Fixed-time Control Research Articles

Fixed-time consensus control for uncertain heterogeneous multi-agent systems with high-order dynamics and time-varying delay under generic topologies

This article is concerned with the fixed-time control problem of uncertain high-order heterogeneous multi-agent systems with time-varying delays for both directed and undirected topologies. Applying the free-weighting matrix approach, a sliding mode controller is designed through the Lyapunov–Krasovskii functional and the conditions are derived with the help of linear matrix inequalities to attain fixed-time consensus tracking control of such systems. Two numerical simulations are included to verify the capability of the derived control law with respect to different initializations.

Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems with Unmodeled Dynamics

This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the fuzzy-logic systems (FLSs) are implemented to address the challenge of accurately approximating the unknown nonlinear terms that arise during the derived control algorithm process. By employing fixed-time command filters (FTCF), the “explosion of complexity” issues encountered in traditional backstepping methods will be effectively resolved. Moreover, error compensation mechanisms are derived to effectively mitigate the filtering errors that may arise from the FTCFs. The computational burden associated with FLSs is reduced through the utilization of the weight vector estimation method based on the maximal norm and an adaptive approach. A fixed-time adaptive fuzzy tracking controller is developed within the backstepping control framework to ensure the boundedness of all signals and achieve fixed-time convergence of the tracking error for the controlled system. Illustrative examples are conducted to illustrate the viability of the derived controller.

Adaptive Fuzzy Fixed-Time Control for Uncertain Nonlinear Systems with Mismatched Disturbances

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases.

Dynamic event-triggered fixed-time consensus control for coupled multi-permanent magnet synchronous motors stochastic system with prescribed performance

With the ubiquity of permanent magnet synchronous motors (PMSM), multi-PMSMs are increasingly being elastically coupled to achieve greater output power. The authors establish a general mathematical model of coupled multi-PMSMs system. The dynamic analysis of the coupled multi-PMSMs system is analyzed using coupled three-PMSMs system as an example, and a dynamic event-triggered fixed-time consensus controller with prescribed performance is constructed for coupled PMSMs stochastic system. In addition, Interval Type-3 Fuzzy System (IT3FS) is employed to estimate unknown functions, the computing cost is reduced by updating the weights based on only one adaptive law per PMSM. To enhance the efficiency of communication resource utilization, a dynamic event-triggered mechanism is introduced, where the triggering condition depends on a dynamic auxiliary variable. Moreover, fixed-time control technical is applied to guarantee the setting time and a novel fixed-time prescribed performance function (PPF) is constructed to constrain consensus errors. To cope with the “complexity explosion”, a fixed-time tracking differentiator (TD) is introduced and the corresponding filtered error compensation signals is designed. Finally, the authors demonstrate the system is fixed-time stabilized in probability by applying fixed-time stabilization Lyapunov stability criterion, and the simulation results of a coupled three-PMSMs stochastic system show that the presented algorithm is feasible.

Event-Triggered Neuro-Adaptive Fixed-Time Control for Nonlinear Switched and Constrained Systems: An Initial Condition-Independent Method

Event-Triggered Neuro-Adaptive Fixed-Time Control for Nonlinear Switched and Constrained Systems: An Initial Condition-Independent Method

A Novel Faster Fixed-Time Adaptive Control for Robotic Systems With Input Saturation

In this paper, an adaptive anti-saturation fixed-time control method with a faster convergence rate is studied for uncertain robotic systems. Firstly, a new segmental sliding variable is constructed to solve the singularity problem brought by the terminal sliding mode control (TSMC) and achieve a faster convergence rate. Secondly, to approximate and compensate for the model uncertainty and the viscous friction parameter, an adaptive neural network (ANN) is employed. Then, a novel auxiliary system is constructed to mitigate the effects of input saturation. Based on this, a novel non-singular TSMC algorithm integrated with the ANN and the auxiliary system is designed, so that the trajectory tracking errors of the robotic system can converge within a faster fixed time with actuator saturation. Finally, the superiority and practicability of the present method are verified by comparative experiments.

Fixed-time trajectory tracking for autonomous surface vehicles via output feedback under various constraints

This paper proposes a novel fixed-time output feedback trajectory tracking control method suitable for autonomous surface vehicles (ASVs). Firstly, various complex uncertainty terms, such as unknown external disturbances, unmodeled errors, and actuator faults are considered in this paper. And these terms are uniformly converted into the total uncertainty terms through model transformation for convenience. Then, a fixed-time extended state observer (FTESO) with the newly expanded state is designed to observe and estimate the total uncertainty terms. Next, the saturation dynamic filter (SDF) is adopted to address the input saturation, and the saturation factors of SDF are incorporated into the trajectory error calculation to reduce the torque mutation caused by an excessive error in the control input. Finally, a fixed-time control law is proposed by taking into account the ASV system error and FTESO estimation state. Simulation experiments show that this method has excellent control performance, and this conclusion is validated through stability proof and case comparison.

