Fixed-time Control Research Articles

Safety-Critical Fixed-Time Formation Control of Quadrotor UAVs with Disturbance Based on Robust Control Barrier Functions

This paper focuses on the safety-critical fixed-time formation control of quadrotor UAVs with disturbance and obstacle collision risk. The control scheme is organized in a distributed manner, with the leader’s position and velocity being estimated simultaneously by a fixed-time distributed observer. Meanwhile, a disturbance observer that combines fixed-time control theory and sliding mode control is designed to estimate the external disturbance. Based on these techniques, we design a nominal control law to drive UAVs to track the desired formation in a fixed time. Regarding obstacle avoidance, we first construct safety constraints using control barrier functions (CBFs). Then, obstacle avoidance can be achieved by solving an optimization problem with these safety constraints, thus minimally affecting tracking performance. The main contributions of this process are twofold. First, an exponential CBF is provided to deal with the UAV model with a high relative degree. Moreover, a robust exponential CBF is designed for UAVs with disturbance, which provides robust safety constraints to ensure obstacle avoidance despite disturbance. Finally, simulation results show the validity of the proposed method.

Cluster formation tracking of networked perturbed robotic systems via hierarchical fixed-time neural adaptive approach

This paper investigates the fixed-time cluster formation tracking (CFT) problem for networked perturbed robotic systems (NPRSs) under directed graph information interaction, considering parametric uncertainties, external perturbations, and actuator input deadzone. To address this complex problem, a novel hierarchical fixed-time neural adaptive control algorithm is proposed based on a hierarchical fixed-time framework and a neural adaptive control strategy. The objective of this study is to achieve accurate CFT of NPRSs within a fixed time. Specifically, we design a distributed observer algorithm to estimate the states of the virtual leader within a fixed time accurately. By using these observers, a neural adaptive fixed-time controller is developed in the local control layer to ensure rapid and reliable system performance. Through the use of the Lyapunov argument, we derive sufficient conditions on the control parameters to guarantee the fixed-time stability of NPRSs. The theoretical results are eventually validated through numerical simulations, demonstrating the effectiveness and robustness of the proposed approach.

Pre-specifiable fixed-time control for quadrotor aircraft with output constraints

For the controller design of quadrotor aircraft with six-DOF, a pre-specifiable fixed-time method combined with state constraints is researched in this paper. The 6-DOF aircraft model is divided into position loop and attitude loop through time scale decomposition method for the convenience of decoupling. Adaptive pre-specifiable fixed-time controllers for the position subsystem and attitude subsystem are proposed to ensure the desired trajectory and the desired attitude angle can be reached within a fixed-time which is independent of initial conditions. Meanwhile, the convergence time can be user-assignable in advance. Time-varying state constraints are considered in the controller design process in order to guarantee the safety of the system and prolong the life of actuator. The Barrier Lyapunov function is applied to ensure quadrotor aircraft’s output constraints are not violated. Finally, the effectiveness of the proposed controller is verified by the simulation experiment.

Fixed-time self-triggered fuzzy adaptive control of N-link robotic manipulators

This paper studies the fixed-time fuzzy adaptive self-triggered control of n-link robotic manipulators. To achieve fixed-time stability, a fuzzy adaptive fixed-time control algorithm is proposed by reconstructing the self-triggered controller and using the singularity-free function, which avoids the singularity problem and obtains fixed-time stability. Meanwhile, the self-triggered mechanism reduces the communication resources between the actuator and the controller, improving the system's transmission efficiency. Through the above thoughts, a kind of fixed-time fuzzy adaptive controller based on the self-triggered mechanism is designed, which guarantees that the tracking error of each joint converges to the prescribed range within a fixed time. Finally, the effectiveness of the proposed algorithm is verified by a simulation example of the two-link robotic manipulator.

