Tracking Control Problem Research Articles

The velocity tracking problem for Navier–Stokes equations with pointwise-integral control constraints in time-space

In this work, we study the velocity tracking control problem of the evolutionary two-dimensional Navier–Stokes system. The regularizing Tikhonov term is not involved in the cost functional and pointwise-integral control constraints in time-space are considered. First- and second-order optimality conditions are established using a suitable extended cone for the sufficient ones. We also address the numerical approximation of the control problem, proving the convergence of the discrete problems and establishing error estimates between the optimal discrete and continuous states.

Observer-Based Event-Triggered Fuzzy Control for Switched Multi-Agent Systems with State Constraints and Sensor Faults

In this paper, we consider the output feedback event-triggered tracking control problem for a class of switched nonlinear multi-agent systems (MASs) with sensor faults and state constraints. For unknown nonlinear functions in the system, fuzzy logic systems are used to approximate them. To address sensor faults, sensor error compensation coefficients are designed to compensate for the errors caused by sensor faults. Meanwhile, state observer is designed to estimate the unmeasurable states in the system, providing necessary information for control design. Based on directed switching networks containing a directed spanning tree, an event-triggered output feedback controller is designed to enable the MAS to track the leader agent. By constructing a suitable barrier Lyapunov function, the stability of the system is analyzed, and it is proved that the consensus tracking can be achieved without violating the state constraints, the uniform boundedness of all the closed-loop system signals is ensured and the Zeno behavior can be eliminated. Finally, the effectiveness of the proposed algorithm is verified through a simulation example.

Robust bilinear tracking control of a parabolic trough solar collector via saturation

This paper investigates the problem of robust tracking control of heat transport in a Parabolic Trough Solar Collector (PTSC), where the output has to track a desired reference trajectory. In this work, the PTSC is modeled by state-space bilinear dynamics. The manipulated variable is the pump volumetric flow rate, and the source term, i.e., solar irradiance, is assumed to be unmeasured. In addition, the actuator’s physical constraints induce saturation bounds on the manipulated variable and need to be considered explicitly in the controller design. To deal with these challenges, we first propose a saturated state-feedback law that meets the control objectives. Then, we reconstruct the unknown time-varying source term using an adaptive estimator. Later, through Lyapunov stability analysis, we prove that the closed-loop system and the output tracking error are uniformly ultimately stable. Numerical simulations attest to the performance of the proposed control strategy.

Modified Smith predictor-based robust tracking control design for fractional-order singular semi-Markovian jump systems

This paper focuses on addressing the robust tracking control problem as well as the compensation of delay and external disturbances for fractional-order singular semi-Markovian jump systems. Moreover, a multi-periodic modified repetitive control scheme is developed to guarantee the exact tracking performance of the considered system. Subsequently, by implementing the Majhi-Atherton modified Smith predictor approach, input delays and disturbances occurring in the addressed system are compensated. Precisely, the incorporation of disturbance estimator with the conventional Smith predictor frame can accurately estimate and attenuate the external disturbances. Further, the linear matrix inequality-based conditions for ascertaining the required results are procured with the aid of Lyapunov stability theory. Following this, by solving the acquired criteria, the precise framework of the gain matrices can be reckoned. Finally, the effectiveness and supremacy of the suggested control approach are assessed by using the outcomes of simulations obtained from two numerical examples.

Enhancing prescribed-time trajectory tracking control for a stratospheric airship with prescribed performance

This paper studies the tracking control problem for stratospheric airships with user-specified performance. Dealing with the infinite gain phenomenon in the prescribed-time stability, a new stability criterion with bounded gain is proposed by using a new time-varying scaling function. Moreover, a same-side performance function and a novel barrier Lyapunov function are incorporated into the control algorithm, which can compress the feasible domain of tracking error to minimize the overshoot and solve the difficult in tracking error not converging to zero simultaneously. The proposed scheme guarantees the airship capable of operating autonomously with satisfactory transient performance and tracking accuracy, where the performance parameters can be designed artificially and link to the physical process directly. Finally, the effectiveness of the proposed control scheme is verified by theoretical analysis and numerical simulation.

