Tracking Control Law Research Articles

Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only

In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is shown to be robust to noisy measurements and it has the advantage to provide on-line finite-time (or non-asymptotic) state estimations. Based on these estimations, a quasi-homogeneous second-order sliding mode tracking control law including estimated position error integrals is designed illustrating the possibilities of finite-time acceleration feedback via algebraic state estimation.

Distributed consensus tracking control for nonlinear multiagent systems with state delays and unknown control coefficients

AbstractIn this article, the distributed consensus tracking problem is investigated for a group of heterogeneous nonlinear multiagent systems (MASs). The dynamic of each follower is subject to multiple time‐varying state delays and unknown non‐identical control coefficients. Most existing results for MASs with unknown non‐identical control coefficients are on the condition that only the specific Nussbaum‐type function can be used. This constraint is removed by employing the enhanced Nussbaum functions. Some appropriate Lyapunov–Krasovskii functionals are constructed to compensate the delayed nonlinear functions. By applying the finite‐time command filters to backstepping technique, a novel distributed adaptive consensus tracking control law is developed, which is independent of multiple state delays. It is proved that each follower's output can track the leader. Finally, the validness of the proposed control algorithm is illustrated by two simulation examples.

Data-Driven Adaptive Disturbance Observers for Model-Free Trajectory Tracking Control of Maritime Autonomous Surface Ships.

In this article, we address the disturbance/ uncertainty estimation of maritime autonomous surface ships (MASSs) with unknown internal dynamics, unknown external disturbances, and unknown input gains. In contrast to existing disturbance observers where some prior knowledge on kinetic model parameters such as the control input gains is available in advance, reduced- and full-order data-driven adaptive disturbance observers (DADOs) are proposed for estimating unknown input gains, as well as total disturbance composed of unknown internal dynamics and external disturbances. An advantage of the proposed DADOs is that the total disturbance and input gains can be simultaneously estimated with guaranteed convergence via data-driven adaption. We apply the proposed full-order DADO for the trajectory tracking control of an MASS without kinetic modeling and present a model-free trajectory tracking control law for the ship based on the DADO and a backstepping technique. We report the simulation results to substantiate the efficacy of the proposed DADO approach to model-free trajectory tracking control of an autonomous surface ship without knowing its dynamics.

Adaptive super-twisting sliding mode control for maximum power point tracking of PMSG-based wind energy conversion systems

This paper proposes a super-twisting adaptive sliding mode control law for maximum power point tracking of wind energy conversion systems based on permanent magnet synchronous generators (PMSGs). The employed sliding mode control algorithm can be considered an effective solution, as it retains the robustness properties of classical sliding mode control methods in the presence of disturbances and parameter uncertainties; at the same time, it provides chattering reduction via gain adaptation and generation of second-order sliding modes. In our work, a nonlinear multi-input multi-output tracking control problem is solved to maximize the captured power. Simulation results are presented using real wind speed data, and discussed for the proposed controller and four other sliding mode control solutions for the same problem, in the presence of variations of stator resistance, stator inductance and magnetic flux linkage. The proposed controller achieves the best trade-off between tracking performance and chattering reduction among the five considered solutions: compared to a standard sliding mode control algorithm, it reduces the amount of chattering from two to five orders of magnitude, and the steady-state error on PMSG rotor velocity of one order of magnitude. Also, it reduces the above-mentioned steady-state error of four orders of magnitude with respect to a previously-proposed linear quadratic regulator based integral sliding mode control law for the same system.

Intelligent controller for nonholonomic wheeled mobile robot: A fuzzy path following combination

This research article presents a novel solution of controller design for the autonomous path-following maneuver of a nonholonomic wheeled mobile robotic (WMR) system subjected to static and dynamic obstacles. Currently, autonomously operated nonholonomic vehicles, capable of completing tasks avoiding collisions, are deployed for low-profile household applications to sophisticated space missions. The geometrically constrained path-following controller with embedded intelligence for collision avoidance is designed based on a twofold hybrid control law. The hybrid control law combines the feedback linearization controller (FBC) with the fuzzy logic controller (FLC). The feedback linearization controller helps the mobile robot to remain on its desired path, while the fuzzy logic controller helps the mobile robot to avoid critical obstacles around the reference path. It is analytically proven that the proposed hybrid control law converges the robot asymptotically to the desired path when it is safely away from obstacles. Further, when the robot detects an obstacle in its sensing range, obstacle avoidance control law acts locally and it deviates itself from the desired path to avoid collision assuring stability through a bounded tracking control law. Considering bounded sensor measurement uncertainties during obstacle detection, it is observed that the fuzzy logic-based collision-avoidance algorithm behaves in a robust manner. The hybrid controller is designed and tested in a simulated environment with the real-life parameters of a nonholonomic wheeled mobile robot. The robot is capable of traversing through the geometrically constrained desired paths avoiding obstacles in an improved manner compared to the existing method. Moreover, the robot is also capable of returning back to its original path when obstacles are safely away. The performance of the novel hybrid control strategy is illustrated for several geometrically constrained paths via simulation to show its effectiveness in terms of fulfilling dual objectives of path following and simultaneous collision avoidance in an improved manner.