A cooperative perception based adaptive signal control under early deployment of connected and automated vehicles

Connected vehicle-based adaptive traffic signal control requires certain market penetration rates (MPRs) to be effective, usually exceeding 10%. Cooperative perception based on connected and automated vehicles (CAVs) can effectively improve overall data collection efficiency and reduce required MPR. However, the distribution of observed vehicles under cooperative perception is highly skewed and imbalanced, especially under very low CAV MPRs (e.g., 1%). To address this challenge, this paper proposes a novel deep reinforcement learning-based adaptive traffic signal control (RL-TSC) method that integrates a traffic flow model, known as the cell transmission model (CTM), denoted as CAVLight. Traffic states estimated from the CTM are integrated with the data collected from the cooperative perception environment to update the states in the CAVLight model. The design of reward function aims for reducing total vehicle delays and stabilizing agent behaviors. Extensive numerical experiments under a real-world intersection with varying traffic demand levels and CAV MPRs are conducted to compare the performance of CAVLight and other benchmark algorithms, including a fixed-time controller, an actuated controller, the max pressure model, and an optimization-based adaptive TSC. Results demonstrate the superiority of CAVLight in performance and generalizability over benchmarks, especially under 1% CAV MPR scenario with high traffic demands. The influence of CTM integration on CAVLight is further explored through RL agent policy visualization and sensitivity analysis in CTM parameters and CAV perception capabilities (i.e., detection range and detection accuracy).

Fuzzy adaptive fixed-time control for output-constrained uncertain nonstrict-feedback time-delay systems

This paper deals with the problem of fuzzy adaptive fixed-time control for a class of uncertain nonlinear nonstrict feedback systems with time delays and output constraints. The negative effects of time delays on system performance and stability are overcome by introducing a new Barrier Lyapunov–Krasovskii (BLK) function and an innovative inequality. In addition, the singularity problem that arises in the process of deriving the control and adaptive laws, is solved by the proposed BLK function. The controller is designed in the backstepping framework which ensures that the system output does not violate predefined constraints. The proposed controller needs less information from the system and therefore has less implementation complexity than previous references, which leads to a more straightforward implementation. A fuzzy system approximation is utilized to overcome the uncertainties of the model. It is guaranteed that all closed-loop system signals converge to small neighborhoods around zero in a fixed time. Finally, an example is presented to verify that the proposed method achieves the control objectives.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Adaptive Fixed-time Control for Multiple Switched Coupled Neural Networks

Adaptive Fixed-time Control for Multiple Switched Coupled Neural Networks

Enhanced tracking control for n-DOF robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation

This work proposes a fixed-time terminal sliding mode control scheme with time delay estimation (FxTSM-TDE) for unknown nonlinear robotic systems under uncertainties and unknown bounded disturbances. The idea of the fixed-time terminal sliding mode control method (FxTSM) is thoroughly explained and analyzed. The FxTSM approach has been used to achieve nonsingular fixed-time control, non-chatter control inputs, and superior trajectory tracking performance. Then, the proposed approach for estimating the unknown robot dynamics utilizes the TDE approach. The Lyapunov analysis is used to establish the fixed-time stability of the system. The effectiveness of the suggested approach is evaluated, demonstrated, and contrasted with the existing control schemes by illustrating the results of the proposed method's enhanced performance in tracking accuracy, robustness, and convergence speed when implemented in robotic manipulator dynamics. The results indicate that the existing scheme has corresponding root mean square (RMS) error values of 0.0235 and 0.0283, while the proposed scheme has values of 0.0178 and 0.0188, respectively.

Fixed-time control of teleoperation systems based on adaptive event-triggered communication and force estimators

Abstract A fixed-time control strategy based on adaptive event-triggered communication and force estimators is proposed for a class of teleoperation systems with time-varying delays and limited bandwidth. Two force estimators are designed to estimate the operator force and environment force instead of force sensors. With the position, velocity, force estimate signals, and triggering error, an adaptive event-triggered scheme is designed, which automatically adjusts the triggering thresholds to reduce the access frequency of the communication network. With the state information transmitted at the moment of event triggering while considering the time-varying delays, a fixed-time sliding mode controller is designed to achieve the position and force tracking. The stability of the system and the convergence of tracking error within a fixed time are mathematically proved. Experimental results indicate that the control strategy can significantly reduce the information transmission, enhance the bandwidth utilization, and ensure the convergence of tracking error within a fixed time for teleoperation systems.

Fixed-time active fault-tolerant control for dynamical systems with intermittent faults and unknown disturbances

In this article, the problem of fixed-time active fault-tolerant control is investigated for dynamical linear systems with intermittent faults and unknown disturbances. Unlike traditional active fault-tolerant control, fixed-time control is taken into account in this article since intermittent faults appear and disappear within a certain period of time. The entire active fault-tolerant control framework is composed of fault detection, fault isolation, fault and state estimation as well as the reconfigurable controller. Using the homogeneity-based observers, states and faults are well estimated and a fault diagnosis scheme is proposed for the sake of detecting and isolating intermittent faults in a fixed time. The fault-tolerant controller, which provides global practical fixed-time stability of the closed-loop system, has two switching states corresponding to the appearance and disappearance of intermittent faults. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, two examples are exploited to demonstrate the effectiveness of theoretical results.