Barrier-critic-disturbance approximate optimal control of nonzero-sum differential games for modular robot manipulators

In this paper, for addressing the safe control problem of modular robot manipulators (MRMs) system with uncertain disturbances, an approximate optimal control scheme of nonzero-sum (NZS) differential games is proposed based on the control barrier function (CBF). The dynamic model of the manipulator system integrates joint subsystems through the utilization of joint torque feedback (JTF) technique, incorporating interconnected dynamic coupling (IDC) effects. By integrating the cost functions relevant to each player with the CBF, the evolution of system states is ensured to remain within the safe region. Subsequently, the optimal tracking control problem for the MRM system is reformulated as an NZS game involving multiple joint subsystems. Based on the adaptive dynamic programming (ADP) algorithm, a cost function approximator for solving Hamilton–Jacobi (HJ) equation using only critic neural networks (NN) is established, which promotes the feasible derivation of the approximate optimal control strategy. The Lyapunov theory is utilized to demonstrate that the tracking error is uniformly ultimately bounded (UUB). Utilizing the CBF’s state constraint mechanism prevents the robot from deviating from the safe region, and the application of the NZS game approach ensures that the subsystems of the MRM reach a Nash equilibrium. The proposed control method effectively addresses the problem of safe and approximate optimal control of MRM system under uncertain disturbances. Finally, the effectiveness and superiority of the proposed method are verified through simulations and experiments.

Longitudinal and Lateral Cooperative Control of Preview Intelligent Vehicles with Stabilization

Aiming at the highly nonlinear and coupled longitudinal and transverse motion control problems of intelligent vehicle path tracking control, a new method of preview MPC path tracking control is proposed by combining visual preview model and model predictive control theory. The method first locally linearizes the nonlinear prediction model and transforms the MPC optimization solution problem into a quadratic programming problem. The longitudinal vehicle speed and the preview distance are then treated as known in each control time domain, an exponential model is applied to characterize the longitudinal vehicle speed, and a transverse angular velocity-center of mass lateral deflection (r-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r-\\beta $$\\end{document}) phase plane plot is applied to characterize the vehicle stability. Finally, proportional integral differential stability controller is designed to improve vehicle stability. Simulation and test results show that: Compared with the MPC tracking control method, the preview MPC control method proposed in this paper can optimize the vehicle tracking performance on different adhesion coefficient road surfaces and improve the tracking accuracy, and this enhancement effect is more obvious at high speeds.

Fractional‐order fast terminal sliding mode trajectory tracking control of quadrotor UAV based on finite time disturbance observer

AbstractIn this paper, a novel trajectory tracking control problem of the quadrotor UAV is addressed, which considers the system uncertainties and unknown external disturbances meanwhile. To ensure a rapid convergence rate of the states, fast terminal sliding mode control (FTSMC) algorithm is improved combining with a fractional order method. In addition, finite‐time observer is designed to handle disturbances and enhance the robustness of the system. The closed‐loop finite‐time stability of the quadrotor UAV system is established using Lyapunov theory in accordance with the novel control law. To evaluate the effectiveness of our proposed strategy, various simulations under different scenarios are conducted respectively. These simulation results clearly demonstrate the superiority of our control scheme, which we refer to as fractional‐order fast terminal sliding mode control (FOFTSMC).

Approximation-based adaptive two-bit-triggered bipartite tracking control for nonlinear networked MASs subject to periodic disturbances

PurposeThis paper aims to investigate the problem of adaptive bipartite tracking control in nonlinear networked multi-agent systems (MASs) under the influence of periodic disturbances. It considers both cooperative and competitive relationships among agents within the MASs.Design/methodology/approachIn response to the inherent limitations of practical systems regarding transmission resources, this paper introduces a novel approach. It addresses both control signal transmission and triggering conditions, presenting a two-bit-triggered control method aimed at conserving system transmission resources. Additionally, a command filter is incorporated to address the problem of complexity explosion. Furthermore, to model the uncertain nonlinear dynamics affected by time-varying periodic disturbances, this paper combines Fourier series expansion and radial basis function neural networks. Finally, the effectiveness of the proposed methodology is demonstrated through simulation results.FindingsBased on neural networks and command filter control method, an adaptive two-bit-triggered bipartite control strategy for nonlinear networked MASs is proposed.Originality/valueThe proposed control strategy effectively addresses the challenges of limited transmission resources, nonlinear dynamics and periodic disturbances in networked MASs. It guarantees the boundedness of all signals within the closed-loop system while also ensuring effective bipartite tracking performance.

Neural Network Adaptive Inverse Control of Flexible Joint Space Manipulator Considering the Influence of Gravity.

With the aim of correcting the problem of trajectory tracking control of a flexible joint space manipulator in environments with different gravity, a neural network adaptive inverse control algorithm based on singular perturbation theory is proposed to resist the disturbance caused by system uncertainty. Firstly, the dynamic model of a flexible joint space manipulator with the influence of gravity is established, and then the system is divided into a fast subsystem and a slow subsystem using singular perturbation theory. The velocity feedback control rate is designed for the fast subsystem to suppress the elastic vibration caused by the joint flexibility. For the slow subsystem, the uncertain term and known term are separated by the inverse control algorithm, where the uncertain term is approximated online by the RBF neural network, and the robust control rate is designed to compensate for the approximation error. The simulation results show that the control method can not only effectively reduce the high-frequency vibration caused by the flexible joint but also resist the system disturbance so that a good track control effect is achieved.

