Fixed-time Control Method Research Articles

An adaptive fast super-twisting disturbance observer-based dual closed-loop attitude control with fixed-time convergence for UAV

In this paper, a fixed-time dual closed-loop attitude control method is investigated for a quadrotor unmanned aerial vehicle. Firstly, a fixed-time adaptive fast super-twisting disturbance observer is presented for estimating the unknown external disturbance. A modified adaptive law is employed based on an equivalent control method to obtain proper observer gains. Secondly, a fixed-time controller is designed by using a universal barrier Lyapunov function to satisfy asymmetric tracking error constraints. Then, a tracking differentiator is utilised to arrange the transition process. Finally, the implementation of the developed method in a quadrotor unmanned aerial vehicle is performed. Through stability analysis and simulation results, the effectiveness and superiority of the proposed fixed-time control method are validated.

A Novel Real-Time Traffic Signal Control Strategy for Emergency Vehicles

Intelligent traffic signal control strategies for emergency vehicles (EV) is a research hotspot in intelligent transportation systems. Its research results will promote the shortening of the travel time of EVs, which is vital to saving lives and reducing property losses. This paper proposes a novel real-time traffic signal control strategy. The first step is called on-demand signal timing for reducing road saturation, which makes it possible that ordinary vehicles(OV) give way to EVs and make EVs travel faster, according to three indicators: the emergency response level(ERL), the congestion level of the road section(CLRS), and the time urgency level(TUL). The second step is called novel signal preemption, which combines non-intrusive preemption and intrusive preemption. This step provides green indicates and makes EVs pass through intersections quickly without stopping. The final step is called the recovery cycle strategy, which restores the road network to the normal situation as soon as possible by using linear programming(LP) to find the shortest green time in each phase after an EV passes the intersection. This paper conducts simulation experiments on an urban traffic simulator SUMO. The experimental results show that our novel strategy can shorten the travel time and reduce the traffic impact on the road network caused by prioritizing the EVs significantly. Compared with the fixed-time control method (FTCM), Min’s flexible signal preemption method(FSPM), and Qin’s intrusive signal preemption method (ISPM), our method can optimize travel time by up to 62.85%, 50.83%, and 11.62%, respectively.

Fixed-time sliding mode attitude control of a flexible spacecraft with rotating appendages connected by magnetic bearing.

This study focuses on the attitude control of a flexible spacecraft comprising rotating appendages, magnetic bearings, and a satellite platform capable of carrying flexible solar panels. The kinematic and dynamic models of the spacecraft were established using Lagrange methods to describe the translation and rotation of the spacecraft system and its connected components. A simplified model of the dynamics of a five-degrees-of-freedom (DOF) active magnetic bearing was developed using the equivalent stiffness and damping methods based on the magnetic gap variations in the magnetic bearing. Next, a fixed-time sliding mode control method was proposed for each component of the spacecraft to adjust the magnetic gap of the active magnetic bearing, realize a stable rotation of the flexible solar panels, obtain a high inertia for the appendage of the spacecraft, and accurately control the attitude. Finally, the numerical simulation results of the proposed fixed-time control method were compared with those of the proportional-derivative control method to demonstrate the superiority and effectiveness of the proposed control law.

Gaussian mixture model based fixed-time control for safe proximity to spacecraft with complex shape obstacle

Autonomous spacecraft proximity technology is vital for current and future on-orbit service missions, especially to solve the difficult problem of ultra-close-range safe proximity to complex-shaped spacecraft. This paper designs a novel Gaussian mixture model (GMM) based artificial potential function (APF) to describe the movement constraint, which is generated by the complex shape of the target spacecraft. Next, a novel GMM-FTC controller is designed by combining fixed-time control (FTC) with GMM-APF. The proposed GMM-FTC not only retains the advantages of FTC method, whose stabilization time is independent of the initial state, but also solves the collision avoidance in the presence of complex shape obstacle. Finally, numerical simulation verifies the effectiveness of the developed method.

Deep Q-network-based traffic signal control models.

