Tracking Control Of Nonlinear Systems Research Articles

Low-Computation Tracking Control of Nonlinear Systems With Asymmetric Full-State Constraints and Unknown Control Directions

This article considers the tracking control problem for an uncertain feedback nonlinear system with asymmetric time-varying full-state constraints and unknown control directions. We propose a new low-computation full-state constrained robust control algorithm, that removes the feasibility conditions of virtual controllers and solves the unknown control direction problem without using the Nussbaum gain technique. By introducing nonlinear transformation functions, the original constrained systems are converted into new unconstrained tracking error systems, and the new systems eliminate the limitation of the initial conditions. Then, to seek the correct control directions, an orientation function with error conversion is constructed, which avoids introducing Nussbaum-type functions and logic switching rules. The proposed method possesses inherent robustness against model uncertainties and disturbances, and guarantees that the full-state constraints and the tracking error of systems enter into a prescribed set in a fixed time. Finally, simulation examples are presented to demonstrate the superiority and effectiveness of the developed control algorithm.

Decentralized adaptive neural safe tracking control for nonlinear systems with conflicted output constraints

The issue of decentralized adaptive safe tracking control for interconnected large-scale nonlinear systems (ILSNSs) with conflicted output constraints is discussed in this paper. By “conflicted output constraints”, we mean that the output constraint functions conflict with reference signal, i.e., the reference signal is not completely constrained within the constraint range. In existing methods, it is always assumed that the reference signal is constrained within the constraint region. In practice, the constraints may be detected during system operation and conflict with the reference signal given in advance. In this particular case, the existing methods based on barrier Lyapunov function (BLF) or nonlinear transformation function (NTF) are invalid. From a new point of view, this article designs a new safety reference signal (SRS) which is completely restricted within the constraint range by using the boundary protection approach. Meanwhile, a prescribed performance function which can arbitrarily define the convergence time and tracking accuracy is introduced so that the system output can better track the SRS. Then, combining backstepping technique and radial basis function neural network (RBFNN), a new controller is constructed, under which a desired tracking trajectory can be obtained under the premise of ensuring safety performance. Furthermore, by adding a dynamic event triggering mechanism (DETM) between the actuator and the plant, the communication burden is effectively reduced. Simulation results verify the scheme developed.

Disturbance Compensation-Based Optimal Tracking Control for Perturbed Nonlinear Systems

This paper investigates the disturbance compensation-based optimal tracking control for nonlinear systems in the presence of uncertain dynamic drift and extraneous disturbance by using the adaptive dynamic programming (ADP). First, an extended state observer (ESO)-based disturbance rejection controller is designed to estimate the comprehensive disturbances of system. Then, a novel composite controller capable of online learning is developed based on disturbance rejection controller and optimal regulation law, where the optimal regulation law is conducted by ADP framework to stabilize the dynamics of tracking error and minimize predefined value function. Particularly, an improved critic-only weight updating algorithm is inserted in ADP for ensuring the finite time convergence of critic weight without resorting to traditional actor-critic structures enduring remarkable computational burden. Based on Lyapunov analysis, it is proved that the tracking errors and weight estimation errors of critic network are uniformly ultimately bounded and the pursued controller approximates to the optimal policy. Finally, simulation results are shown to check the superiority of involved strategy, and the value function can be decreased by 25% with consistent tracking performance.

Adaptive fault‐tolerant tracking control for nonlinear systems with unknown control coefficient and input saturation

SummaryIn this article, the tracking control problem is investigated for a class of nonlinear systems in the presence of unknown disturbance, input saturation, actuator fault, and unknown control coefficient. A novel disturbance observer‐based adaptive fault‐tolerant tracking control strategy is proposed with regard to nonlinear systems. Based on the Gaussian error function, the auxiliary dynamic system is designed to offset effects caused by the input saturation. Moreover, the Nussbaum‐type function is employed to avert control singularity and deal with the unknown control coefficient. A theoretical analysis indicates that the boundedness of all signals in the closed‐loop system can be guaranteed. Finally, two examples with one concerning the dynamic point‐the‐bit rotary steerable drilling tool system are given to confirm the validity of the method.

