Tracking Control Scheme Research Articles

Data-driven output consensus for a class of discrete-time multiagent systems by reinforcement learning techniques

The primary objective of this research paper is to examine the challenges associated with optimization and tracking control in discrete-time multiagent systems. This study begins by defining the optimal tracking control issue within the framework of a leader–follower multiagent system. A novel approach based on policy iteration is introduced for calculating the control law and performance index. The paper also includes an analysis of the convergence properties of this technique, ensuring its effectiveness in reaching optimal solutions. To facilitate this, an actor–critic neural network framework is utilized to approximate the control law and iterative performance index function. The proposed approach enables the real-time implementation of the policy iteration method, eliminating the requirement for prior knowledge of the system’s dynamics. The paper concludes with a series of simulation experiments that demonstrate the practicality and efficiency of the developed optimal tracking control strategies.

Conditional adaptive time series compensation and control design for multi-axial real-time hybrid simulation

The structural performance of critical infrastructure during extreme events requires testing to understand the complex dynamics. Shake table testing of buildings to evaluate structural integrity is expensive and requires special facilities that can allow for the construction of large-scale test specimens. An attractive alternative is a cyber-physical testing technique known as Real-Time Hybrid Simulation (RTHS), where a large-scale structure is decomposed into physical and numerical substructures. A transfer system creates the interface between physical and numerical substructures. The challenge occurs when using multiple actuators connected with a coupler (i.e., transfer system) to create translation and rotation at the interface. Tracking control strategies aim to reduce time delay errors to create the desired displacements that account for the complex dynamics. This paper proposes two adaptive control methodologies for multi-axial real-time hybrid simulations that improve capabilities for a higher degree of coupling, boundary, complexity, and noise reduction. One control method integrates the feedback proportional derivative integrator (PID) control with a conditional adaptive time series (CATS) compensation and inverse decoupler. The second proposed control method is based on a coupled Model Predictive Control (MPC) with the CATS compensation. The performance of the proposed methods is evaluated using the virtual multi-axial benchmark control problem consisting of a steel frame as the experimental substructure. The transfer system consists of a coupler that connects two hydraulic actuators generating the translation and rotation acting at the joint. Through sensitivity analysis, parameters were tuned for the decoupler components, CATS compensation, and the control design for PID, LQG, and MPC. Comparative results among different control methods are evaluated based on performance criteria, including critical factors such as reduction in the time delay of bothactuators. The research findings in this paper improve the tracking control systems for the multi-axial RTHS of building structures subjected to earthquake loading. It provides insight into the robustness of the proposed tracking control methods in addressing uncertainty and improves the understanding of multiple output controllers that could be used in future cyber-physical testing of civil infrastructure subjected to natural hazards.

Prescribed-time fault-tolerant tracking control for Markov jump nonlinear systems based on saturation dynamics filters

This paper investigates the problem of prescribed-time fault-tolerant tracking control for a class of Markov jump nonlinear systems affected by actuator faults and input saturation. First, a new time-varying constraint function and an error transformation are invoked to transform the original prescribed-time tracking control problem into a tracking control problem with deferred constraint for tracking error. Furthermore, the parameter correction terms are designed, on which a novel Markov jump saturation dynamic filter is constructed to handle the unfavorable effect of input saturation. Meanwhile, the projection operator technique and the norm estimation methodology are integrated to devise adaptive laws to estimate the unknown actuator faults evolving in accordance with the Markov chain. A new prescribed-time fault-tolerant tracking control scheme is put forward that realizes the deferred constraint on the tracking error, which in turn ensures that the tracking error of the system converges to a prescribed accuracy within a prescribed-time. Finally, two simulation examples, one of which implements a prescribed-time fault-tolerant tracking control for rotary steerable drilling tool system, are presented to illustrate the effectiveness and practicality of the developed scheme.

Event-Triggered Fractional-Order Tracking Control for an Uncertain Nonlinear System With Output Saturation and Disturbances.

In this article, an event-triggered (ET) fractional-order adaptive tracking control scheme (ATCS) is studied for the uncertain nonlinear system with the output saturation and the external disturbances by using the nonlinear disturbance observer (NDO) and the neural networks (NNs). Based on NNs, the system uncertainties are approximated. An NN-based NDO is designed to estimate the bounded disturbances. Combining the NNs, the output of the designed NDO, the fractional-order theory, and the ET mechanism, an ATCS is proposed under the output saturation. According to the stability analysis, all the closed-loop signals are semiglobally uniformly ultimately bounded based on the investigative ATCS. The simulation results and the comparative experiment verifications are shown to indicate the viability of the developed control scheme.