Voltage and Fuel Utilization Control Strategy for Solid Oxide Fuel Cell Based on Active Disturbance Rejection Control

ABSTRACTSolid oxide fuel cell (SOFC) systems have become a research focus because of their clean and high‐efficiency properties. Control of output voltage and fuel utilization is critical to the energy management for multi‐energy systems incorporating SOFC energy supply. However, maintaining precise control of the system's voltage in the presence of perturbations can be challenging. Moreover, the system's voltage control process can lead to fuel utilization fluctuations, which may affect the economy and safety. The design of the controller must meet both of these requirements. The stringent control requirements lead to poor parameter adaptability of existing controllers. This paper designs a nonlinear function and adopts a nonlinear/linear active disturbance rejection controller (ADRC) based on state switching to solve the output voltage tracking control problem of SOFC and maintain the fuel utilization rate in the ideal range. The simulation experimental results show that the proposed method has the advantages of strong and superior parameter adaptability with less control effort, which provides theoretical guidance for the design of the output voltage controller of the actual SOFC system.

Optimized trajectory tracking control with disturbance resistance for wheeled mobile robot

When unavoidable disturbances exist in practical applications, the unicycle wheeled mobile robot (WMR) with non-holonomic constraint is challenging to be accurately controlled in finite time. An optimized dual closed-loop strategy is proposed in this paper to solve the trajectory tracking control problem of the unicycle WMR. The control strategy with fast time convergence and anti-disturbance properties consists of kinematic and dynamics controllers and an optimization algorithm. The kinematic controller is designed with an improved backstepping method to eliminate the non-holonomic constraints. The robust sliding mode control (SMC) method with fixed-time convergence is used to construct the dynamics controller. The optimization algorithm enhances the performance of the strategy and achieves accurate control. The global convergence and robustness of the strategy are theoretically demonstrated. The effectiveness of the strategy is verified by comparison in simulations.

Fixed-time second-order sliding mode output feedback trajectory tracking control for an autonomous surface vehicle with model uncertainties and prescribed performance

This paper investigates the fixed-time trajectory tracking control problem of autonomous surface vehicle system with asymmetric performance constraints. The external disturbances, model uncertainties and the difficulty of velocity measurement are all taken into account in the controller design. Asymmetric performance constraints are firstly studied to improve the transient and steady-state performance of the tracking error system. Next, a fixed-time extended state observer is developed to estimate the unknown velocity and external disturbances. Both the fixed-time first-order and the second-order PID-type sliding surfaces are designed. Further, two continuous output feedback controllers are built to achieve high control accuracy and low energy consumption and to achieve fixed-time stability of the closed-loop system. Finally, abundant simulations for CyberShip II demonstrate the effectiveness of the proposed algorithms.

Prescribed finite-time tracking control with input buffer for a manipulator system

The prescribed finite-time trajectory tracking control problem with input buffer is investigated for a linkage manipulator system. The backstepping method is used to design the prescribed finite-time trajectory tracking controller. A new prescribed finite-time performance function is proposed, which can more easily regulate control performance. With the help of this performance function, a constraint control law is designed for the tracking error, and a better transient performance than the existing prescribed finite-time performance function can be obtained under the same parameter conditions for the trajectory tracking process of the manipulator system. At the same time, a control input buffer function is designed, which solves both the overvoltage problem of control input caused by the overlarge position error of the manipulator and the problem that the manipulator system is difficult to start under heavy load. The simulation experiments verify the effectiveness and superiority of the proposed controller.

Analysis of a Dry Friction Force Law for the Covariant Optimal Control of Mechanical Systems with Revolute Joints

This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control.

Adaptive output feedback command filter control based on extreme learning machine for nonaffine time delay systems with input saturation

This paper is concerned with the tracking control problem of nonlinear time delay systems. For time delay systems, we consider nonaffine pure-feedback structure. Additionally, the case where the time delay systems are subject to input saturation and unknown states is also taken into account. To begin with, a mean value theorem and an implicit function theorem are exploited to transform the systems into an affine form. Afterwards, a state observer is developed to estimate the unknown state variables and an extreme learning machine (ELM) is used to approximate the unknown functions. The output of the command filter replaces the virtual control signal'derivative, thereby circumventing the problem of ‘explosion of complexity’. Meanwhile, compensation signals are introduced to eliminate the filtering errors in a dynamic surface control (DSC). A Lyapunov–Krasovskii functional is designed to mitigate the unknown constant state time delay. During the controller design process, combining a prescribed performance control (PPC) with a command filter control, the tracking error can converge to a predetermined bound. Additionally, the effect of input saturation is eliminated with the aid of an auxiliary system. Finally, the effectiveness of such controller is further proved by taking an electromechanical system as an application object.

