Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

Neural network robust control of a 3-DOF hydraulic manipulator with asymptotic tracking

Multiaxial hydraulic manipulators are complicated systems with highly nonlinear dynamics and various modeling uncertainties, which hinders the development of high-performance controller. In this paper, a neural network feedforward with a robust integral of the sign of the error (RISE) feedback is proposed for high precise tracking control of hydraulic manipulator systems. The established nonlinear model takes three-axis dynamic coupling, hydraulic actuator dynamics, and nonlinear friction effects into consideration. A radial basis function neural network (RBFNN) is synthesized to approximate the uncertain system dynamics and external disturbance, which can greatly reduce the dependence on accurate system model. In addition, a continuous RISE feedback law is judiciously integrated to deal with the residual unknown dynamics. Since the major unknown dynamics can be estimated by the RBFNN and then compensated in the feedforward design, the high-gain feedback issue in RISE feedback control will be avoided. The proposed RISE-based neural network robust controller theoretically guarantees an excellent semi-global asymptotic stability. Comparative simulation is performed on a 3-DOF hydraulic manipulator, and the obtained results verify the effectiveness of the proposed controller.     

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.     

Model reference tracking control of continuous-time periodic linear systems with actuator jumping fault and its applications in orbit maneuvering

This paper deals with the model reference tracking control problem of continuous-time periodic linear systems when the actuator occurs jumping fault. The main contribution is to formulate the parametric design algorithm for the systems by utilizing the parametric solution of the generalized Sylvester matrix equations. The existence condition of the controller is deduced based on the Lyapunov stability theory. The controller consists of the additive contribution of two terms: a feedback term and a feedforward term. The feedback term is the feedback control law which can stabilize the system with finite expected cost. The feedforward term is the complete parametric feedforward tracking compensator. The simulation for flying around mission is carried out about two spacecrafts in elliptical orbit. The simulation results show the effectiveness of the proposed approach.

     

Nonlinear asymptotic attitude tracking control of an underactuated 3-degree-of-freedom helicopter using neural network feedforward term

This paper proposes a new asymptotic attitude tracking controller for an underactuated 3-degree-of-freedom (DOF) laboratory helicopter system by using a nonlinear robust feedback and a neural network (NN) feedforward term. The nonlinear robust control law is developed through a modified inner-outer loop approach. The application of the NN-based feedforward is to compensate for the system uncertainties. The proposed control design strategy requires very limited knowledge of the system dynamic model, and achieves good robustness with respect to system parametric uncertainties. A Lyapunov-based stability analysis shows that the proposed algorithms can ensure asymptotic tracking of the helicopter’s elevation and travel motion, while keeping the stability of the closed-loop system. Real-time experiment results demonstrate that the controller has achieved good tracking performance.     

A new revised desired compensation adaptive control for enhanced tracking: application to RA-PKMs

A new controller based on desired compensation adaptation law (DCAL) is proposed in this paper. The original DCAL control input can be split up into three main separate terms; an adaptive feedforward term, a proportional-derivative (PD) feedback term and a compensation term. Inspired from the fact that nonlinear time-varying feedback gains lead to improved performance, we propose in this work to revisit DCAL control scheme by replacing the constant feedback gains in the PD feedback term by nonlinear time-varying ones. The proposed nonlinear gains are automatically adjusted according to the variation of the tracking error yielding improved tracking performance. Besides, to cope with the internal forces issue that appears in the case of redundantly actuated parallel kinematic manipulators (RA-PKMs), we propose to use a projection operator to reduce these forces. The projection operator, which is based on the kinematics of the manipulator, reduces the part of the control inputs responsible for internal forces. To demonstrate the relevance of the proposed control strategy, both standard DCAL and the proposed extended DCAL controller are experimentally implemented on a three degree of freedom (3-DOF) RA-PKM called Dual-V. Based on the obtained results, it is shown that the proposed controller outperforms the original one in terms of tracking performance while reducing the control effort.     