Command filtered adaptive tracking control of nonlinear systems with prescribed performance under time‐variant parameters and input delay

AbstractIn this article, a command filtered asymptotic adaptive prescribed performance control method is presented for nonlinear systems with time‐variant parameters, input delay, and external disturbances. The feature of the concerned system is more general and practical, which makes the controller development more complicated. By exquisitely constructing a set of auxiliary systems, both the command filtered errors and input delay are actively compensated simultaneously. Then a smooth nonlinear term with an updated gain is introduced into the controller design to concurrently compensate for time‐variant parameters and external disturbances. With the integration of the command filtered technique, the adaptive control and the prescribed performance function, a command filter‐based adaptive prescribed performance control framework is skillfully exploited, in which tracking errors of all the states are restricted into the preset regions. Based on the Lyapunov theory, both the transient and zero‐error asymptotic convergence performance can be guaranteed with the developed control method. Finally, simulation results demonstrate the preponderance of the exploited approach.

Fixed-time robust trajectory tracking control for quadrotor UAV with disturbances

Trajectory tracking control of nonlinear system with disturbances has been extensively investigated. A novel fixed-time robust trajectory tracking control scheme for quadrotor unmanned aerial vehicle (UAV) with disturbances is proposed in this paper. First, the quadrotor system is split into position and attitude loops. With the purpose of restraining coupling disturbances on position loop forced by imperfect attitude tracking, a novel fixed-time unknown input observer (UIO) is devised to accurately estimate the disturbances, with the unique feature that does not need the upper bound of disturbances or the derivatives. Second, taking unmeasurable velocity and unknown external disturbances into account for attitude loop, a fixed-time extended state observer (ESO) is proposed to precisely observe them within a fixed time. Third, considering control accuracy and convergence rate, robust fixed-time controllers are, respectively, designed for position and attitude loops, and the convergence time of overall system is independent of system initial states. Then, a comprehensive stability proof for the two-loop system is presented with a combination of bi-limit homogeneity and Lyapunov technique. Finally, simulations and comparisons are performed to demonstrate the effectiveness of the designed control scheme.

Fast finite-time command filter-based adaptive composite tracking control for nonlinear systems

Fast finite-time command filter-based adaptive composite tracking control for nonlinear systems

A new event-triggered adaptive tracking controller for nonlinear systems with unknown virtual control coefficients

This paper investigates the adaptive event-triggered tracking control problem for nonlinear systems with virtual control coefficients being unknown nonlinear functions. Firstly, different from approximators using fuzzy logics/neural networks or Nussbaum gain technique, a new transformation with less computation is introduced based on a monotone decreasing positive continuous function to handle uncertain virtual control coefficients (UVCCs). Furthermore, a novel event-triggered threshold scheme is firstly developed, which can switch between the fixed and relative threshold strategies smoothly. Finally, an adaptive event-triggered tracking controller is constructed, whose effectiveness is verified by both theoretical analysis and simulations.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control for Nonlinear Systems With Full-State Constraints and Application to a Single-Link Robot.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

Approximate Optimal Curve Path Tracking Control for Nonlinear Systems with Asymmetric Input Constraints

This paper proposes an approximate optimal curve-path-tracking control algorithm for partially unknown nonlinear systems subject to asymmetric control input constraints. Firstly, the problem is simplified by introducing a feedforward control law, and a dedicated design for optimal control with asymmetric input constraints is provided by redesigning the control cost function in a non-quadratic form. Then, the optimality and stability of the derived optimal control policy is demonstrated. To solve the underlying tracking Hamilton–Jacobi–Bellman (HJB) equation in consideration of partially unknown systems, an integral reinforcement learning (IRL) algorithm is utilized using the neural network (NN)-based value function approximation. Finally, the effectiveness and generalization of the proposed method is verified by experiments carried out on a high-fidelity hardware-in-the-loop (HIL) simulation system for fixed-wing unmanned aerial vehicles (UAVs) in comparison with three other typical path-tracking control algorithms.

