Fixed-time Control Design Research Articles

Barrier lyapunov function-based homogeneous fixed-time controller design for a double integrator system

This study proposes a controller design for the fixed-time stabilisation of a double integrator system (DIS), taking into account both output and state constraints. The controller combines Barrier Lyapunov Function (BLF)-based control method with homogeneous fixed-time controllers to provide faster convergence, eliminate the singularity of BLF-based fixed-time control algorithms, and guarantee precise convergence to the origin while maintaining the constraints. Three different cases including output constraint, output and state constraints, and fixed-time extended-state observer-based control for the disturbed DIS are studied. Several sets of simulations are carried out and comparisons are made with several finite-time and fixed-time controllers. In addition, the proposed control system is applied to the lateral control of an autonomous vehicle. Simulation results outline faster convergence, faster response, less sensitivity to sensor noise, more capability in disturbance rejection, and more accurate positioning compared to previous control systems.

Fixed-Time Controller Design for Aero-Engines: A Switched System Approach

Fixed-Time Controller Design for Aero-Engines: A Switched System Approach

A New Event-Triggered Adaptive Fixed-Time Control Design for Uncertain Nonlinear Systems.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

Adaptive Fuzzy Nonsingular Fixed-Time Control for a Class of MIMO Nonstrict Feedback System

This paper studies the adaptive fuzzy practical fixed-time control design for MIMO nonlinear systems with non-strict feedback. The extant practical fixed-time stability criterion cannot obtain an accurate settling time upper bound or exists some constraints on parameters that lead to a conservative result. Thus a novel practical fixed-time stability criterion is proved in this paper to resolve the above problem and can obtain the precise value of the settling time upper bound. The control singular issue caused by the fixed-time stability criterion form is avoided by introducing adding power integration method. Compared with other approaches, this method is easy to apply in control design, and it's convenient to prove its effectiveness. And fuzzy logic system is adopted to approximate the unknown nonlinear items. Combining the proposed fixed-time stability criterion, traditional backstepping scheme, and fuzzy logic system, an adaptive practical fixed-time controller is proposed. The simulation of the actual physical system demonstrates the effectiveness of the controller and practical fixed-time criterion.

Fixed-Time Controller Design for a Quadrotor UAV with Asymmetric Output Error Constraints

Fixed-Time Controller Design for a Quadrotor UAV with Asymmetric Output Error Constraints

Adaptive Predefined-Time Bipartite Consensus Tracking Control of Constrained Nonlinear MASs: An Improved Nonlinear Mapping Function Method.

This work focuses on the problem of predefined-time bipartite consensus tracking control for a class of nonlinear MASs with asymmetric full-state constraints. A predefined-time bipartite consensus tracking framework is developed, where both cooperative communication and adversarial communication among neighbor agents are implemented. Different from the finite-time and the fixed-time controller design methods for MASs, the prominent advantage of the controller design algorithm presented in this work is that our algorithm can make the followers track either the output or the opposite output of the leader within the predefined time in accordance to the user requirements. In order to obtain the desired control performance, an improved time-varying nonlinear transformed function is skillfully introduced for the first time to handle the asymmetric full-state constraints and radial basis function neural networks (RBF NNs) are employed to deal with the unknown nonlinear functions. Then, the predefined-time adaptive neural virtual control laws are constructed by using the backstepping technique, while their derivatives are estimated by the first-order sliding-mode differentiators. It is theoretically testified that the proposed control algorithm not only guarantees the bipartite consensus tracking performance of the constrained nonlinear MASs in the predefined time but also remains the boundedness of all the resulting closed-loop signals. Finally, the simulation research on a practical example shows the validity of the presented control algorithm.