Practical fixed-time neural control for MIMO non-strict feedback nonlinear systems: an adaptive neural network approach

ABSTRACT This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method.

Disturbance observer based fixed-time control of stochastic systems

In this paper, the novel fixed-time anti-disturbance control scheme is proposed for a class of stochastic systems subjected to multiple disturbances and faults, and the disturbances consist of derivative-bounded disturbances and multiply noise. Based on the pole placement method, the fixed-time disturbance observer (Fixed-time DO) is devised to estimate derivative-bounded disturbances and an adaptive law is employed to approach the time-varying fault. Then a composite fixed-time controller is constructed to make the system converge to equilibrium position within a pre-specified time. At the same time, simulation examples illustrate that the proposed controller is effective and the convergence time is not related to the initial states of the system.

Distributed Event-Triggered Control for Manipulator with Fixed-Time Disturbance Observer

This article studies an event-triggered fixed-time trajectory tracking control problem of an n-joint manipulator system. Firstly, a fixed-time disturbance observer is proposed to reconstruct the total disturbance composed of external disturbances and model uncertainties, using the estimation as feedforward compensation to enhance the system robustness. Subsequently, based on the backstepping framework, a fixed-time controller with an event-triggering mechanism is designed for the manipulator to ensure the convergence of tracking errors to zero within a fixed time. Additionally, two event-triggering conditions are devised to reduce the transmission time of control input and the computation time of control output. Simultaneously, Zeno behavior is excluded through theoretical proof, validating the fixed-time stability of the closed-loop system. Finally, simulation verification is conducted on a two-joint manipulator, with results confirming the effectiveness of the control strategy.

Unified Fuzzy Control of High-Order Nonlinear Systems With Multitype State Constraints.

This article presents a unified adaptive fuzzy control approach for high-order nonlinear systems (HONSs) with multitype state constraints. Existing methods always require the upper and lower constraint boundaries are strictly positive and negative functions (or constants), respectively, which is often inconsistent with the actual constraints. In this article, "multitype state constraint" means that the upper and lower constraint boundaries include multiple types, such as both being strictly positive (or negative), sometime be positive or negative, and so on (cases ①-⑥). By designing a unified mapping function (UMF), the multitype state constraints are processed under removal the feasibility conditions (FCs). Furthermore, a technical design makes the proposed method also applicable to unconstrained HONSs without changing the control structure. By means of a fuzzy-logic system (FLS) and fixed-time stability theory (FTST), the proposed algorithm can ensure that the tracking error converges to a zero-centered neighborhood within a fixed time, and the singularity which often appears in the existing fixed-time control (FTC) methods of HONSs is effectively avoided. Simulation results demonstrate the scheme developed.

Exploiting Traffic Light Coordination and Auctions for Intersection and Emergency Vehicle Management in a Smart City Mixed Scenario.

IoT (Internet-of-Things)-powered devices can be exploited to connect vehicles to smart city infrastructure, allowing vehicles to share their intentions while retrieving contextual information about diverse aspects of urban viability. In this paper, we place ourselves in a transient scenario in which next-generation vehicles that are able to communicate with the surrounding infrastructure coexist with traditional vehicles with limited or absent IoT capabilities. We focus on intersection management, in particular on reusing existing traffic lights empowered by a new management system. We propose an auction-based system in which traffic lights are able to exchange contextual information with vehicles and other nearby traffic lights with the aim of reducing average waiting times at intersections and consequently overall trip times. We use bid propagation to improve standard vehicle trip times while allowing emergency vehicles to free up the way ahead without needing ad hoc system for such vehicle, only an increase in their budget. The proposed system is then tested against two baselines: the classical Fixed Time Control system currently adopted for traffic lights, and an auction strategy that does not exploit traffic light coordination. We performed a large set of experiments using the well known MATSim transport simulator on both a synthetic Manhattan map and on a map we built of an urban area located in Modena, Northern Italy. Our results show that the proposed approach performs better than the classical fixed time control system and the auction strategy that does not exploit coordination among traffic lights.

Disturbance observer-based fixed time control for bidirectional DC-DC converter with input voltage and load uncertainty

The bidirectional DC-DC converter serves a vital role in the energy recovery system of new energy vehicles. However, external interference and parameter uncertainty can easily affect its dynamic performance. A disturbance observer-based fixed time control strategy for bidirectional DC-DC is proposed to address the impact of input voltage and load uncertainty on bidirectional converters. Firstly, the bidirectional converter model undergoes coordinate transformation, and disturbance observers are designed to compensate for input voltage and load disturbances. Secondly, based on the fixed time control theory, a fixed-time controller is devised for the bidirectional DC-DC converter to facilitate fast tracking and adjustment of output voltage without requiring measurement of input voltage and load current. Finally, simulation and experiment evaluations are conducted to assess the proposed scheme’s effectiveness in output voltage regulation.