Adaptive tracking control for an unmanned autonomous helicopter using neural network and disturbance observer

In this paper, an adaptive tracking control scheme is investigated for a medium scale unmanned autonomous helicopter (UAH) with unknown external disturbances and system uncertainties to achieve improvement on the flight performance. The neural networks (NNs) are employed to compensate the system uncertainties. The second-order disturbance observers are introduced to restrain the compound disturbances which are combined with the NN approximation errors and the external disturbances. Accordingly, the tracking control law is designed for the UAH. The closed-loop stability of the whole UAH system is proved by using Lyapunov function method. Simulation results show that the developed control scheme can effectively solve the tracking control problems of UAH and certainly accomplish strong robustness with respect to the external disturbances and system uncertainties.

Task-Space Trajectory Tracking Control for Coordinated Manipulation Using Sampled Coupling Data

This letter studies the task-space synchronization control problem of networked manipulators which are commanded to track the desired task-space trajectories to achieve the coordinated manipulation transportation tasks in industrial and logistic applications. To guarantee the practical applicability and increase information transmission efficiency, sampled data-coupling strategy is utilized and the transmission delays as well as dynamics uncertainties are modelled explicitly. Firstly, the discrete-time-style synchronization error with sampled data is transferred into an equivalent continuous-time version with time-varying communication delays. Secondly, a distributed task-space tracking control law is presented based on the dynamic model by introducing the task-space end-position synchronization error for coordinated manipulation tasks of networked manipulators. Thirdly, a sufficient condition is derived from the Lyapunov-Krasovskii stability analysis approach to ensure the convergence of the dynamic control of each manipulator. By solving the proposed condition, the upper bound of the acceptable sampling period can be calculated. Simulational experiment results on a group of PUMA560 manipulators validate the task-space trajectory tracking performance, end-position synchronization performance and robustness to external force interference of the multiple-manipulator systems. To the best knowledge of the authors, this is the first letter which resolves the task-space tracking control of coordinated manipulators in the presence of coupling data sampling, transmission delays and dynamics model uncertainties.

Adaptive neural tracking control for high angle of attack maneuver with average dwell time

SummaryThis article attempts to study the high angle of attack maneuver from the perspective of switched system control. In view of the complex aerodynamic characteristics, an improved longitudinal attitude motion model is presented, which is a switched stochastic nonstrict feedback nonlinear system with distributed delays. The significant design difficulty is the completely unknown diffusion and drift terms and distributed delays with all state variables. Based on a technical lemma and neural networks, an improved smooth state feedback control law for nonstrict feedback systems is proposed without any growth assumptions. To eliminate the influence of distributed delays, an improved Lyapunov–Krasovskii function is constructed, which skillfully removes the constraint of the upper bound of the delay change rate. Then, by combining the average dwell‐time scheme and stochastic backstepping technique, an adaptive neural network tracking control law is designed, which extends a newly proposed switched system stability condition to the stochastic switched system. Theoretical analysis and flight control simulation experiments are provided to illustrate the effectiveness of the proposed control method.

Pattern-Moving-Based Partial Form Dynamic Linearization Model Free Adaptive Control for a Class of Nonlinear Systems

This work addresses a pattern-moving-based partial form dynamic linearization model free adaptive control (P-PFDL-MFAC) scheme and illustrates the bounded convergence of its tracking error for a class of unknown nonaffine nonlinear discrete-time systems. The concept of pattern moving is to take the pattern class of the system output condition as a dynamic operation variable, and the control purpose is to ensure that the system outputs belong to a certain pattern class or some desired pattern classes. The P-PFDL-MFAC scheme mainly includes a modified tracking control law, a deviation estimation algorithm and a pseudo-gradient (PG) vector estimation algorithm. The classification-metric deviation is considered as an external disturbance, which is caused by the process of establishing the pattern-moving-based system dynamics description, and an improved cost function is proposed from the perspective of a two-player zero-sum game (TP-ZSG). The bounded convergence of the tracking error is rigorously proven by the contraction mapping principle, and the validity of the theoretical results is verified by simulation examples.