Distributed event-triggered formation control of UGV-UAV heterogeneous multi-agent systems for ground-air cooperation

Within the context of ground-air cooperation, the distributed formation trajectory tracking control problems for the Heterogeneous Multi-Agent Systems (HMASs) is studied. First, considering external disturbances and model uncertainties, a graph theory-based formation control protocol is designed for the HMASs consisting of Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs). Subsequently, a formation trajectory tracking control strategy employing adaptive Fractional-Order Sliding Mode Control (FOSMC) method is developed, and a Feedback Multilayer Fuzzy Neural Network (FMFNN) is introduced to estimate the lumped uncertainties. This approach empowers HMASs to adaptively follow the expected trajectory and adopt the designated formation configuration, even in the presence of various uncertainties. Additionally, an event-triggered mechanism is incorporated into the controller to reduce the update frequency of the controller and minimize the communication exchange among the agents, and the absence of Zeno behavior is rigorously demonstrated by an integral inequality analysis. Finally, to confirm the effectiveness of the proposed formation control protocol, some numerical simulations are presented.

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.

Distributed prescribed-time cooperative formation tracking control of networked unmanned surface vessels under directed graph

To investigate the formation tracking control problem of networked unmanned surface vessels (USVs) under a directed graph, this article provides a prescribed-time distributed cooperative formation tracking control scheme that specifies tracking error convergence time in advance. Firstly, aiming at the unknown state of the leading USV, a distributed prescribed-time state observer is designed for the following USVs, which can quickly and accurately estimate the position and speed of the leading USV in a prescribed time. Then, based on the state observer, the prescribed-time sliding surface is designed, and the prescribed-time cooperative formation tracking controller is constructed using the prescribed-time sliding mode surface. In addition, a fast adaptive compensation law is developed to mitigate the issue of input saturation. The analysis based on Lyapunov theory displays that the upper bounds of the convergence time of the observer, the sliding mode surface, and the controller proposed in this study explicitly exist in the controller parameters, so they can be easily adjusted in the control design process and are not restricted by the initial state. Finally, the simulation results demonstrate that the proposed approach exhibits high reliability and effectiveness.

A Walking Trajectory Tracking Control Based on Uncertainties Estimation for a Drilling Robot for Rockburst Prevention

A walking trajectory tracking control approach for a walking electrohydraulic control system is developed to reduce the walking trajectory tracking deviation and enhance robustness. The model uncertainties are estimated by a designed state observer. A saturation function is used to attenuate sliding mode chattering in the designed sliding mode controller. Additionally, a walking trajectory tracking control strategy is proposed to improve the walking trajectory tracking performance in terms of response time, tracking precision, and robustness, including walking longitudinal and lateral trajectory tracking controllers. Finally, simulation and experimental results are employed to verify the trajectory tracking performance and observability of the model uncertainties. The results testify that the proposed approach is better than other comparative methods, and the longitudinal and lateral trajectory tracking average absolute errors are controlled in 10.23 mm and 22.34 mm, respectively, thereby improving the walking trajectory tracking performance of the walking electrohydraulic control system for the coal mine drilling robot for rockburst prevention.

Research on Optimization of Intelligent Driving Vehicle Path Tracking Control Strategy Based on Backpropagation Neural Network

To enhance path tracking precision in intelligent vehicles, this study proposes a lateral–longitudinal control strategy optimized with a Backpropagation (BP) neural network. The strategy employs the BP neural network to dynamically adjust prediction and control time-domain parameters within an established Model Predictive Control (MPC) framework, effectively computing real-time front-wheel steering angles for lateral control. Simultaneously, it integrates an incremental Proportional–Integral–Derivative (PID) approach with a meticulously designed acceleration–deceleration strategy for accurate and stable longitudinal speed tracking. The strategy’s efficiency and superior performance are validated through a comprehensive CarSim(2020)/Simulink(2020b) simulation, demonstrating that the proposed controller adeptly modulates control parameters to adapt to various road adhesion coefficients and vehicle speeds. This adaptability significantly improves tracking and driving dynamics, thereby enhancing accuracy, safety, stability, and real-time responsiveness in the intelligent vehicle tracking control system.

Robust tracking and model following of uncertain nonlinear systems with some uncertainties and dead-zone inputs

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results.

Neural Network-Based Distributed Consensus Tracking Control for Nonlinear Multi-Agent Systems with Mismatched and Matched Disturbances

In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent systems subject to matched and mismatched uncertainties is addressed. In particular, the dynamics of the leader agent are modeled with uncertain terms, i.e., the leader’s higher-order information, such as velocity and acceleration, is unknown to all followers. To solve this problem, a robust consensus tracking control scheme that combines a neural network-based distributed observer, a barrier function-based disturbance observer, and a tracking controller based on the back-stepping method was developed in this study. Firstly, a neural network-based distributed observer is designed, which is able to achieve effective estimation of leader information by all followers. Secondly, a tracking controller was designed utilizing the back-stepping technique, and the boundedness of the closed-loop error system was proved using the Lyapunov-like theorem, which enables the followers to effectively track the leader’s trajectory. Meanwhile, a barrier function-based disturbance observer is proposed, which achieves the effective estimation of matched and mismatched uncertainties of followers. Finally, the effectiveness of the robust consensus tracking control method designed in this study was verified through numerical simulations.