Prescribed-time tracking control for nonlinear systems with guaranteed performance

This paper studies the problem of the prescribed-time tracking control for a class of strict-feedback nonlinear systems with guaranteed performance. We will design a controller to achieve the following: one is to achieve the prescribed-time tracking, in which the settling time is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will; the other is to achieve prescribed performance composed of both the time-varying output constraint (TVOC) and the non-overshooting response. First, sufficient conditions on the prescribed-time tracking control with guaranteed performance are proposed. Then, based on the method of time-varying Barrier Lyapunov function (BLF) and LGV-backstepping, a recursive algorithm is developed to construct a controller to achieve the prescribed-time tracking control with guaranteed performance. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.

Iterative Learning Control for Output Tracking of Nonlinear Systems With Unavailable State Information.

This work presents a novel design framework of adaptive iterative learning control (ILC) approach for a class of uncertain nonlinear systems. By using the closed-loop reference model that can be viewed as an observer, the proposed adaptive ILC approach can be adapted to deal with the output tracking problem of nonlinear systems with unavailable system states. In the systems considered, two classes of uncertainties are taken into account, including parametric input disturbances and input distribution uncertainties. To facilitate the controller design and convergence analysis, the composite energy function (CEF) methodology is employed. The design framework in this brief is novel and widely applicable, which extends the CEF-based ILC approach to output tracking control of nonlinear systems without requiring full knowledge of state information and complicated observer design process. To show the effectiveness of the proposed design framework and control algorithms, two numerical examples are illustrated.

Adaptive output feedback event-triggered tracking control for nonlinear systems with unknown control coefficient

In this work, we are committed to dealing with the issue of global adaptive practical tracking for a class of uncertain nonlinear systems based on two kinds of event-triggered output feedback mechanisms. Compared with the highly relevant works, the class of nonlinear systems under investigation have not only unknown control coefficient without the precise information of its bounds, but also more general nonlinearities including any bounded disturbance. In order to deal with the relaxed restrictions, we develop a new pair of observer and output feedback controller with an improved dynamic gain, where the dynamic gain is ingeniously embedded in the backstepping design. Also, to economize communication and/or computation resources, two event-triggered control schemes via output feedback are presented with the time-varying threshold and dynamic threshold, respectively. It is worth emphasizing that the improved backstepping method can simplify the control design especially in the case of the dynamic threshold because of avoiding using hyperbolic tangent function. With the help of Barba˘lat’s lemma, it is shown that all closed-loop signals are globally bounded and system output (i.e., tracking error) will converge to the preset interval in a finite time. Finally, two examples are given to illustrate the effectiveness of the proposed control approach.

Event-Triggered Adaptive Fuzzy Tracking Control for Nonlinear Systems With Unknown Control Directions

This article addresses an event-triggered adaptive fuzzy tracking control problem for nonlinear systems with unknown control directions. To achieve the practical tracking, fuzzy logic systems are employed to approximate unknown nonlinear function. Nussbaum functions are adopted to address the problem of the unknown control directions. The newly designed controller not only guarantees the tracking error that converges to an arbitrary small neighborhood near the zero but also reduces the communication burden from the controller to the actuator. Moreover, the feasibility of the proposed event-triggered mechanism is verified by excluding Zeno behavior. Finally, the simulation result proves the effectiveness of the designed control scheme.

Event-Triggered Fuzzy Adaptive Fixed-Time Tracking Control for Nonlinear Systems.

In this article, the problem of event-based adaptive fuzzy fixed-time tracking control for a class of uncertain nonlinear systems with unknown virtual control coefficients (UVCCs) is considered. The unknown nonlinear functions of the considered systems are approximated by fuzzy-logic systems (FLSs). Moreover, a novel Lyapunov function is designed to remove the requirement of lower bounds of the UVCC in control laws. In addition, an event-triggered control method is developed by using the backstepping technique to save the network resources. Through theoretical analysis, the event-based fixed-time controller was proposed, which can guarantee that all signals of the controlled system are bounded and the tracking error can converge to a small neighborhood of the origin in a fixed time. Meanwhile, the convergence time is independent of the initial states. Two numerical examples are presented to demonstrate the effectiveness of the proposed approach.