Independent tracking and regulation adaptive control with forgetting factor

This paper considers a discrete-time adaptive control algorithm with a forgetting factor applicable to minimum phase plants. The tracking and regulation objectives are independently specified. The relevance of the eigenvalues of the gain matrix (F_k) used in the updating equation for the adaptive parameters ($\text{}\text{?}\text{gq(k)}$) is shown. It is proved that if the maximum eigenvalue of the inverse of the gain matrix F_k has an upper bound and a non-zero lower bound then the global convergence of the control algorithm is insured. The result of the design is a simple control scheme using a linear constant feedforward controller and a nonlinear feedback controller. The performance of the control structure in tracking and regulation are evaluated by simulations.     

Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance

To reduce the adverse effects on the control performance and disturbance rejection caused by system uncertainty, a novel internal model based robust inversion feedforward and feedback 2DOF control approach was proposed for LPV system with disturbance. The proposed control approach combines the internal model control and robust inversion based 2DOF control, it utilizes internal model based control to reject external disturbance, utilizes robust inversion 2DOF control to enhance the control resolution and guarantee the system control performance. At first, a LMI synthesis approach for LPV system model identification and a disturbance compensator optimization design method which could minimize H_∞ norm of output error caused by disturbance are presented. Then, combined with internal loop for disturbance compensation, a robust inversion feedforward controller is designed by robust inversion approach and the feedback controller which could render the requirements of reference signal tracking performance and robustness satisfied is obtained by the H_∞ mixed sensitivity synthesis approach. Finally, atomic force microscopy (AFM) vertical positioning simulation experiments are conducted and the experiment results showed that the proposed control approach could achieve better output performance and disturbance rejection compared with conventional internal model based control and robust inversion based 2DOF control approach.     

Several algorithms for finite-model adaptive control

Finite-model adaptive control problem is studied for a class of discrete-time nonlinear uncertain systems. This problem was motivated by recent efforts on the capability and limitation of feedback mechanism and has the characteristics of “essentially” finite internal uncertainties. To solve this type of problem, based on different ideas, we introduce several approaches, controller falsification, controller combination, and pseudo-parameter estimation, to design the feedback control law and rigorously establish the stability of closed-loop system for several typical algorithms in these approaches. Our results show that, under reasonably weak conditions, capable feedback control laws exist dealing with the finite internal uncertainties of the system. These results together with related results in companion papers provide partial answers to the finite-model adaptive control problem and may lead to deeper understanding on the capability of the whole feedback mechanism.     

A nodal link perceptron network with applications to control of anonholonomic system

A new perceptron neural network (PNN) for functional approximation and control of a general class of nonlinear systems is introduced. The basic structure of the network along with the conditions for its exponential convergence under a suitable training law are derived. A novel discrete-time control strategy is formulated that employs the PNN for direct online estimation of the feedforward control input. The developed controller can be applied to both discrete- and continuous-time plants. Unlike most of the existing direct adaptive or learning schemes, the nonlinear plant is not assumed to be feedback linearizable. The developed controller is then applied for tracking control of a nonholonomic (free-flying) robot. The simulation results of this application demonstrate a perfect tracking performance after the network is fully trained.     

一种新型的移动机器人轨迹跟踪控制方法

主要是对非完整约束下移动机器人的轨迹跟踪控制进行了研究,提出了一种新型的基于移动机器人运动模型、具有全局渐近稳定性的跟踪控制方法。这种非线性控制方法主要分为前馈和反馈两个部分：前馈部分是一种滑模控制器,它是基于反演设计的思想设计了切换函数,采用指数趋近律,减少了滑模变结构控制的抖动,并使用Lyapunov第一法对控制系统进行了稳定性分析,证明了滑模跟踪控制器是稳定的;反馈部分是基于Lyapunov函数的方法设计的反馈控制器。通过前馈部分和反馈部分的相互作用,提高了移动机器人轨迹跟踪控制的精度。实验结果表明与一般的跟踪控制方法相比,控制效果明显改善,跟踪误差能在较短时间内收敛,具有很好的抗干扰性能。     

A new separation result for a class of quadratic-like systems with application to Euler-Lagrange models

A separation result for some kind of global stabilization via output feedback of a class of nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and some unboundedness observability on the other hand is presented. They allow to design, for any domain of output initial condition, some dynamic output feedback controller achieving global stability. It is also highlighted how disturbance attenuation can further be achieved on the same basis. As an example, the proposed conditions are shown to be satisfied by the class of so-called Euler-Lagrange systems, for which a tracking output feedback control law is thus proposed.     