Fixed-Time Control for a Class of Nonlinear PH-DAE Systems

The globally fixed-time stabilization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control for the port-Hamiltonian differential algebraic equation (PH-DAE) is addressed by applying the structural properties of the port-Hamiltonian (PH) systems, and the interconnection and damping assignment passivity-based control (IDA-PBC) technique. For fixed-time control design of the differential algebraic equation systems, the main obstacle lies that the algebraic variables are hidden in the system and their dynamics are ambiguous. We propose an available and effective approach to overcome this obstacle. The system variables are decomposed into differential component and the algebraic component, and the explicit representation of the dynamics of algebraic component is obtained. Fist, we investigate the locally fixed-time stabilization control as well as globally attractive for PH-DAE. Second, we focus on solving the globally fixed-time stabilization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control problems by jointly taking advantage of the locally fixed-time stabilization control for the origin and the globally fixed-time attractivity control for a predeterminate region. Finally, in order to address fixed-time stabilization control and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control for PH-DAE, new controllers are designed. Moreover, the convergence time of systems can be easily estimated after external disturbance vanishes. The efficiency of the theoretical results acquired in present article is verified via two examples with numerical simulation.

Fixed-Time Fuzzy Control of Uncertain Robots With Guaranteed Transient Performance

In this article, an adaptive fixed-time fuzzy control scheme is proposed for an uncertain robot manipulator with user-defined performance. A novel symmetrical barrier Lyapunov function is designed based on the error conversion mechanism and the performance function such that the tracking errors will not violate the prescribed output constraints. A novel adaptive law is constructed and incorporated into the fixed-time controller design such that all the closed-loop signals can be bounded and achieve practical fixed-time convergence regardless of the initial conditions. Finally, the feasibility and superiority of the proposed scheme are demonstrated based on simulation and experimental studies using a Baxter robot.

On asymptotic fixed-time controller design for uncertain nonlinear systems with pure state constraints

&lt;abstract&gt;&lt;p&gt;This study investigates the problem of asymptotic fixed-time tracking control (AFXTTC) for uncertain nonlinear systems (UNS) subject to pure state constraints. To study this problem, we define asymptotic fixed-time stability (AFXTS) and thus a criterion for determining AFXTS. Dynamic surface control (DSC) is combined with fuzzy logic systems (FLSs) to construct a new adaptive fuzzy asymptotic fixed-time controller. A barrier Lyapunov function (BLF) is introduced to ensure that constraints on all states are satisfied. The proposed criterion is used to analyze the AFXTS of the system, and the effectiveness and superiority of the theoretical analysis results are verified through simulations.&lt;/p&gt;&lt;/abstract&gt;

Fixed-Time Fault-Tolerant Tracking Control of Fixed-Wing UAVs with Actuator Fault and Unmatched Disturbances

This paper presents a dynamic surface fixed-time fault-tolerant control strategy for the longitudinal dynamic model of fixed-wing unmanned aerial vehicles (UAVs). Firstly, a novel disturbance observer is constructed to precisely estimate the lumped disturbance. Secondly, without fractional power terms in the designed fixed-time fault-tolerant controller, the potential singular value problem is tactfully avoided, which often exists in the stability analysis of the traditional fixed-time controller design. Thirdly, a novel fixed-time filter is proposed to overcome the phenomenon of “differential explosion” in the backstepping control scheme. Lyapunov stability analysis guarantees that the tracking errors can converge to the neighborhood of the origin in the fixed time. The simulation results verify the effectiveness of the proposed control scheme.

Fixed-time integral sliding mode control design for a class of uncertain nonlinear systems based on a novel fixed-time stability condition

This paper develops a different approach to fixed-time controller design by introducing a totally novel fixed-time stability condition formulated according to the Lyapunov function technique. Based on this condition, a fixed-time sliding mode control law is derived for a class of uncertain nonlinear systems. This controller assures complete robustness of the closed-loop system against matched uncertainties and exogenous disturbances from the beginning owing to the elimination of the reaching phase by benefiting from a novel integral terminal sliding surface. This surface constructed in accordance with the proposed condition determines whole dynamics of the closed-loop system and guarantees its fixed-time stability. Numerical simulations are reported to validate the effectiveness of the theoretical results.