Bi-level path tracking control of tractor semi-trailers by coordinated active front steering and differential braking

In recent years, autonomous tractor semi-trailers have been considered a promising solution for transportation on highways, ports, and large logistics centers to improve safety and efficiency. However, due to the complicated dynamics introduced by articulation structure, there are still challenges in achieving high-precision path tracking and stability control for tractor semi-trailers, especially in critical scenarios. In this work, a bi-level path tracking control scheme for the autonomous tractor semi-trailer is proposed. At the higher level, a robust model predictive controller coordinating active front steering and differential braking is devised for addressing path tracking, stability control and robustness for an autonomous tractor semi-trailer. At the lower level, incorporating a logic switching mechanism, the designed optimal braking torque distribution module and the PID-based longitudinal control module prioritize the implementation of differential braking and target speed tracking. Simulation results demonstrate that the proposed control strategy offers remarkable path tracking performance in three designed testing scenarios.

Trajectory Tracking Control Design for 4WS Vehicle Based on Particle Swarm Optimization and Phase Plane Analysis

With the rapid development of today’s society, the traffic environment has become more and more complex. As an essential part of intelligent vehicles, trajectory tracking has attracted significant attention for its stability and safety. It is prone to poor accuracy and instability in extreme working conditions like high speed. In this paper, a trajectory tracking control strategy to ensure lateral stability at a high speed and low attachment limit conditions is proposed for distributed drive vehicles. The model predictive controller (MPC) was used to control the front wheel angle, and the particle swarm optimization (PSO) algorithm was designed to optimize the MPC control parameters adaptively. The sliding mode controller controls the rear wheel angle, and the vehicle instability degree is judged by analyzing the β − β˙ phase plane. The controllers of different instability degrees are designed herein. Finally, a torque divider is designed to consider the actuation anti-slip. The designed controller is verified by Carsim and MATLAB-Simulink co-simulation. The results show that the trajectory tracking controller designed in this paper effectively improves the tracking accuracy under the premise of ensuring stability.

Optimal trajectory tracking for uncertain linear discrete‐time systems using time‐varying Q‐learning

SummaryThis article introduces a novel optimal trajectory tracking control scheme designed for uncertain linear discrete‐time (DT) systems. In contrast to traditional tracking control methods, our approach removes the requirement for the reference trajectory to align with the generator dynamics of an autonomous dynamical system. Moreover, it does not demand the complete desired trajectory to be known in advance, whether through the generator model or any other means. Instead, our approach can dynamically incorporate segments (finite horizons) of reference trajectories and autonomously learn an optimal control policy to track them in real time. To achieve this, we address the tracking problem by learning a time‐varying ‐function through state feedback. This ‐function is then utilized to calculate the optimal feedback gain and explicitly time‐varying feedforward control input, all without the need for prior knowledge of the system dynamics or having the complete reference trajectory in advance. Additionally, we introduce an adaptive observer to extend the applicability of the tracking control scheme to situations where full state measurements are unavailable. We rigorously establish the closed‐loop stability of our optimal adaptive control approach, both with and without the adaptive observer, employing Lyapunov theory. Moreover, we characterize the optimality of the controller with respect to the finite horizon length of the known components of the desired trajectory. To further enhance the controller's adaptability and effectiveness in multitask environments, we employ the Efficient Lifelong Learning Algorithm, which leverages a shared knowledge base within the recursive least squares algorithm for multitask ‐learning. The efficacy of our approach is substantiated through a comprehensive set of simulation results by using a power system example.

Unified preassigned performance-guaranteed tracking control for systems with unknown control direction

This paper suggests a unified tracking control scheme for systems suffering from unknown control direction and preassigned performance requirement. Distinguished from the existing Nussbaum function-based control methods, the presented approach achieves a unified control framework that encompasses the asymptotic or finite-time stability by introducing sliding mode technique when the nonlinear systems suffer from the unknown control direction issue. Two kinds of stabilities can be obtained only via choosing specific functions. Moreover, the suggested control approach can also deal with the changing of control direction. The stability is analyzed, and the total method rigorously guarantees the tracking errors’ required performance criterion. The simulation results of the second order inverted pendulum model serve as verification of the proposed method. Furthermore, as an alternative application scenario, the attitude tracking issue of hypersonic vehicles is dealt with by the presented method subjected with the time-varying control coefficient.