Adaptive tracking control for nonlinear system in pure-feedback form with prescribed performance and unknown hysteresis

Abstract The finite-time tracking control issue for a class of nonlinear pure-feedback system with prescribed performance and unknown hysteresis is investigated in this work. To solve the Bouc-Wen hysteresis with unknown parameters and direction conditions, the Nussbaum function and auxiliary virtual control function are used. A finite-time performance function is applied in prescribed performance, which can make the tracking error is limited to a pre-given boundary in finite time. Moreover, the mean-value theorem is applied to solve the difficulty of pure-feedback form. Combined with backstepping technique, an adaptive tracking control scheme is designed to make sure that all the closed-loop signals are bounded and that the tracking error converges to pro-given boundary. Finally, a simulation example is presented to show the effectiveness of the proposed control scheme.

Adaptive asymptotic tracking control for nonlinear systems with state constraints and input saturation

In this study, an adaptive asymptotic tracking control scheme is designed for strict-feedback nonlinear systems with state constraints and input saturation. First of all, the asymmetric time-varying constraints on the states are realized by introducing the corresponding function transformations, thus the feasibility conditions are eliminated and the requirements of constrained boundary functions are relaxed. Meanwhile, to ensure that the system output asymptotically tracks the desired signal, a new nonlinear function of the tracking error is constructed which is different from other system states. Then, the saturation nonlinearity is approximated by using a smooth function, and an auxiliary system is introduced to compensate for the effect of the error function. During the design process, fuzzy logic systems and command filtered technique are applied to handle the uncertainties and the problem of complexity explosion in adaptive backstepping method, respectively. The proposed scheme guarantees that system states will not exceed the given asymmetric constraint boundaries and the tracking error can converge to zero asymptotically. Finally, the given simulation examples validate the effectiveness of the constructed strategy.

Robust Nonlinear Tracking Control with Exponential Convergence Using Contraction Metrics and Disturbance Estimation

This paper presents a tracking controller for nonlinear systems with matched uncertainties based on contraction metrics and disturbance estimation that provides exponential convergence guarantees. Within the proposed approach, a disturbance estimator is proposed to estimate the pointwise value of the uncertainties, with a pre-computable estimation error bounds (EEB). The estimated disturbance and the EEB are then incorporated in a robust Riemannian energy condition to compute the control law that guarantees exponential convergence of actual state trajectories to desired ones. Simulation results on aircraft and planar quadrotor systems demonstrate the efficacy of the proposed controller, which yields better tracking performance than existing controllers for both systems.

Adaptive multi‐dimensional Taylor network tracking control for nonlinear systems with input saturation and full state time‐varying constraints

SummaryIn this article, an adaptive multi‐dimensional Taylor network (MTN) control approach is developed for nonlinear systems subject to input saturation and full state time‐varying constraints. Using the function approximation property of MTN, an adaptive tracking control method is developed by incorporating the concept of time‐varying state constraints into the construct of barrier Lyapunov functions. The proposed approach not only ensures all closed‐loop system signals are bounded but also that all states of the system never violate the given time‐varying constraints. The most important advantage of the proposed control strategy is that it can obtain satisfactory control effects with low computational cost. Finally, two examples are given to validate the effectiveness of the proposed method.

Safe Learning-Based Feedback Linearization Tracking Control for Nonlinear System With Event-Triggered Model Update

Learning-based methods are powerful in handling complex scenarios. However, it is still challenging to use learning-based methods under uncertain environments while stability, safety, and real-time performance of the system are desired to guarantee. In this letter, we propose a learning-based tracking control scheme based on a feedback linearization controller in which uncertain disturbances are approximated online using Gaussian Processes (GPs). Using the predicted distribution of disturbances given by GPs, a Control Lyapunov Function (CLF) and Control Barrier Function (CBF) based Quadratic Program is applied, with which probabilistic stability and safety are guaranteed. In addition, the trajectory is optimized first by Model Predictive Control (MPC) based on the linearized dynamics systems to further reduce the tracking error. We also design an event trigger for GPs updates to improve efficiency while stability and safety of the system are still guaranteed. The effectiveness of the proposed tracking control strategy is illustrated in numerical simulations.