Robust fixed-time flight controller for a dual-system convertible UAV in the cruise mode

This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle(UAV)in the presence of parameter uncertainties,unmodeled uncertainties and wind disturbances.First,a fixed-time disturbance observer(FXDO)based on the bi-limit homogeneity theory is designed to estimate the lumped disturbance of the convertible UAV model.Then,a fixed-time integral sliding mode control(FXISMC)is combined with the FXDO to achieve strong robustness and chattering reduction.Bi-limit homogeneity theory and Lyapunov theory are applied to provide detailed proof of the fixed-time stability.Finally,numerical simulation experimental results verify the robustness of the proposed algorithm to model parameter uncertainties and wind disturbances.In addition,the proposed algorithm is deployed in a open-source UAV autopilot and its effectiveness is further demonstrated by hardware-in-the-loop experimental results.

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.

Fixed-Time Sliding Mode Control With Varying Exponent Coefficient for Modular Reconfigurable Flight Arrays

The modular system can change its physical structure by self-assembly and self-disassembly between modules to dynamically adapt to task and environmental requirements. Recognizing the adaptive capability of modular systems, we introduce a modular reconfigurable flight array(MRFA) to pursue a multifunction aircraft fitting for diverse tasks and requirements,and investigate the attitude control and the control allocation problem by using the modular reconfigurable flight array as a platform. First, considering the variable and irregular topological configuration of the modular array, a center-of-mass-independent flight array dynamics model is proposed to allow control allocation under over-actuated situations. Secondly, in order to meet the stable, fast and accurate attitude tracking performance of the MRFA, a fixed-time convergent sliding mode controller with state-dependent variable exponent coefficients is proposed to ensure fast convergence rate both away from and near the system equilibrium point without encountering the singularity. It is shown that the controller also has fixed-time convergent characteristics even in the presence of external disturbances. Finally,simulation results are provided to demonstrate the effectiveness of the proposed modeling and control strategies.

Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems

The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information.This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented.

Fixed-Time Output Consensus Tracking for High-Order Multi-Agent Systems With Directed Network Topology and Packet Dropout

This paper studies the problem of fixed-time output consensus tracking for high-order multi-agent systems(MASs)with directed network topology with consideration of data packet dropout.First,a predictive compensation based distributed observer is presented to compensate for packet dropout and estimate the leader’s states.Next,stability analysis is conducted to prove fixed time convergence of the developed distributed observer.Then,adaptive fixed-time dynamic surface control is designed to counteract mismatched disturbances introduced by observation error,and stabilize the tracking error system within a fixed time,which overcomes explosion of complexity problem and singularity problem.Finally,simulation results are provided to verify the effectiveness and superiority of the consensus tracking strategy proposed.The contribution of this paper is to provide a fixed-time distributed observer design method for high-order MAS under directed graph subject to packet dropout,and a novel fixed-time control strategy which can handle mismatched disturbances and overcome explosion of complexity and singularity problem.

Adaptive Fixed-Time Control of Nonlinear MASs With Actuator Faults

The adaptive fixed-time consensus problem for a class of nonlinear multi-agent systems(MASs)with actuator faults is considered in this paper.To approximate the unknown nonlinear functions in MASs,radial basis function neural networks are used.In addition,the first order sliding mode differentiator is utilized to solve the“explosion of complexity”problem,and a filter error compensation method is proposed to ensure the convergence of filter error in fixed time.With the help of the Nussbaum function,the actuator failure compensation mechanism is constructed.By designing the adaptive fixed-time controller,all signals in MASs are bounded,and the consensus errors between the leader and all followers converge to a small area of origin.Finally,the effectiveness of the proposed control method is verified by simulation examples.

Command Filtered Finite/Fixed-time Heading Tracking Control of Surface Vehicles

This paper investigates the heading tracking problem of surface vehicles with unknown model parameters.Based on finite/fixed-time control theories and in the context of command filtered control,two novel adaptive control laws are developed by which the vehicle can track the desired heading within settling time with all signals of the closed-loop system are uniformly bounded.The effectiveness and performance of the schemes are demonstrated by simulations and comparison studies.

Dynamic Event-Triggered Fixed-Time Consensus Control and Its Applications to Magnetic Map Construction

This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.

Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems

This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.

Fixed-time Consensus for Leader-follower Second-order Multi-agent Systems

We analyse the fixed-time consensus problem for multi-agent systems with leaderfollower mode. Based on a follower’s observation structure for the leader’s information, it is proved that the estimation errors can be converged to zero at a fixed time. From this stability and a sliding mode structure, we derive a control input of followers, which provides a critical support for fixed-time consensus. The simulation results demonstrate that this control approach does conduce to the implementation of the fixed-time synchronization.

Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller

This paper studies the fixed-time output-feedback control for a class of linear systems subject to matched uncertainties.To estimate the uncertainties and system states,we design a composite observer which consists of a high-order sliding mode observer and a Luenberger observer.Then,a robust output-feedback controller with fixed-time convergence guarantee is constructed.Rigorous theoretical proof shows that with the proposed controller,the system states can converge to zero in fixed-time free of the initial conditions.Finally,simulation comparison with existing algorithms is given.Simulation results verify the effectiveness of the proposed controller in terms of its fixed-time convergence and perfect disturbance rejection.

Observer-based multivariable fixed-time formation control of mobile robots

This paper proposes a multivariable fixed-time leaderfollower formation control method for a group of nonholonomic mobile robots, which has the ability to estimate multiple uncertainties. Firstly, based on the state space model of the leader-follower formation, a multivariable fixed-time formation kinematics controller is designed. Secondly, to overcome uncertainties existing in the nonholonomic mobile robot system, such as load change,friction, external disturbance, a multivariable fixed-time torque controller based on the fixed-time disturbance observer at the dynamic level is designed. The designed torque controller is cascaded with the formation controller and finally realizes accurate estimation of the uncertain part of the system, the follower tracking of reference velocity and the desired formation of the leader and the follower in a fixed-time. The fixed-time upper bound is completely determined by the controller parameters, which is independent of the initial state of the system. The multivariable fixed-time control theory and the Lyapunov method are adopted to ensure the system stability.Finally, the effectiveness of the proposed algorithm is verified by the experimental simulation.

A Sample of Semi-Actuated Traffic Control versus Fixed-Time Traffic Control

Fixed-time control of traffic signals pursues the regulation of phases based on historical data of traffic demand, in this way, neglecting of the random arrival rates of traffic flow on different intersection streams causes increasing of the stops and delays and fuel consumption at the same time. Coordinated semi-actuated control due to ability to respond traffic demands on both main and secondary directions, based on road detector registration saves the coordinated features, serving the unused time to the main road, while the secondary clears early. In this paper, the authors analyzed and explained comparatively the results of LOS （level of service） parameters of the current state of control （fixed-time） with the proposed control （semi-actuated coordinated） of the artery of length 2,348 km consisted of four signalized T intersections. Highway Capacity Manual and Synchro/Sim Traffic software are used for analysis and optimization of parameters in this paper.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated.For cooperative-competitive network,two different control protocols,fixed-time group consensus and fixed-time eventtriggered group consensus,are designed.It is demonstrated that there is no Zeno behavior under the designed eventtriggered control.Meanwhile,it is proved that for an arbitrary initial state of the system,group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory.Finally,a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.

A Review on Sources,Extractions and Analysis Methods of a Sustainable Biomaterial:Tannins

Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly to substitute petroleum-based products.They are a definite class of sustainable materials of the forestry industry.They have been in operation for hundreds of years to manufacture leather and now for a growing number of applications in a variety of other industries,such as wood adhesives,metal coating,pharmaceutical/medical applications and several others.This review presents the main sources,either already or potentially commercial of this forestry by-materials,their industrial and laboratory extraction systems,their systems of analysis with their advantages and drawbacks,be these methods so simple to even appear primitive but nonetheless of proven effectiveness,or very modern and instrumental.It constitutes a basic but essential summary of what is necessary to know of these sustainable materials.In doing so,the review highlights some of the main challenges that remain to be addressed to deliver the quality and economics of tannin supply necessary to fulfill the industrial production requirements for some materials-based uses.

Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.

Team-based fixed-time containment control for multi-agent systems with disturbances

We investigate the fixed-time containment control(FCC)problem of multi-agent systems(MASs)under discontinuous communication.A saturation function is used in the controller to achieve the containment control in MASs.One difference from using a symbolic function is that it avoids the differential calculation process for discontinuous functions,which further ensures the continuity of the control input.Considering the discontinuous communication,a dynamic variable is constructed,which is always non-negative between any two communications of the agent.Based on the designed variable,the dynamic event-triggered algorithm is proposed to achieve FCC,which can effectively reduce controller updating.In addition,we further design a new event-triggered algorithm to achieve FCC,called the team-trigger mechanism,which combines the self-triggering technique with the proposed dynamic event trigger mechanism.It has faster convergence than the proposed dynamic event triggering technique and achieves the tradeoff between communication cost,convergence time and number of triggers in MASs.Finally,Zeno behavior is excluded and the validity of the proposed theory is confirmed by simulation.