Interactive strategy of shared control vehicle and automated vehicles based on adaptive non-cooperative game

Considering the complex traffic environment in the future, an interactive strategy between human-machine shared control vehicle (HSCV) and automated vehicles (AVs) based on the adaptive non-cooperative game (NCG) theory is proposed to ensure the safety of vehicles interaction control involving drivers with different characteristics. In HSCV, first, considering the environmental risk potential field (ERPF) and the human-machine conflict coefficient, an adaptive weight distribution method is designed to realize the weight distribution between a driver and an automation system. Subsequently, the steering angle command imposed by a driver is introduced into the game solving process between HSCV and AVs, enabling adaptive dynamic game through weight adjustment. During V2V interaction, based on NCG and distributed model predictive control, a motion planning controller (MOPC) is designed to integrate the optimal solution problem of path planning and tracking control and solve the interaction problem with constraints. Two typical interactive scenarios are used to verify the feasibility of the strategy. The results demonstrate that the interaction strategy considering the different drivers’ operating commands not only realizes the interaction between a driver and an ego vehicle but also realizes the interaction between an ego vehicle and nearby vehicles to ensure the safety of vehicles.

A Finite-Time Path Tracking Control Scheme for Unmanned Vehicles Based on Multidimensional Taylor Network and Adaptive Filtering

Aiming at the path tracking control problem of unmanned vehicles under the conditions of model uncertainty and measurement noise, a finite-time path tracking control scheme based on multidimensional Taylor network (MTN) is proposed. The MTN model is used to characterize the uncertainty of the unmanned vehicle model, and the improved back propagation (BP) algorithm is used as its learning algorithm; an adaptive MTN filter is designed to filter out the measurement noise, MTN is used as a filter, and the least mean square (LMS) algorithm is used as its learning algorithm; an MTN finite-time controller is designed to perform precise path tracking control on the unmanned vehicle, which can quickly and accurately track the reference path; according to the finite-time control theory, the convergence proof verifies the effectiveness of the proposed method through unmanned vehicle simulation experiments.

Adaptive Saturated Obstacle Avoidance Trajectory Tracking Control for Euler–Lagrange Systems With Velocity Constraints

ABSTRACTThis article pays attention to the obstacle avoidance trajectory tracking control problem for uncertain Euler–Lagrange (EL) systems subject to velocity constraints and input saturation. The existing obstacle avoidance results do not consider velocity constraints under input saturation, which means that an EL system may not be able to obtain sufficient control inputs to avoid a collision with an obstacle if it has a high speed when approaching the obstacle. Therefore, the velocity constraints in the obstacle avoidance tracking control are considered in this paper. A novel velocity constraint function that depends on the distance between the system and the obstacle is proposed. Integral‐multiplicative Lyapunov‐barrier functions (LBFs) are constructed and incorporated into the backstepping procedure to design an adaptive fuzzy obstacle avoidance tracking control scheme. Moreover, an auxiliary dynamic system is designed by constructing a bounded nonlinear vector related to an auxiliary variable to compensate for the effects of saturation. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the protocol achieves obstacle avoidance for the EL system without violating the velocity constraints inside the obstacle detection region, while also guaranteeing the ultimate uniform boundedness of all the closed‐loop signals. Numerical simulations are presented to demonstrate the efficacy of the proposed control strategy.

Quaternion-based fixed-time tracking control for an autonomous underwater vehicle with consideration of measurement bias

This article investigates trajectory and attitude tracking control problem of a 6-degree of freedom (DOF) autonomous underwater vehicle (AUV) subject to measurement bias and external disturbance. First, the model dynamics of rotational channels are established by unit-quaternion, which possesses simplicity and broader applicability compared to the Euler angle such that the maneuver signal could be uniquely determined. Meanwhile, by introducing constraint of the logarithm function and initial value, the unwinding phenomenon existing in rotation motion can be avoided tactfully. Considering the high requirement for sensor accuracy, the resulting measurement bias in position and velocity channels, making AUV into a mismatched system and bring the uncertain term in the process of controller design. Therefore, the echo state network (ESN) with online updates performance is applicable to approximate uncertain term simultaneously generated by measurement bias and unknown external disturbance. Then, by incorporating composite hyperbolic tangent function, the quasi-fast terminal sliding mode (QTSM) surface is constructed to realize the fixed-time convergence peculiarity of the AUV tracking system. Compared with the existing methods, the proposed algorithm can regulate artificially the stable schedule of the AUV tracking system and possess the capacity of bias tolerance and anti-disturbance. Finally, simulation results verify the validity and feasibility of the developed control algorithm.