Tracking Control Of Nonlinear Systems Research Articles

Novel adaptive neural networks control with event-triggered for uncertain nonlinear system

In this paper, the issue of developing an event-triggered adaptive tracking controller for a class of uncertain nonlinear system is investigated. The radial basis function neural networks (RBFNN) is employed to approximate the uncertain parts, where the time-varying approximation errors are combined. However, it causes the dimensionality of RBFNN’s weight vector larger, which means more network resources are needed. It is a tough task to develop an adaptive tracking controller for nonlinear systems suffered network resources constraint. To save network resources, an event-triggered scheme is developed. Then, with the aid of adaptive backstepping technique, an event-triggered adaptive tracking control approach is established. With the developed event-triggered adaptive tracking controller, the boundedness of all signals in the closed-loop system can be guaranteed. Moreover, it can achieve the balance of tracking performance and the utilization of network resources. Finally, two simulation examples are given to verify the effectiveness of the proposed control scheme.

Quantized tracking control for nonlinear systems with unstable linearization

Quantized tracking control for nonlinear systems with unstable linearization

Event-Triggered Adaptive Fuzzy Tracking Control for Nonlinear Systems

In this paper, the problem of event-triggered adaptive fuzzy tracking control for nonlinear systems with external disturbance is explored. The fuzzy logic system method is utilized to design the event-triggered adaptive controller under two different event-triggered mechanisms to ensure that the tracking error converges to zero in any small neighborhood, and all the signals in the closed loop systems are bounded. In addition, two different ways are given to prove that the Zeno phenomenon will not occur. Finally, two simulation examples are given to demonstrate the validity of the proposed control scheme.

Global tracking control of quadrotor based on adaptive dynamic surface control

This paper presents a global nonlinear tracking control system for a quadrotor unmanned aerial vehicle (UAV) in the presence of underactuation, external disturbances and model uncertainties. Quadrotor systems lack enough independent control inputs to control their entire configuration space directly due to underactuation. The proposed solution is to adopt a cascade feedback technique that splits the system dynamics into attitude and position dynamics. The proposed controller is developed directly on the special Euclidean group with a region of attraction covering the entire configuration space where its stability is proven using Lyapunov functions. The controller guarantees the asymptotical convergence of tracking error in the presence of model uncertainties and external disturbances. In particular, the control method combines three techniques: a second-order sliding mode control (SMC), a dynamic surface control, and a non-parametric adaptation mechanism. The SMC is used to stabilize the position dynamics (internal dynamics) by generating a proper attitude command for the attitude controller. The DMC control guarantees the attitude dynamics stability globally and tracking performance while avoiding the mathematical complexities associated with the highly nonlinear dynamics. The adaptation mechanism includes a radial basis function neural network to observe uncertainties without the need for prior training. The uncertainties considered include unmodeled dynamics, external disturbances and parameter uncertainties including the mass and inertial matrices as well as motor coefficients. The desirable features of the proposed control system are illustrated by both numerical simulation and experiments on a UAV testbed.

Finite-Time Tracking Control for Nonlinear Systems via Adaptive Neural Output Feedback and Command Filtered Backstepping.

This article is concerned with the tracking control problem for uncertain high-order nonlinear systems in the presence of input saturation. A finite-time control strategy combined with neural state observer and command filtered backstepping is proposed. The neural network models the unknown nonlinear dynamics, the finite-time command filter (FTCF) guarantees the approximation of its output to the derivative of virtual control signal in finite time at the backstepping procedure, and the fraction power-based error compensation system compensates for the filtering errors between FTCF and virtual signal. In addition, the input saturation problem is dealt with by introducing the auxiliary system. Overall, it is shown that the designed controller drives the output tracking error to the desired neighborhood of the origin at a finite time and all the signals in the closed-loop system are bounded at a finite time. Two simulation examples are given to demonstrate the control effectiveness.

Command-filter-based adaptive tracking control for nonlinear systems with unknown input quantization and mismatching disturbances

In this article, the adaptive tracking control problem is investigated for a class of uncertain nonlinear systems with input quantization and mismatching disturbances. The effect of the mismatching disturbances is compensated by introducing smooth functions in the virtual controllers. By combining the novel command filters with backstepping method, an adaptive controller is designed and the problem of ”explosion of complexity” can be solved. It has also been proved that all the signals in the closed-loop systems are bounded and the system output can asymptotically track the reference signal. Finally, simulation examples are provided to verify the effectiveness of the proposed method.

Iterative Learning Control for Output Tracking of Systems with Unmeasurable States

In this work, a new design framework of adaptive iterative learning control (ILC) approach for a class of uncertain nonlinear systems is presented. By making use of the closed-loop reference model which works as an observer, the developed adaptive ILC method is able to be adopted to deal with the output tracking problem of nonlinear systems without requiring the measurability of system states. In the system, the uncertainties are formed by the product of unknown parameters and state functions that are also unknown as the system states are not available. In order to facilitate the controller design and convergence analysis, the composite energy function (CEF) method is employed, and the accurate tracking task can be realized successfully. The proposed approach extends CEF-based ILC approach sucessfully to output tracking control of nonlinear systems without requiring the system states information and complicated observer design. The effectiveness of the proposed ILC scheme is verified through an illustrative numerical example.