Fixed-Time Filtered Adaptive Parameter Estimation and Attitude Control for Quadrotor UAVs

In this article, a fixed-time filtered adaptive parameter estimation and control scheme is proposed for attitude tracking of quadrotor unmanned aerial vehicles. A nonsingular fixed-time sliding mode surface is constructed to avoid the existence of the singularity issue resulted from the differentiation of the sliding mode variable. Through designing auxiliary filtered matrices, a fixed-time parameter update law is developed to achieve the fixed-time parameter convergence. Then, an adaptive neural controller is designed to ensure the fixed-time convergence of attitude tracking errors in the presence of the model uncertainties. Instead of using any piecewise continuous functions, the possible singularity issue in the conventional fixed-time controller design can be overcome by constructing auxiliary functions, and thus the fixed time stability analysis becomes more concise. The efficiency of the presented scheme is validated through experiments on a practical Quanser quadrotor platform.

Neuro-adaptive fixed-time control with novel command filter design for nonlinear systems with input dead-zone

This paper designs novel command filters (CFs) and a singularity-free controller with fixed-time performance for strict feedback nonlinear systems with input dead-zone. Compared with traditional filter designs, such as dynamic surface control and CFs, the novel CFs designed in this paper can guarantee fixed-time convergence of filter errors and compensating signals. Moreover, the controller design excludes the singularities of control signals, which might result in severe oscillation and usually appear in the conventional fixed-time controller design. To compensate the input dead-zone, a compensation filter is constructed, where controller design and stability analysis can be simplified. In the end, a simulation example is given to verify the effectiveness of the theoretical results.

Singularity-Free Fixed-Time Fuzzy Control for Robotic Systems With User-Defined Performance

In this article, the singularity-free adaptive fuzzy fixed-time control problem is studied for an uncertain n-link robotic system with the position tracking error constraint. The controlled robotic system can be described as a multiple-input-multiple-output system.To implement the user-defined performance, an improved error conversion mechanism based on performance functions is presented such that the converted error is limited to an interval greater than zero, and an appropriate barrier Lyapunov function (BLF) is constructed to avoid the breach of position tracking error constraint. The fuzzy approximator is utilized to estimate the unknown functions. The significance and challenges of this article are to establish a new error conversion mechanism and design corresponding BLF that can be integrated into fixed-time control design to present a singularity-free adaptive fuzzy fixed-time control scheme. Benefits of the proposed adaptive fixed-time controller in comparison to the current approaches are that it cannot cause the singularity issue appearing in backstepping-based fixed-time control design and ensures quick transient response. Combining with Lyapunov stability theory, the boundedness of the closed-loop signals is ensured, and the position tracking error can be constrained in the user-defined performance boundaries. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Fixed-time SOSM controller design subject to an asymmetric output constraint

This paper addresses the problem of fixed-time controller design for the second-order sliding mode (SOSM) dynamics with asymmetric output constraints. Based on the construction of a barrier Lyapunov function (BLF) and the technique of adding a power integrator, a fixed-time SOSM controller that can be used to handle the asymmetric output constraint issue is developed. A strict Lyapunov stability analysis shows that the developed SOSM controller guarantees that the sliding variable can converge to the origin within a fixed time that is irrelevant to the system initial conditions. Meanwhile, the system output will never invade the boundary of the preset asymmetric constrained area. Finally, two examples are given to verify the effectiveness and the feasibility of the proposed scheme.

Adaptive Neural Network Fixed-Time Control Design for Bilateral Teleoperation With Time Delay.

In this article, subject to time-varying delay and uncertainties in dynamics, we propose a novel adaptive fixed-time control strategy for a class of nonlinear bilateral teleoperation systems. First, an adaptive control scheme is applied to estimate the upper bound of delay, which can resolve the predicament that delay has significant impacts on the stability of bilateral teleoperation systems. Then, radial basis function neural networks (RBFNNs) are utilized for estimating uncertainties in bilateral teleoperation systems, including dynamics, operator, and environmental models. Novel adaptation laws are introduced to address systems' uncertainties in the fixed-time convergence settings. Next, a novel adaptive fixed-time neural network control scheme is proposed. Based on the Lyapunov stability theory, the bilateral teleoperation systems are proved to be stable in fixed time. Finally, simulations and experiments are presented to verify the validity of the control algorithm.