Traffic congestion has become common in urban areas worldwide. To solve this problem, the method of searching a solution using artificial intelligence has recently attracted widespread attention because it can solve complex problems such as traffic signal control. This study developed two traffic signal control models using reinforcement learning and a microscopic simulation-based evaluation for an isolated intersection and two coordinated intersections. To develop these models, a deep Q-network (DQN) was used, which is a promising reinforcement learning algorithm. The performance was evaluated by comparing the developed traffic signal control models in this research with the fixed-time signal optimized by Synchro model, which is a traffic signal optimization model. The evaluation showed that the developed traffic signal control model of the isolated intersection was validated, and the coordination of intersections was superior to that of the fixed-time signal control method.

Fixed-time consensus of nonlinear multi-agent system with uncertain disturbances based on event-triggered strategy

This paper presents a fixed-time consensus problem for multi-agent systems (MASs) with nonlinear dynamics and uncertain disturbances, the event-triggered strategy is proposed to address this issue. Firstly, based on event-triggered control theory, a fixed-time consensus protocol is proposed, which can avoid continuous communication and greatly reduces the power consumption of proposed protocols. Secondly, based on graph topology, fixed-time control method and Lyapunov theory, the novel fixed-time consensus criteria of MASs with nonlinearity under Lipschitz condition and uncertain disturbances bounds is derived via the designed protocols. Furthermore, the consensus can be guaranteed by setting the proper parameters, it should be pointed out that for any given initial state, the MASs can reach consensus within the setting time. Thirdly, by utilizing the above control strategy, the MASs have no Zeno behavior. Finally, two simulation examples and the practical application of unmanned air vehicles (UAVs) verify the reliability of proposed control scheme.

Fixed-Time Synergetic Control-Based Chaos Suppression for Eighth-Order IFOCIM Drive System

This paper investigates chaos suppression in widely used indirect field oriented controlled induction machine (IFOCIM) drive system using fixed-time synergetic control method. The complex eighth-order IFOCIM drive system shows chaotic oscillations during a specific range of the integral gain of the PI speed controller. The conventional synergetic control method is improved by employing the fixed-time theory, the characteristics of the designed controller are chattering free and the convergence time is limited within a fixed-time upper bound depending on the controller parameters. The fixed-time synergetic control method is used to converge a selected macro variable to the origin within the fixed time upper bound. The controller can stabilize the chaotic system dynamics in a good way within a short time.

Event-triggered integral sliding mode fixed time control for trajectory tracking of autonomous underwater vehicle

In this paper, an event-triggered integral sliding mode fixed-time control method for trajectory tracking problem of autonomous underwater vehicle (AUV) with disturbance is investigated. Initially, the global fixed time stability is ensured with conventional periodic sampling method for reference trajectory tracking. By introducing fixed time integral sliding mode manifold, fixed time control strategy is expressed for the AUV, which can effectively eliminate the singularity. Correspondingly, in order to reduce the damage caused by chattering phenomenon, an adaptive fixed-time method is proposed based on the designed continuous integral terminal sliding mode (ITSM) to ensure that the trajectory tracking for AUV is achieved in fixed-time with external disturbance. In order to reduce resource consumption in the process of transmission network, the event-triggered sliding mode control strategy is designed which condition is triggered by an event. Also, Zeno behavior is avoided by proof of theoretical. It is shown that the upper bounds of settling time are only dependent on the parameters of controller. Theoretical analysis and simulation experiment results show that the presented methods can realize the control object.

Prescribed Finite Time Stabilization of Linear Systems With State Constraints

This paper studies the prescribed finite time stabilization control problem of multi-input linear control systems subject to uncertainties and state constraints. Different from finite-time and fixed-time control methods, a novel switching nonsingular coordinate transformation function based on the block decomposition technique is developed, resulting in a solution that the control action is continuous and bounded based on the transformed system. Moreover, the boundedness of closed-loop system states is ensured with prescribed finite time performance. Furthermore, we incorporate the barrier Lyapunov function into the stabilization control design to restrain the amplitudes of system states. Numerical examples are provided to verify the effectiveness of the proposed prescribed finite time control strategy.