Disturbance compensation based model‐free adaptive tracking control for nonlinear systems with unknown disturbance

AbstractThis paper considers a novel model‐free adaptive tracking control for nonlinear perturbed systems. A general dynamic linearization model with disturbance input is first developed for nonlinear systems based on the pseudo‐partial derivatives (PPDs) method and input/output (I/O) data. Due to the unknown disturbance input, an online disturbance estimation algorithm is proposed based on optimization by minimizing a cost function. Furthermore, an adaptive tracking control strategy with disturbance compensation is developed, such that the tracking error of nonlinear systems is convergent and closed‐loop systems are strongly robust. Finally, a comparing simulation is provided to demonstrate the effectiveness of the proposed approach.

Quantized adaptive tracking control for nonlinear systems with actuator backlash compensation

In this paper, the problem of adaptive tracking control is investigated for nonlinear systems with asymmetric actuator backlash. We assume that the nonlinearities of the systems are unknown and the external disturbances are bounded. First, the control input will be quantized by a hysteresis-type quantizer, which can reduce the communication rate of the control signal. Then, the asymmetric actuator backlash is approximated to a new model, and a novel adaptive controller with the quantizer is designed via an adaptive backstepping technique to guarantee all the signals of the closed-loop tracking error system are uniform ultimate boundedness. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

Finite-time adaptive fuzzy tracking control for nonlinear systems with disturbances and dead-zone nonlinearities

This paper studies the problem of finite-time adaptive fuzzy tracking control for a class of nonlinear systems with unknown parameter uncertainties, nonsymmetric dead-zone inputs and mismatched external disturbances. Firstly, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions of the system model. Then, a novel finite-time adaptive tracking control scheme with disturbance estimator is developed to handle the unknown disturbance, which is more effective than the existing methods of disturbance rejection. Moreover, based on Lyapunov stability analysis of semi-global practical finite-time stable (SGPFS), it is proved that the proposed control scheme can guarantee that the states of system can quickly converge in finite time, and all the closed-loop system error signals are bounded. Finally, two simulation examples are used to demonstrate the effectiveness of the presented control approach.

State tracking control of nonlinear systems using neural adaptive dynamic sliding mode

This paper describes control issues of a general-class, single-input, unknown, nonlinear, non-affine system using dynamic sliding-mode control (DSMC). Chattering can be removed in DSMC with an inte...

Tracking control of nonlinear systems with improved performance via transformational approach

SummaryIn this work, we present a transformation‐based adaptive control design, for uncertain strict‐feedback nonlinear systems, to achieve given performance specifications in terms of convergence rate/time, overshoot, steady‐state (zero‐error) precision, in addition to the primary stability requirement. For the case with no uncertainty and known control coefficient, by introducing a time‐varying scaling function and an error‐dependent transformation, we develop a control strategy that is able to achieve exponential and uniform convergence of the tracking error and at the same time maintain the output tracking overshoot to be as small as desired without the need for trajectory initialization resetting. For the case with nonparametric uncertainties and unknown control directions, by employing an additional time‐varying scaling function together with a self‐tuning Nussbaum function, we develop a control scheme that not only secures asymptotic tracking but also guarantees finite time transient process in that the tracking error, prior to converging to zero, is regulated into a prespecified residual set within a prescribed time. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

Adaptive finite-time tracking control for nonlinear systems with unmodeled dynamics using neural networks

This paper presents a novel adaptive finite-time tracking control scheme for nonlinear systems. During the design process of control scheme, the unmodeled dynamics in nonlinear systems are taken into account. The radial basis function neural networks (RBFNNs) are adopted to approximate the unknown nonlinear functions. Meanwhile, based on RBFNNs, the assumptions with respect to unmodeled dynamics are also relaxed. This paper provides a new finite-time stability criterion, making the adaptive tracking control scheme more suitable in the practice than traditional methods. Combining RBFNNs and the backstepping technique, a novel adaptive controller is designed. Under the presented controller, the desired system performance is realized in finite time. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control method.

Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator

This paper studies the problem of adaptive fuzzy asymptotical quantized tracking control of non-strict-feedback systems with unmodeled dynamics. A dynamic signal is used to cope with the unmodeled dynamics and fuzzy systems are introduced to approximate the packaged unknown nonlinearities. Based on backstepping technique and fuzzy approximation property, a systemic fuzzy adaptive control scheme is proposed. By the utilization of Lyapunov theory, the semi-globally uniformly ultimate boundedness of all closed-loop system signals and asymptotical tracking performance are guaranteed. The main contributions of this work are two aspects: (i) a backstepping-based quantized control algorithm is firstly extended to nonlinear systems with unmodeled dynamics and non-strict-feedback structure; (ii) the semi-globally asymptotic tracking control scheme is independent of the quantized parameter. Simulation results verify the presented control approach.