Fixed-Time Formation Control of Unicycle-Type Mobile Robots With Visibility and Performance Constraints

This article presents a fixed-time leader-follower formation control protocol for a swarm of unicycle-type mobile robots with visibility and performance constraints. Under a vision-based formation control framework, mobile robots calculate their control signals with only the local relative distance and bearing angle provided by onboard stereo or RGB-D cameras. Since the sensing capability of the fixed onboard cameras is subject to limited range and angle of view, the field-of-view constraints are considered to ensure that each follower can always detect its leader and meanwhile avoid collision with the leader. The time-varying and asymmetric performance constraints on formation tracking errors are applied to guarantee the transient and stead-state performance. Furthermore, the proposed control protocol can be extended to address the control design problem without constraint requirements. Based on the fixed-time control design and Lyapunov analysis, formation tracking errors are shown to converge to a small neighborhood of zero in fixed settling time. Simulation and experiment studies are performed to illustrate the effectiveness of the formation control protocol.

Fixed-time control design for nonlinear uncertain systems via adaptive method

This article addresses a fixed-time tracking problem of uncertain nonlinear system. Firstly, a sufficient condition for practical fixed-time stability is given. Secondly, on the basis of the sufficient condition, a novel adaptive control strategy is proposed. The designed parameter adaptive law is expressed as a nonlinear differential equation, which is different from the existing adaptive design method. Under the proposed adaptive control scheme, the system performance can be guaranteed in a fixed time, and the upper bound of the settling time is merely affected by the control design parameters, which is independent on the initial states of system. Then, based on the new established inequalities, the fixed-time stability of the closed-loop system is proved. Finally, an example is provided to illustrate the effectiveness of the main result.

U-Model Based Adaptive Neural Networks Fixed-Time Backstepping Control for Uncertain Nonlinear System

Under U-model control design framework, a fixed-time neural networks adaptive backstepping control is proposed. The majority of the previously described adaptive neural controllers were based on uniformly ultimately bounded (UUB) or practical finite stable (PFS) theory. For neural networks control, it makes the control law as well as stability analysis highly lengthy and complicated because of the unknown ideal weight and unknown approximation error. Moreover, there has been very limited research focus on adaptive law for neural networks adaptive control in finite time. Based on fixed-time stability theory, a fixed-time bounded theory is proposed for fixed-time neural networks adaptive backstepping control. The most outstanding novelty is that fixed-time adaptive law for training weights of neural networks is proposed for fixed-time neural networks adaptive control. Furthermore, by combining fixed-time adaptive law and Lyapunov-based arguments, a valid fixed-time controller design algorithm is presented with universal approximation property of neural networks to ensure the system is fixed-time bounded, rather than PFS or UUB. The controller guarantees closed-loop system fixed-time bounded in the Lyapunov sense. The benchmark simulation demonstrated effectiveness and efficiency of the proposed approach.

Fixed-time stabilization control for port-Hamiltonian systems

In this paper, the locally fixed-time and globally fixed-time stabilization problems for the port-Hamiltonian (PH) systems via the interconnection and damping assignment passivity-based control technique are discussed. The definitions of fixed-time stability region (or region of attraction) and fixed-time stability boundary are given in this paper. From this starting point, the sufficient condition of globally fixed-time attractivity of a prespecified locally fixed-time stability region is obtained. Combining the locally fixed-time stability and the globally fixed-time attractivity of a prespecified locally fixed-time stability region, the globally fixed-time stabilization problem for PH system is effectively solved. Furthermore, the globally fixed-time control scheme independent of locally fixed-time stability region has also been derived by constructing a novel Lyapunov function. A illustrative example shows that the results obtained in this paper work very well in fixed-time control design of PH systems.