Fixed-time leader-following/containment consensus for a class of nonlinear multi-agent systems

This study focuses on the fixed-time leader-following consensus problem for a class of multi-agent system with multi-dimensional nonlinear dynamics. First, the distributed static fixed-time control protocol is put forward to settle this issue. Different from the existing fixed-time control methods, the proposed control protocol is continuous such that the chattering phenomenon can be avoided. Note that the proposed static fixed-time controller is dependent on the global information of network topology. To address above issue, the fully distributed adaptive fixed-time controller is further proposed. Moreover, the results in fixed-time leader-following consensus are extended to containment consensus. And the case of directed graph is also considered. Finally, several examples are provided to illustrate the feasibility of the theoretical results.

Fixed-time leader-following/containment consensus of nonlinear multi-agent systems based on event-triggered mechanism

This study focuses on the fixed-time event-triggered leader-following consensus issue for nonlinear multi-agent system with uncertain disturbances. First, two distributed fixed-time controllers based on event-triggered mechanism are put forward to address this issue. Different from the existing finite-time control techniques, the proposed controller can guarantee that the settling time does not depend on the initial conditions and the continuous controller updates cannot be required. Moreover, compared with the existing fixed-time control methods, the fixed-time event-triggered tracking problem for multi-dimensional nonlinear multi-agent system with uncertain disturbances is considered for the first time in this paper. To avoid continuous communication among agents, a novel triggering mechanism is further proposed. Furthermore, the fixed-time event-triggered containment consensus with multiple leaders is considered. No agent exhibits the Zeno behavior in these two consensus issues. The effectiveness of main theoretical findings is demonstrated by two illustrative examples finally.

Fixed-time control for automatic carrier landing with disturbance

This paper addresses the fixed-time control problem for automatic carrier landing. By transforming a six-degrees-of-freedom fixed-wing aircraft model into the affine form with angle of attack controlled by thrust independently, backstepping technique is able to be adopted as the main control frame. Subsequently, for the purpose of improving convergent performance and success rate for carrier landing, fixed-time control method for a high-order multivariable system is proposed, and it is applied to the automatic carrier landing control system. In order to realize complete fixed-time convergence performance for the closed-loop system, fixed-time disturbance observers are employed in the control structure to efficiently estimate the external disturbances. Moreover, nonlinear fixed-time filters are incorporated to avoid tedious derivative calculation without affecting the fixed-time convergence performance of the system. Finally, the comparative simulation results with other methods demonstrate the effectiveness and superiority of proposed fixed-time control scheme.

Neuro‐adaptive fixed‐time trajectory tracking control for human‐in‐the‐loop teleoperation with mixed communication delays

The fixed-time master–slave trajectory tracking control problem of the human-in-the-loop teleoperation systems with mixed communication delays (including time-varying delays and random delays), parametric uncertainties, and external disturbances is discussed in this study. Based on the non-singular terminal sliding mode control technique, a novel neuro-adaptive fixed-time control algorithm is designed to solve the above-mentioned problem. Moreover, to improve the steady-state performance of the presented control algorithm, the combination of the radial basis function neural networks, parametric adaptive laws and fixed-time control method is newly-designed and used to reduce the effects of parametric uncertainties and external disturbances. By employing the Lyapunov argument, the sufficient conditions on the control parameters for guaranteeing the fixed-time stability of the controlled teleoperation system are derived. Besides, the authors also present the upper bound of the settling time and prove that it is independent of the initial condition. Finally, several simulation examples are performed to verify the effectiveness of the theoretical results.