Adaptive tracking control of nonlinear systems with dynamic uncertainties using neural network

ABSTRACTIn this paper, an adaptive neural tracking control approach is proposed for a class of nonlinear systems with dynamic uncertainties. The radial basis function neural networks (RBFNNs) are used to estimate the unknown nonlinear uncertainties, and then a novel adaptive neural scheme is developed, via backstepping technique. In the controller design, instead of using RBFNN to approximate each unknown function, we lump all unknown functions into a suitable unknown function that is approximated by only a RBFNN in each step of the backstepping. It is shown that the designed controller can guarantee that all signals in the closed-loop system are semi-globally bounded and the tracking error finally converges to a small domain around the origin. Two examples are given to demonstrate the effectiveness of the proposed control scheme.

Observer-based adaptive prescribed performance tracking control for nonlinear systems with unknown control direction and input saturation

Abstract In this paper, the problem of observer-based adaptive tracking control is investigated for a class of nonlinear systems with unknown control direction, input saturation and tracking error constraint. The Nussbaum function is employed to address the unknown control direction and a state observer is constructed by neural networks (NNs) to estimate the unmeasurable states. A new error constraint transformation is proposed to guarantee that the tracking error satisfies the prescribed performance. Then, a novel adaptive prescribed performance neural network (NN) output feedback tracking control method is designed. It is proved that the designed controller can guarantee the boundedness of all the signals in the closed-loop system and the prescribed time-varying tracking performance. Finally, simulations on two examples are performed to illustrate the efficiency of the proposed control method.

Deep reinforcement learning based finite-horizon optimal tracking control for nonlinear system

Abstract Reinforcement learning (RL) can be used to obtain an approximate numerical solution to the Hamilton-Jacobi-Bellman (HJB) equation. Recent advances in machine learning community enable the use of deep neural networks (DNNs) to approximate high-dimensional nonlinear functions as those that occur in RL, accurately without any domain knowledge. In the standard RL setting, both system and cost structures are unknown, and the amount of data needed to obtain an accurate approximation can be impractically large. Meanwhile, when the structures are known, they can be used to solve the HJB equation efficiently. Herein, the model-based globalized dual heuristic programming (GDHP) is proposed, in which the HJB equation is separated into value, costate, and policy functions. A particular class of interest in this research is finite horizon optimal tracking control (FHOC) problem. Additional issues that arise, such as time-varying functions, terminal constraints, and delta-input formulation, are addressed in the context of FHOC. The DNN structure and training algorithm suitable for FHOC are presented. A benchmark continuous reactor example is provided to illustrate the proposed approach.

Multidimensional Taylor network optimal control of SISO nonlinear systems for tracking by output feedback

SummaryIt is difficult or even impossible for the existing nonlinear system control methods to realize the real‐time tracking control of nonlinear systems in the presence of modeling errors by output feedback. For that sake, multidimensional Taylor network (MTN) optimal control method is proposed for the real‐time optimal tracking control of the SISO nonlinear constant system with modeling errors as such. On the basis of the original MTN, the control input item is added to the nonlinear dynamic model, which is then termed as the MTN optimal controller (MTNOC). Its initial parameters are trained by the conjugate gradient method and the minimum principle, according to the calculated optimal input and output of the controlled object in open‐loop status. The propagation learning algorithm is adopted to improve the MTN product term weights and eliminate the modeling errors during the real system adjustment process. Simulation results show that the MTNOC promises a high response rate. Despite the errors in the modeling process, MTNOC manages to stabilize the system for tracking the desired output. The experiment of overlaying an additional signal on the input signal proves MTNOC to be of excellent tracking characteristics, capable of inhibiting the disturbance signal to some extent. In short, by realizing the optimal closed‐loop tracking control of the SISO nonlinear constant system by output feedback, MTNOC guarantees its real‐time control accuracy, dynamic performance, robustness, and anti‐disturbance capability.

Performance guaranteed tracking control of nonlinear systems under anomaly actuation: A neuro-adaptive fault-tolerant approach

Abstract In this work, we investigate the performance guaranteed tracking control problem of a class of multi-input multi-output (MIMO) nonlinear systems with anomaly actuation. By introducing new forms of parameter estimation error together with Lyapunov function, and using neural network approach, the obstacles caused by anomaly actuation can be handled gracefully and the assumptions on control gain matrices in existing results are significantly relaxed. Furthermore, a strictly increasing function is introduced to form a scaling speed transformation, which directly impacts both the controller law and the adaptive law, accelerating the learning rate and thus enhancing the tracking performance. It is shown that all the closed-loop signals are uniformly bounded and the tracking error converges to an adjustable residual set with a pre-assignable decay rate during the tracking process. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure.

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.