Event‐triggered adaptive tracking control for stochastic nonlinear systems under predetermined finite‐time performance

SummaryIn this paper, an event‐triggered adaptive tracking control strategy is proposed for strict‐feedback stochastic nonlinear systems with predetermined finite‐time performance. Firstly, a finite‐time performance function (FTPF) is introduced to describe the predetermined tracking performance. With the help of the error transformation technique, the original constrained tracking error is transformed into an equivalent unconstrained variable. Then, the unknown nonlinear functions are approximated by using the multi‐dimensional Taylor networks (MTNs) in the backstepping design process. Meanwhile, an event‐triggered mechanism with a relative threshold is introduced to reduce the communication burden between actuators and controllers. Furthermore, the proposed control strategy can ensure that all signals of the closed‐loop system are bounded in probability and the tracking error is within a predefined range in a finite time. In the end, the effectiveness of the proposed control strategy is verified by two simulation examples.

Artificial neural network-based direct power control to enhance the performance of a PMSG-wind energy conversion system under real wind speed and parameter uncertainties: An experimental validation

With the increasing emphasis on embedding advanced technology into system controls, the Direct Power Control (DPC) approach has garnered considerable attention due to its simple and highly adaptable algorithm. This approach has been increasingly recognized in numerous applications. However, the variable frequency, harmonic distortion of the currents, and power ripples caused by Hysteresis controllers and switching tables decrease its effectiveness and robustness, affecting the system’s performance. For this reason, this paper proposed a new DPC based on Artificial Neural Network (ANN) approaches. In this approach, the hysteresis comparator and the switching table are substituted with ANN controllers and then applied on both sides: machine-side converter (MSC) and grid-side converter (GSC) of a Permanent Magnet Synchronous Generator based Wind Energy Conversion System (PMSG-WECS). Moreover, to make the system more efficient in varying wind conditions, this study expands the utilization of the artificial neural networks (ANN) to encompass the maximum power point tracking (MPPT) control strategy. To demonstrate the effectiveness of the proposed approach on the system behaviors, a simulation test was carried out in the Matlab/Simulink environment, using a real wind profile of a Moroccan city (Essaouira). In comparison to the classical DPC control, the simulation results showed the superior performance of the proposed ANN-DPC control in terms of reference tracking, response time, overshoot, precision, and its capacity to reduce the rate of power ripples and total harmonic distortion (THD) in the injected currents. Furthermore, a robustness test was also included in this work to check the robustness of the proposed control against parameters variation. In conclusion, the feasibility and effectiveness of the ANN-DPC control approach were confirmed through experimental validation using the dSPACE DS1104 board.

Predefined-Time Tracking Control of Unmanned Surface Vehicle under Complex Time-Varying Disturbances

Aiming at the unmanned surface vehicle (USV) trajectory tracking control under complex time-varying environment, a predefined-time convergence sliding mode disturbance observer (PTC-SMO) is introduced to effectively handle the internal parameter uncertainties and external environmental disturbances, thereby guaranteeing precise compensation of the lumped disturbance term within a set time. Then, in order to achieve precise tracking of the desired trajectory using USV under a predetermined time constraint, a novel fast trajectory tracking control strategy with predefined-time convergence (PTC-FTTCS) is established to improve tracking performance and ensure that the trajectory tracking error converges quickly in the predefined time. Through rigorous comparative simulation under ideal conditions and time-varying disturbances, the results demonstrate reliable trajectory tracking and disturbance handling effects, and the tracking performance and disturbance observation performance are significantly better than state-of-the-art methods.

Port-Hamiltonian modeling and jumping trajectory tracking control for a bio-inspired quadruped robot

Applying jumping locomotion into autonomous mobile robot is an effective way for improving abilities to overcome barriers and pass through complex terrains. In this paper, based on the designed structural framework for bio-inspired quadruped jumping robot, dynamic model is established by utilizing port-Hamiltonian with dissipation (pHd) method, and a passivity-based control strategy for the robot joints trajectory tracking is presented. First, morphology and biomimetics knowledges of frogs (a kind of animals with excellent jumping skill) motivate us to complete a bio-inspired jumping robot framework based on frog’s motion mechanism and body structure with torsional springs as energy storage device. Then, combining system passivity and dissipation, port-Hamiltonian method is utilized to build a dynamic model for expressing the relationship of energy and force in the designed robot. Jumping process analysis of different stages is also designed for ensuring the robot to complete taking-off and landing stages successfully. Next, with the definition of extending feasible robotic joint trajectory by La Salle invariant set principle, interconnection and damping assignment passivity-based control (IDA-PBC) method is exerted to obtain a trajectory controller for realizing smoothly and stably trajectory tracking in joint space. At last, simulation results show the reasonableness of the designed framework. By comparing our method with state-feedback and sliding mode control, effectiveness of the dynamic model and trajectory controller is also verified.