Velocity-free attitude tracking for rigid spacecraft via bounded control

This article investigates the attitude tracking control problem for a rigid spacecraft without angular velocity feedback, in which external disturbances, parametric uncertainties, and input saturation are considered. Initially, an angular velocity observer is developed incorporated with adaptive technique, which could tackle the unmeasurable angular velocity and system uncertainties simultaneously. By introducing adaptive updating law into the proposed observer, the synchronized uncertainties are handled such that robustness of the observer is enhanced, even in the presence of external disturbances. Further, for solving the input constraints problem, command filter and backstepping method are utilized; thus, a bounded attitude tracking control law is derived. Finally, the attitude tracking performance is evaluated by numerical examples.

Adaptive Fault-Tolerant Control for Attitude Tracking of Flexible Spacecraft With Limited Data Transmission

This article investigates the fault-tolerant control for attitude tracking problem of flexible spacecraft in the presence of actuator degradation, external disturbance, and signal quantization, where a logarithmic encoder-decoder scheme is employed for input quantization. A quantized adaptive terminal sliding mode control law is proposed to solve the attitude tracking problem. In this design, the quantizer parameters are injected to the controller gains to reject quantization errors, and the designed controller can compensate the effects of the unknown information, including actuator efficiency factors, external disturbance, and bounds of rigid-flexible coupled nonlinearity. It is shown that the attitude of the spacecraft can track the desired objective under the developed attitude controller. Finally, a simulation example is provided to verify the validness of the proposed attitude tracking control law.

On the Backward Path Tracking Control of N-Trailer Systems

This paper considers the lateral control of articulated wheeled vehicles in backward motion. The parameterized articulated vehicle is composed of a car-like truck and N passive trailers, resulting in one single steerable axle. First a nonlinear path tracking control law based on exact linearization of an offset model is reviewed and the general stability conditions of such systems is presented. Second, a stability analysis for some vehicle cases is performed and verified in simulation. The possible application of this path tracking control law in real world articulated vehicles is discussed, and its limitations are shown.

Design of nonlinear optimal tracking control law based on finite-time stability for quadratic performance index

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

Distributed Output Tracking Control of Nonlinear Multi-Agent Systems with Unknown Time-Varying Powers

In this paper, we investigate the distributed output tracking problem for high-order nonlinear multi-agent systems (MASs) with unknown time-varying powers. For one leader case, by using the algebra graph theory and adding a power integrator, the distributed tracking control law is successfully designed to achieve that the tracking errors can be adjusted to be arbitrarily small, while ensuring that all the signals of the closed-loop system are bounded. Then we extend this result to the case of multiple leaders and solve the containment tracking problem, the designed distributed nonlinear controller can guarantee that the followers' outputs of the systems eventually converge to a limit point in the convex hull spanned by the leaders' outputs. Finally, two simulation examples are used to illustrate the effectiveness of the designed schemes.

Intelligent optimal tracking with asymmetric constraints of a nonlinear wastewater treatment system

AbstractThe wastewater treatment is an effective method for alleviating the shortage of water resources. In this article, a data‐driven iterative adaptive tracking control approach is developed to improve the control performance of the dissolved oxygen concentration and the nitrate nitrogen concentration in the nonlinear wastewater treatment plant. First, the model network is established to obtain the steady control and evaluate the new system state. Then, a nonquadratic performance functional is provided to handle asymmetric control constraints. Moreover, the new costate function and the tracking control policy are derived by using the dual heuristic dynamic programming algorithm. In the present control scheme, two neural networks are constructed to approximate the costate function and the tracking control law. Finally, the feasibility of the proposed algorithm is confirmed by applying the designed strategy to the wastewater treatment plant.

Neural optimal tracking control of constrained nonaffine systems with a wastewater treatment application

In this paper, we aim to solve the optimal tracking control problem for a class of nonaffine discrete-time systems with actuator saturation. First, a data-based neural identifier is constructed to learn the unknown system dynamics. Then, according to the expression of the trained neural identifier, we can obtain the steady control corresponding to the reference trajectory. Next, by involving the iterative dual heuristic dynamic programming algorithm, the new costate function and the tracking control law are developed. Two other neural networks are used to estimate the costate function and approximate the tracking control law. Considering approximation errors of neural networks, the stability analysis of the proposed algorithm for the specific systems is provided by introducing the Lyapunov approach. Finally, via conducting simulation and comparison, the superiority of the developed optimal tracking method is confirmed. Moreover, the trajectory tracking performance of the wastewater treatment application is also involved for further verifying the proposed approach.