Logic-Based Fixed-Time Control for Uncertain Nonlinear Systems With Unknown Control Directions.

The fixed-time control problem is investigated for a class of uncertain nonlinear systems subjected to multiple unknown control directions. The control coefficients of nonlinear systems under consideration are time varying and their signs are not required to be identical. To tackle this challenge, a switching mechanism along with a novel dynamic boundary function is proposed. Utilizing the devised dynamic boundary function, adaptive parameters are introduced into the controller to effectively handle system uncertainties. It is proved that the system output converges to a small neighborhood of the origin in fixed time and the boundedness of all system signals is maintained. Finally, two simulation examples are used to show the validity of the presented switching control strategy.

Task-space tracking for networked heterogeneous robotic systems via adaptive neural fixed-time control

The task-space distributed adaptive neural network (NN) fixed-time tracking problem is studied for networked heterogeneous robotic systems (NHRSs). In order to address this complex problem, we propose a NN-based fixed-time hierarchical control approach that transforms the problem into two sub-problems: a distributed fixed-time estimation problem and a local fixed-time tracking problem, respectively. Specifically, distributed estimators are constructed so that each follower can acquire the dynamic leader’s state in a fixed time. Then, the neural networks (NNs) are employed to approximate the compounded uncertainty consisting of the unknown dynamics of robotic systems and the boundary of the compounded disturbance. More importantly, to guarantee that the tracking errors can converge into a small neighborhood of equilibrium in a fixed time independent of the initial state, the adaptive neural fixed-time local tracking controller is proposed. Another merit of the proposed controller is that the approximation errors are addressed in a novel way, eliminating the need for prior precise knowledge of uncertainties and improving the robustness and convergence speed of unknown robotic systems. Finally, the experimental results demonstrate the effectiveness and advantages of the proposed control method.

Resilient Neuroadaptive Distributed Fixed-Time Attitude Coordination Control for Multiple Spacecraft.

This work studies the attitude coordination tracking problem for multiple spacecraft with consideration of unintended faults (communication link faults and actuator faults), inertial uncertainties, and external disturbances under a directed communication graph. A resilient neuroadaptive distributed fixed-time control scheme is investigated to solve this challenging problem. First, an improved adaptive distributed observer is established for followers to estimate the states of the leader when considering communication link faults. The proposed observer improves the resilience against communication link faults. Subsequently, to further cope with the problem of actuator faults, inertial uncertainties, and external disturbances, based on the proposed observer and the technique of adding a power integrator, a neuroadaptive distributed fixed-time attitude coordination controller is developed. Unlike the existing controllers, the proposed one requires less information when dealing with faults and lumped uncertainties, and has a lower-computational cost. Moreover, the fixed-time stability of the closed-loop system is ensured under the designed resilient neuroadaptive distributed control scheme. Finally, comparative simulations are carried out to manifest the effectiveness of the investigated coordination control method.

Adaptive fixed-time stabilization for high-order uncertain nonlinear systems with unknown measurement sensitivities

This paper investigates the adaptive fixed-time stabilization problem for a class of uncertain high-order nonlinear systems with unknown measurement sensitivities and unknown control magnitude. Compared to existing practical fixed-time control approaches, our control strategy is capable of driving all states of uncertain high-order systems to the origin within a fixed time, rather than just ensuring their boundedness. Additionally, this study relaxes the restrictions on the nonlinear functions of the system, while overcoming challenges such as unknown control magnitude and unknown measurement sensitivity without prior boundaries. To achieve the control objectives, our control strategy consists of two main steps. Firstly, we divide the initial value of the high-order system into two cases, and construct adaptive controllers separately for each case by adding a power integral technique and backstepping method. Subsequently, the reliance of the stability time of the closed-loop high-order system on the initial value is eliminated by designing an appropriate controller switching mechanism. Finally, we provide a simulation example to validate the effectiveness of our control strategy.

