggered mechanism is used to improve the utilization of communication resources while avoiding Zeno behavior. The control protocol based on the command-filtered backstepping technique is proposed to ensure that the followers can converge to the convex hull formed by the leaders. Moreover, the closed-loop stability of stochastic MASs is proved to be semiglobal practical fixed-time stability. Finally, a numerical example simulation and an actual system simulation about a group of five single-link manipulator systems are presented to verify the effectiveness of the proposed method.

Adaptive Finite-Time Consensus Tracking Control for Coopetition Flexible Joint Multi-Manipulators With Full-State Constraints

In this paper, the adaptive full-state constraints bipartite consensus tracking problem for coopetition flexible joint multi-manipulator systems with finite-time convergence is investigated. Based on the finite-time convergent method, the command filtered backstepping technique is introduced to ensure the excellent convergence performance without the influence of the repeated differential problem which is called explosion of complexity, and the error compensation mechanism is proposed to reduce the error caused by the filtering progress. Furthermore, by using the barrier Lyapunov functions, the state of the system and error compensation signals are proved to be constrained in their respective expected ranges. It is worth mentioning that the flexible joint multi manipulator system is in the mode of coopetition. Finally, the practicability of the proposed algorithm is exhibited in the simulation.

Adaptive resilient control design for nonlinear time‐delay systems against unknown state‐dependent deception attacks

AbstractThis article investigates the adaptive resilient control problem for a class of nonlinear time‐delay systems (TDSs) with unknown state‐dependent deception attacks. For the purpose of overcoming the issue of “explosion of complexity” existing in the traditional backstepping control design and improving filter performance, an improved fractional‐order command filtered backstepping technique is adopted to obtain the filtered signals of the virtual control laws. Furthermore, the corresponding auxiliary system and attack compensator are constructed to compensate the effects of input delay and unknown sensor deception attacks. Stability results prove that all the signals in the closed‐loop systems are semi‐globally uniformly ultimately bounded (SGUUB) by using the proposed adaptive resilient controller. Finally, two simulation examples are provided to show the effectiveness of the developed control method.

Command filtered finite-time control for nonlinear systems with state constraints and its application to TCP network

This work studies the issue of finite-time tracking control for a class of nonlinear systems with state constraints. By means of command filtered backstepping technique, finite-time theory and Barrier Lyapunov Functions (BLF), a novel finite-time command filtered backstepping approach is presented to guarantee the finite-time convergence of tracking errors. The new proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors by Dynamic Surface Control (DSC), but also can guarantee that the state variables are restricted in compact bounding sets. Moreover, the proposed controller is designed and applied to Transmission Control Protocol/Active Queue Management (TCP/AQM) network systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a TCP network simulation example.

Event-Triggered Adaptive Practical Fixed-Time Trajectory Tracking Control for Unmanned Surface Vehicle

This brief investigates the fixed-time trajectory tracking control problem for unmanned surface vehicle with unknown dynamics based on command filtered backstepping technique and fixed-time stability theory. Distinct from the existing results where the control execution is periodic and the computational burden is overlarge, a novel event-triggered adaptive practical fixed-time fuzzy controller is designed to guarantee the fixed-time stability of the closed-loop system (CLS), where the controller is aperiodically updated only at the event-sampled instants. Theoretical analysis proves that the tracking errors can diminish to an arbitrarily small neighborhood of the origin within a fixed time interval and the prescribed convergence time is free of the initial states of the surface vehicle under the proposed control method. Finally, the simulation results are provided to demonstrate the validity of the developed control approach.

Distributed Adaptive Neural Consensus Tracking Control for Multiple Euler-Lagrange Systems with Unknown Control Directions

This paper investigates the distributed adaptive neural consensus tracking control for multiple Euler-Lagrange systems with parameter uncertainties and unknown control directions. Motivated by the Nussbaum-type function and command-filtered backstepping technique, the error compensations and neural network approximation-based adaptive laws are established, which can not only overcome the computation complexity problem of backstepping but also make the consensus tracking errors reach to the desired region although the control directions and system nonlinear dynamics are both unknown. Numerical example is given to show the proposed algorithm is effective at last.

Quantized feedback adaptive command filtered backstepping control for a class of uncertain nonlinear strict-feedback systems

An adaptive command filtered backstepping control design strategy in the presence of quantized states is presented for uncertain nonlinear systems in the strict-feedback form. A uniform quantizer quantizes all state variables, and the quantized state variables are only available for feedback. The existing quantized feedback recursive control design is only applicable to systems with nonlinearities matched to the control input because of its restriction that the partial derivatives of the virtual control laws with respect to state variables should be constants. Compared with the existing result, the primary contribution of this paper is to develop a quantized feedback recursive design using the command filtered backstepping technique for dealing with unmatched nonlinearities without this restriction. An adaptive tracking scheme using quantized states is constructed to compensate for quantization effects, and a new stability analysis strategy is established by analyzing the boundedness of the quantization errors of signals in the command filtered backstepping design framework. The stability of the closed-loop system is analyzed in the sense of uniform ultimate boundedness.

