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 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.

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.

Contract Mechanism of Water Environment Regulation for Small and Medium Sized Enterprises Based on Optimal Control Theory

The small and scattered enterprise pattern in the county economy has formed numerous sporadic pollution sources, hindering the centralized treatment of the water environment, increasing the cost and difficulty of treatment. How enterprises can make reasonable decisions on their water environment behavior based on the external environment and their own factors is of great significance for scientifically and effectively designing water environment regulation mechanisms. Based on optimal control theory, this study investigates the design of contractual mechanisms for water environmental regulation for small and medium-sized enterprises. The enterprise is regarded as an independent economic entity that can adopt optimal control strategies to maximize its own interests. Based on the participation of multiple subjects including the government, enterprises, and the public, an optimal control strategy model for enterprises under contractual water environmental regulation is constructed using optimal control theory, and a method for calculating the amount of unit pollutant penalties is derived. The water pollutant treatment cost data of a paper company is selected to conduct empirical numerical analysis on the model. The results show that the increase in the probability of government regulation and public participation, as well as the decrease in local government protection for enterprises, can achieve the same regulatory effect while reducing the number of administrative penalties per unit. Finally, the implementation process of contractual water environmental regulation for small and medium-sized enterprises is designed.

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.

Unified Control Theory from PID to ACPID

To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all intricate factors, including internal dynamics and external bounded disturbance, into a single total disturbance. This enables the mapping of various nonlinear systems onto a linear disturbance system. Based on the theory of PID control and the characteristic equation of a critically damping system, Zeng’s stabilization rules (ZSR) and an ACPID control force based on a single speed factor have been designed. ACPID control theory is both simple and practical, with significant scientific significance and application value in the field of control engineering.

From Control Theory to Gravitational Waves

When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D1:η→ξ such that Dξ = η implies D1η = 0. When D is involutive, the procedure provides successive first-order involutive operators D1,...,Dn when the ground manifold has dimension n. Conversely, when D1 is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D1η = 0. If this is possible, that is when the differential module defined by D1 is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D1 is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D1 is formally surjective, controllability just amounts to the formal injectivity of ad(D1), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4). We prove that all these works are already explicitly using the self-adjoint Einstein operator, which cannot be parametrized and the comparison needs no comment. As a byproduct, they are all based on a confusion between the so-called div operator D2 induced from the Bianchi operator and the Cauchy operator, adjoint of the Killing operator D which is parametrizing the Riemann operator D1 for an arbitrary n. This purely mathematical result deeply questions the origin and existence of gravitational waves, both with the mathematical foundations of general relativity. As a matter of fact, this new framework provides a totally open domain of applications for computer algebra as the quoted test can be studied by means of Pommaret bases and related recent packages.

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.

Revised barrier function-based adaptive finite-and fixed-time convergence super-twisting control

This paper presents an adaptive gain,finite-and fixedtime convergence super-twisting-like algorithm based on a revised barrier function,which is robust to perturbations with unknown bounds.It is shown that this algorithm can ensure a finite-and fixed-time convergence of the sliding variable to the equilibrium,no matter what the initial conditions of the system states are,and maintain it there in a predefined vicinity of the origin without violation.Also,the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control.Moreover,it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function.This feature will be beneficial when the algorithm is implemented in practice.After that,the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time t=0 is discarded.Finally,the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.

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.

Refined disturbance observer based prescribed performance fixed-time control of high-speed EMS trains with track irregularities

High-speed Electromagnetic Suspension(EMS)train is continuously impacted by the irregularity of the track,which worsens the levitation performance of the train.In this paper,a composite control scheme for the EMS is proposed to suppress track irregularities by integrating a Refined Disturbance Observer(RDO)and a Prescribed Performance Fixed-Time Controller(PPFTC).The RDO is designed to estimate precisely the track irregularities and lumped disturbances with uncertainties and exogenous disturbances in the suspension system,and reduce input chattering by applying to the disturbance compensation channel.PPFTC is designed to converge the suspension air gap error to equilibrium point with prescribed performance by completing error conversion,and solve the fast dynamic issue of EMS.And the boundary of overshoot and steady-state is limited in the ranged prescribed.A theoretical analysis is conducted on the stability of the proposed control method.Finally,the effectiveness and reasonability of the proposed composite anti-disturbance control scheme is verified by simulation results.

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.

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.

Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed delays which are closer to reality are taken into the system.Besides,two kinds of control schemes are proposed,including feedback and adaptive control strategies.Based on some lemmas,mathematical inequalities and the designed controllers,a few synchronization criteria are acquired.Moreover,the upper bound of settling time(ST)which is independent of the initial values is given.Finally,the feasibility of our theory is attested by simulation examples.

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.

Optimization of anchorage support parameters for soft rock tunnel based on displacement control theory

In the construction of a soft rock tunnel,it is critical to accurately estimate the pre-stressed anchor support parameters for surrounding rock reinforcement;otherwise,engineering disasters may occur.This paper presents a support parameter selection method that aims to allow deformation as a control objective,which was applied to the tunnel located in Muzailing Highway,Min County,Dingxi City,Gansu Province,China.Through theoretical analysis,we have identified five factors that influence pre-stressing anchorages.The selection of mechanical parameters for the rock mass was carried out using an inverse analysis method.Compared with the measured data,the maximum displacement error of the numerical simulation results was only 0.07 m.The length of anchor cable,circumferential spacing of anchor cable,longitudinal spacing,and pre-stress index are adopted as the input parameters for the support vector machine neural network model based on particle swarm optimization(PSO-LSSVM).Besides,the vault subsidence and the maximum deformation of surrounding rock are considered as output values(performance indices).The goodness of fit between the predicted values and the simulated values exceeds 0.9.Finally,all support parameters within the acceptable deformation range are calculated.The optimal support variables are derived by considering the construction cost and duration.The field application results show that it is feasible to construct the sample database utilizing the numerical simulation approach by taking the displacement as the control target and using the neural network to specify the appropriate support parameters.

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.

Improved Control in Single Phase Inverter Grid-Tied PV System Using Modified PQ Theory

Grid-connected reactive-load compensation and harmonic control are becoming a central topic as photovoltaic(PV)grid-connected systems diversified.This research aims to produce a high-performance inverter with a fast dynamic response for accurate reference tracking and a low total har-monic distortion(THD)even under nonlinear load applications by improving its control scheme.The proposed system is expected to operate in both stand-alone mode and grid-connected mode.In stand-alone mode,the proposed controller supplies power to critical loads,alternatively during grid-connected mode provide excess energy to the utility.A modified variable step incremental conductance(VS-InCond)algorithm is designed to extract maximum power from PV.Whereas the proposed inverter controller is achieved by using a modified PQ theory with double-band hysteresis current controller(PQ-DBHCC)to produce a reference current based on a decomposition of a single-phase load current.The nonlinear rectifier loads often create significant distortion in the output voltage of single-phase inverters,due to excessive current harmonics in the grid.Therefore,the proposed method generates a close-loop reference current for the switching scheme,hence,minimizing the inverter voltage distortion caused by the excessive grid current harmonics.The simulation findings suggest the proposed control technique can effectively yield more than 97%of power conversion efficiency while suppressing the grid current THD by less than 2%and maintaining the unity power factor at the grid side.The efficacy of the proposed controller is simulated using MATLAB/Simulink.