Fixed-Time Synchronization in the pth Moment for Time-Varying Delay Stochastic Multilayer Networks

Since the speed that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment of an output signal norm tends to 0 can be used to measure the quality of the output signal, the stability of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment of complex networks has been widely concerned. This article studies fixed-time synchronization in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment for time-varying delay stochastic multilayer networks, where fixed-time synchronization of multilayer networks is realized by using nonlinear feedback or delay feedback, and the concrete expression of fixed settling time is evaluated. Compared with some existing fixed-time control methods, the optimal combination relationship between the exponential power of fixed-time controllers and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment is given, and the designed controllers are continuous function. Finally, the effectiveness of the method is verified by numerical simulations.

Fixed-time velocity-free sliding mode tracking control for marine surface vessels with uncertainties and unknown actuator faults

In this paper, a novel fixed-time fault-tolerant control scheme is proposed for trajectory tracking of marine surface vessels (MSVs). A fixed-time extended state observer (FXESO) is developed to enhance the robustness. In conjunction with the FXESO, a fixed-time sliding mode control (FXSMC) law is applied to trajectory tracking control. The designed tracking control system can be stabilized to the origin in fixed time in the presence of actuator faults (AF), unmodelled dynamics, unmeasurable system states and exogenous disturbances. Specially, the convergence time of the system is independent of the initial states of an MSV. Meanwhile, a complete proof of closed-loop fixed-time stability is given. Finally, comparative simulations manifest the performance and advantage of the developed fixed-time control method.

Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixedtime control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Practical Fixed-time Position Tracking Control of Permanent Magnet DC Torque Motor Systems

This article focuses on the position control problem for permanent magnet dc torque motor systems. An adaptive position tracking controller is proposed with online parameter adaptation. The position of the permanent magnet dc torque motor under the proposed strategy tracks the reference signal with fixed-time convergence. Different from previous fixed-time control methods, the approach proposed in this article can be implemented under two different modes with continuous transition, which facilitates the controller design in reducing the initial shock of the control signal. An adaptive law with smooth function is presented to counteract the disturbance and attenuate the chattering. Both numerical simulation and real-time experiment are given to verify the effectiveness of the proposed strategy.

Adaptive fixed-time consensus tracking control method for second-order multi-agent systems with disturbances

The consensus tracking control problem is investigated in this paper for second-order multi-agent systems in the presence of external disturbances. A fixed-time consensus tracking control method is presented with the control parameters updated by relative information of system states. The states of multi-agent systems can track the desired signal in fixed time cooperatively. Different from most existing fixed-time control methods, the structure of proposed strategy can be changed with respect to the operation condition by the continuous transition, which facilitates the protocol design in improving both the transient and steady performance. In addition, the adaptive law with smooth function is designed to attenuate the harmful chattering. Numerical simulation is carried out to validate the effectiveness of the proposed strategy.

Fixed-time switching control of underactuated surface vessels with dead-zones: Global exponential stabilization

This paper investigates the problem of global exponential stabilization of underactuated surface vessels (USVs) with actuator dead-zones. By utilizing input and state transformations, the dynamic model of USV is converted into an equivalent system consisting of two cascade connected subsystems. For the transformed system, a switching scheme based on fixed-time control theory is presented. For one of the subsystems with input dead-zones, a fixed-time control method is proposed, which addresses the dead-zone problem while guaranteeing global exponential stabilization. Simulations are given to demonstrate the effectiveness of presented method.

Adaptive fixed-time trajectory tracking control of a stratospheric airship

This paper addresses the fixed-time trajectory tracking control problem of a stratospheric airship. By extending the method of adding a power integrator to a novel adaptive fixed-time control method, the convergence of a stratospheric airship to its reference trajectory is guaranteed to be achieved within a fixed time. The control algorithm is firstly formulated without the consideration of external disturbances to establish the stability of the closed-loop system in fixed-time and demonstrate that the convergence time of the airship is essentially independent of its initial conditions. Subsequently, a smooth adaptive law is incorporated into the proposed fixed-time control framework to provide the system with robustness to external disturbances. Theoretical analyses demonstrate that under the adaptive fixed-time controller, the tracking errors will converge towards a residual set in fixed-time. The results of a comparative simulation study with other recent methods illustrate the remarkable performance and superiority of the proposed control method.