Adaptive fixed-time difference synchronization for different classes of chaotic dynamical systems

This article examines adaptive fixed-time difference synchronization for various classes of chaotic dynamical systems. The adaptive fixed-time control technique has been used in this article to investigate the difference synchronization for the Sprott chaotic system, both with and without delay. The fixed settling time (T) has been estimated successfully. It is also shown that the trajectories of error states approach to the origin within a fixed time (T). The theoretical analysis is validated by simulating Sprott chaotic systems both with and without delay. On the other hand, various nonlinear chaotic systems are explored for difference synchronization in discrete chaotic systems. Several chaotic maps, including Tinkerbell, Henon, and Hitzl-Zele, have been used to achieve synchronization in these discrete systems. The numerical results are presented graphically, verifying the theoretical outcomes of difference synchronization for various classes of chaotic dynamical systems.

Antisaturation fixed-time backstepping fuzzy integral sliding mode control for automatic landing of fixed-wing unmanned aerial vehicles

This paper proposes a robust adaptive fixed-time control for automatic landing systems (ALS) of small-scale fixed-wing UAVs exposed to wind disturbances, parametric uncertainties, and input saturation. The control structure consists of three subsystems, i.e., the guidance system, the attitude control system, and the thrust control system. Considering the landing geometry, the guidance system computes the desired Euler angles to stabilize the dynamics of altitude deviation, lateral deviation, and lateral speed. An auxiliary system is designed to compensate for the effect of input saturation in the attitude control system. The fixed-time method, the backstepping control (BSC), the fuzzy logic control (FLC), and the integral sliding mode control (ISMC) techniques are adopted to synthesize the control law. All three functional parts of the proposed ALS are equipped with a fixed-time fuzzy sliding mode disturbance observer (FSMDO). FLC computes the gains of signum functions adaptively to attenuate the chattering. Fixed-time convergence of the system errors to an arbitrary residual set is proved by comprehensive stability analysis. Finally, the comparative simulation results verify the better dynamic response and stronger robustness under the proposed ALS.

Hierarchical estimator-based fixed-time and prescribed-time bipartite consensus of multiple Euler-Lagrange systems with a directed signed graph

This article addresses the fixed-time and prescribed-time bipartite consensus problem of Euler-Lagrange systems (ELSs) under a directed sign graph, taking into consideration both the parametric uncertainties and external disturbances. Novel hierarchical control algorithms employing estimator approaches are proposed to tackle the aforementioned challenges. More specifically, the control protocol is first designed to accomplish fixed-time bipartite consensus (Fix-TBC). The settling time obtained by using fixed-time control algorithm is restricted to its upper bound, but it may result in a conservative estimation of the bound. Consequently, it indicates the need for designing another control protocol to address the prescribed-time bipartite consensus (Pre-TBC) problem. By invoking Lyapunov stability theory, some sufficient conditions for achieving fixed-time and prescribed-time bipartite consensus of the ELSs are derived. Numerical examples are ultimately provided to demonstrate results.

Internal/Boundary Control-Based Fixed-Time Synchronization for Spatiotemporal Networks.

This article is concerned about fixed-time (FT) synchronization of spatiotemporal networks (STNs) with the Robin boundary condition. Above all, a switching-type FT stability theorem and an integral inequality are established, which provide a novel theoretical tool for the rigorous analysis of FT control in STNs. Subsequently, three kinds of nontrivial power-law controllers are developed which are separately acted on the interior, the boundary, and the whole of the spatial domain. Based on these control schemes and Lyapunov-like method, several flexible criteria are obtained to achieve FT synchronization of STNs, and the upper bound of the synchronization time is explicitly estimated. Note that, the derived results here are also perfectly applicable to STNs with Neumann or Dirichlet boundary condition. Several illustrate examples are presented at final to confirm the developed controllers and criteria.

Fixed-time controller for altitude/yaw control of mini-drone based on nonsingular terminal sliding mode: Real-time implementation with uncertainties

To obtain fixed-time stability and finite-time convergence of altitude and yaw motions of a mini-quadrotor subjected to perturbations, this paper proposes a new altitude/yaw motion finite-time tracking control. First, a nonsingular terminal sliding manifold is proposed for both subsystems whose states converge to their desired values in finite-time. To address the uncertainties of the system, a robust fixed-time switching controller is proposed whose stability is proposed and its settling-time depends only on control of the parameters and not the initial conditions. The validation of the proposed approach is presented based on a real mini-quadrotor.