Optimum Path Tracking Control for the Inverse Problem of Vehicle Handling Dynamics Based on the hp-Adaptive Gaussian Pseudospectral Method

We propose a vehicle path-tracking method based on the hp-adaptive Gaussian pseudospectral method (GPM), which tackles the problem of the slow convergence speed of the optimal control of vehicle path tracking. First, we establish a kinematic vehicle model by considering the path constraints and boundary constraints during the process of tracking the described path of a vehicle. Subsequently, finding the minimum error of the lateral distance between the prescribed path and the expected trajectory is set as the performance objective function. Finally, the vehicle path tracking problem is transformed into an optimal control problem. The optimization algorithm is combined with the sequential quadratic programming algorithm to optimize problems related to the control and state variables and the boundary and path constraints. The simulated results show that the hp-adaptive GPM can improve the convergence rate of the optimal control problem for vehicle path tracking. The proposed hp-adaptive pseudospectral method has a higher solving efficiency compared with traditional approaches for the vehicle path-tracking problem. Concurrently, the verification results of a real vehicle test indicate the feasibility of the proposed algorithm for solving the vehicle path tracking problem. This research provides valuable insight into the design work of lane changes and is an important step towards the design of feedback control laws for path tracking.

An Adaptive RBF-NMPC Architecture for Trajectory Tracking Control of Underwater Vehicles

An adaptive control algorithm based on the RBF neural network (RBFNN) and nonlinear model predictive control (NMPC) is discussed for underwater vehicle trajectory tracking control. Firstly, in the off-line phase, the improved adaptive Levenberg–Marquardt-error surface compensation (IALM-ESC) algorithm is used to establish the RBFNN prediction model. In the real-time control phase, using the characteristic that the system output will change with the external environment interference, the network parameters are adjusted by using the error between the system output and the network prediction output to adapt to the complex and uncertain working environment. This provides an accurate and real-time prediction model for model predictive control (MPC). For optimization, an improved adaptive gray wolf optimization (AGWO) algorithm is proposed to obtain the trajectory tracking control law. Finally, the tracking control performance of the proposed algorithm is verified by simulation. The simulation results show that the proposed RBF-NMPC can not only achieve the same level of real-time performance as the linear model predictive control (LMPC) but also has a superior anti-interference ability. Compared with LMPC, the tracking performance of RBF-NMPC is improved by at least 43% and 25% in the case of no interference and interference, respectively.

Modified Model Free Adaptive Control for a Class of Nonlinear Systems with Multi-threshold Quantized Observations

This paper addresses a pattern-moving-based modified model free adaptive control (PMFAC) scheme and illustrates the convergence of its tracking error for a class of nonlinear systems with unknown model and multi-threshold quantized observations. The basic idea is to consider the system’s quantization error as an external disturbance and an improved performance index function of control law is proposed from the perspective of two-player zero-sum game (TP-ZSG) based on the existed MFAC algorithms. The PMFAC scheme is established which mainly includes an improved tracking control law and a pseudo-partial derivative (PPD) estimation algorithm. Under certain conditions, the bounded convergence of system tracking error and the stability of PMFAC system with quantization errors can be guaranteed. The theoretical results are demonstrated by two numerical examples.

Improved prescribed performance anti-disturbance control for quadrotors

In this paper, an improved prescribed performance anti-disturbance control is investigated for quadrotors suffering from lumped disturbances and constrained onboard communication resources. Relative threshold event-triggered based extended state observers are respectively established in trajectory and attitude subsystems to recover the immeasurable velocity and unknown lumped disturbances with a less sampling cost, while an explicit relationship between the upper bound of estimation errors and the design parameters of event-triggered condition is derived. With the aid of estimation results, an aperiodic sampling based output feedback trajectory tracking control law is developed by inserting a relative threshold sampler into the controller-to-actuator channel, such that an enhanced robustness can be realized without involving excessive resource occupations. Additionally, a modified prescribed performance control is proposed to regulate the transient profile of trajectory tracking with an arbitrarily small overshoot and a fast convergence rate even in face of triggering error. All closed-loop signals are proved to be ultimately uniformly bounded meanwhile Zeno phenomena can be eliminated. The effectiveness of presented algorithm is validated by comparable simulations.