Command filter-based event-triggered fixed-time control for nonlinear systems with prescribed performance and actuator faults

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights’ updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example.

Fixed-Time Coordinated Attitude Control for spacecraft formation flying via event-triggered and delayed communication

This article tackles the challenge of achieving fixed-time coordinated attitude control for spacecraft formation flying when dealing with event-triggered and delayed communication. First and foremost, we introduce a fixed-time observer that leverages event-triggered, time-delayed information to enable follower spacecraft to access the leader’s commands within a directed, switching topology. In particular, the observer possesses the ability to effectively mitigate the impact of communication delays on information propagation. Following this, a fixed-time controller that empowers each follower to precisely follow the leader’s trajectory while maintaining the formation configuration is devised. Ultimately, we validate the feasibility and superiority of the proposed algorithm through numerical simulations and practical spacecraft ground experiments conducted with planar air-floating robots.

Satellite Attitude Control Using Faulty Double Gimbal Variable Speed Control Moment Gyroscope

A rigid satellite attitude control requires stable finite-time attitude convergence in the presence of rotation unwinding, external disturbances, and actuator faults. To achieve this, a new nonsingular fast fixed-time sliding mode controller is proposed to ensure finite-time convergence independent of the initial conditions of the system. Rotation unwinding is addressed using the body and shadow pair of the Modified Rodrigues Parameters (MRPs). Convergence behavior of the states errors in the neighborhood of the MRPs switching surface is also addressed. Attitude control is achieved using a double-gimbal variable-speed control moment gyro (DGVSCMG). For the first time, a DGVSCMG having all possible electrical and mechanical faults is considered for control design. A novel nonsingular fast fixed-time anti-unwinding fault-tolerant sliding control using a new sliding surface is proposed. This eliminates switching of the sliding surfaces and minimizes control chattering. Four new propositions are proposed and proved to establish fast fixed-time global stability of the system for tracking maneuver in fault and fault-free conditions with anti-unwinding. Simulation results are presented and compared with existing fixed-time sliding control approaches. The results show superiority of the proposed anti-unwinding fault-tolerant fast fixed-time control for the tracking maneuver in terms of convergence time, energy efficiency, and fault tolerance.

Adaptive Fixed-Time Control for High-Order Nonlinear Systems With Unknown Control Coefficients and Quantized Input

Adaptive Fixed-Time Control for High-Order Nonlinear Systems With Unknown Control Coefficients and Quantized Input

Fixed-Time-Convergent Sliding Mode Control with Sliding Mode Observer for PMSM Speed Regulation.

This paper focuses on the speed control of a permanent magnet synchronous motor (PMSM) for electric drives with model uncertainties and external disturbances. Conventional sliding mode control (CSMC) can only converge asymptotically in the infinite domain and will cause unacceptable sliding mode chattering. To improve the performance of the PMSM speed loop in terms of response speed, tracking accuracy, and robustness, a hybrid control strategy for a fixed-time-convergent sliding mode controller (FSMC) with a fixed-time-convergent sliding mode observer (FSMO) is proposed for PMSM speed regulation using the fixed-time control theory. Firstly, the FSMC is proposed to improve the convergence speed and robustness of the speed loop, which can converge to the origin within a fixed time independent of the initial conditions. Then, the FSMO is used as a compensator to further enhance the robustness of the speed loop and attenuate sliding mode chattering. Finally, simulation and experimental results show that the proposed method can effectively improve the dynamic performance and robustness of the PMSM speed control system.

Adaptive Neural Fixed-Time Control for Uncertain Nonlinear Systems

The article addresses the adaptive fixed-time system control problem subject to unknown nonlinear functions. By employing backstepping technique, fixed-time control, and neural networks (NNs), an adaptive fixed-time control approach is developed. NNs are utilized to package the unknown nonlinearities in the controlled system. The hyperbolic tangent functions are firstly utilized to solve the singular problem, which may exist in the derivation of virtual controller. Meanwhile, the jitter phenomenon is avoided. The developed controller design scheme not only assures the signals’ boundedness within fixed-time interval, but also makes the tracking error converge. Finally, on the aid of the simulation results, the effective of the designed control technique is shown.

Adaptive Fixed-Time Control for Full State-Constrained Nonlinear Systems: Switched-Self-Triggered Case

Adaptive Fixed-Time Control for Full State-Constrained Nonlinear Systems: Switched-Self-Triggered Case