UDE-Based Robust Command Filtered Backstepping Control for Close Formation Flight

This paper presents an uncertainty and disturbance estimator (UDE)-based nonlinear robust controller for close formation flight in light of the command filtered backstepping technique. To maximize the formation aerodynamic benefits at different flight maneuvers, the formation geometry is described in the wind frame of the leader aircraft. A novel nonlinear robust close formation control algorithm with a two-degree-of-freedom nature is developed. The command filtered backstepping technique is employed to design the baseline formation controller, whereas the UDE is introduced to enhance the robustness of the baseline formation control. The proposed control law can lead to desired tracking performance for the close formation flight under different maneuvers without using the acceleration information of the leader aircraft, asymptotical stability for the close formation flight at a level and straight flight with constant speeds, and enough robustness against the formation aerodynamic effects by purely observing system states and inputs. Numerical simulations are performed to show the feasibility and efficiency of the proposed controller.

Adaptive Neural Consensus Tracking for Nonlinear Multiagent Systems Using Finite-Time Command Filtered Backstepping

This paper is concerned with the finite-time consensus tracking control problems of uncertain nonlinear multiagent systems. A neural network-based distributed adaptive finite-time control scheme is developed, which can guarantee the consensus tracking is achieved in finite time with sufficient accuracy in the presence of unknown mismatched nonlinear dynamics. Such a finite-time feature is achieved by the modified command filtered backstepping technique based on the high-order sliding mode differentiator. Moreover, the proposed control scheme is completely distributed, since the control laws only use the local information. In addition, although mismatched uncertainty nonlinear dynamics are considered, only one parameter needs to be updated for each agent in the control scheme, which will simply the computations and make the proposed scheme more effective for applications. An example is included to verify the presented method.

Distributed zero-sum differential game for multi-agent systems in strict-feedback form with input saturation and output constraint

This paper investigates the distributed differential game tracking problem for nonlinear multi-agent systems with output constraint under a fixed directed graph. Each follower can be taken as strict-feedback structure with uncertain nonlinearities and input saturation. Firstly, by utilizing the command filtered backstepping technique, the distributed tracking control problem of multi-agent systems in strict-feedback form can be transformed into an equivalent distributed differential game problem of tracking error dynamics in affine form by designing a distributed feedforward tracking controller, in which neural networks (NNs) and the auxiliary system are introduced to deal with the unknown nonlinearities and input saturation, respectively. Especially, a novel barrier Lyapunov function (BLF) is firstly introduced to tackle with the output constraint. Subsequently, by using adaptive dynamic programming (ADP) technique, the distributed zero-sum differential game strategy is derived, in which a critic network is constructed to approximate the cooperative cost function online with a novel updating law. Therefore, the whole distributed control scheme not only guarantees the closed-loop signals to be cooperatively uniformly ultimately bounded (CUUB), but also ensures the cooperative cost function to be minimized. Meanwhile, the output constraint and input saturation are not violated. Finally, simulation results demonstrate the effectiveness of the proposed method.

Tracking-Error-Based Universal Adaptive Fuzzy Control for Output Tracking of Nonlinear Systems with Completely Unknown Dynamics

In this paper, an universal adaptive fuzzy control (UAFC) scheme using output tracking error is proposed for practical tracking control of a class of nonlinear systems with unmeasured states and completely unknown perturbed dynamics including unknown dynamics and/or external disturbances. A tracking error system with measurable output is first derived from the output tracking problem, and unmeasured states are observed by an universal fuzzy state observer (UFSO), whereby adaptive fuzzy approximators and an universal adaptive gain are employed to estimate unknown dynamics and dominant unknown residuals, respectively. In conjunction with the rescaled UFSO and observation errors, the UAFC using output tracking error feedback is explicitly constructed, in a recursive manner, by employing the command filtered backstepping technique, whereby intermediate virtual signals and their first derivatives associated with complex dynamics can be reconstructed by second-order filters. Furthermore, adaptive mechanisms for fuzzy approximators and the universal gain pertaining to the UFSO and UAFC are derived from the Lyapunov synthesis. Theoretical analysis proves that all signals of the closed-loop system are bounded and the output tracking error and observation error can converge to an arbitrarily small region determined by a prescribed accuracy. Simulation results demonstrate the effectiveness and superiority of the proposed UAFC scheme.