Adaptive dynamic surface-based differential games for a class of pure-feedback nonlinear systems with output constraints

ABSTRACT

This paper investigates the zero-sum differential game problem for a class of uncertain nonlinear pure-feedback systems with output constraints and unknown external disturbances. A barrier Lyapunov function is introduced to tackle the output constraints. By constructing an affine variable at each dynamic surface control design step rather than utilising the mean-value theorem, the tracking control problem for pure-feedback systems can be transformed into an equivalent zero-sum differential game problem for affine systems. Then, the solution of associated Hamilton–Jacobi–Isaacs equation can be obtained online by using the adaptive dynamic programming technique. Finally, the whole control scheme that is composed of a feedforward dynamic surface controller and a feedback differential game control strategy guarantees the stability of the closed-loop system, and the tracking error is remained in a bounded compact set. The simulation results demonstrate the effectiveness of the proposed control scheme.     

局部对称积分型迭代学习控制

提出了一个新的迭代学习控制（ＩＬＣ）更新律用于连续线性系统的有限时间区间跟踪控制,迭代学习控制作为一个前馈控制,迭代学习控制作为一个前馈控制器加在已有的反馈控制器之上,对于上倥 的反馈控制信号作局部对称积分,所提出的迭代学习控制更新律具备较简单的形式且仅含有两个设计参数,即：学习增益和局部积分的区间长度,给出了收敛性分析以及设计步骤。     

基于控制参数化的注塑工业过程最优反馈控制方法

本文针对一类典型的注塑工业过程系统, 研究了注塑填充过程中产生的熔体流动速度最优跟踪控制问题, 提出了一种基于控制参数化的计算最优反馈控制器设计方法以实现注塑过程中熔融聚合物流动前沿位移的最优跟 踪控制, 进而达到改善注塑零件性能的高效生产目标. 首先, 面向注塑工艺复杂生产过程建立了动态过程系统数学 模型, 提出了注塑机内部熔融聚合物流动前沿位置的动态最优跟踪控制问题; 其次, 设计了一种多级反馈控制律, 通 过控制参数化方法将控制反馈核进行了参数化表示, 将控制器设计问题转化为一序列最优参数决策问题; 然后, 通 过状态灵敏度方程分析方法, 求解出了目标函数及约束条件关于决策变量参数梯度信息的显式表达式, 并基于所提 供的梯度信息结合序列二次规划算法进行了高效优化迭代求解; 最后, 通过实验仿真验证了本文所提出的最优反 馈控制器设计方法的可行性和有效性.     

Nonlinear predictive controller for a permanent magnet synchronous motor drive

A nonlinear predictive controller (NPC) for a permanent magnet synchronous motor (PMSM) is proposed in this paper. Its objective is high performance tracking of the rotor speed trajectory while maintaining the d-axis component of the armature current at zero. The load torque and the mismatched parameters are considered to be unknown perturbations. To ensure robustness against these perturbations, a disturbance observer is designed using a new gain function, and integrated into the control law. The combination of the nonlinear predictive controller and the disturbance observer works as a nonlinear controller. The overall closed-loop system is proved to be globally asymptotically stable depending on the design parameters. The validity of the proposed controller was tested by simulations. Satisfactory results were obtained with respect to the tracking of the speed trajectory and disturbance rejection.     

A self-adjusting active compliance controller for multiple robots handling an object

This paper presents the concept and experimental validation of a self-adjusting active compliance controller for n robots handling its compliant behaviour concerning partly unknown flexible object. The control strategy is based on the decomposition of the 6n-dimensional position/force space and includes a feedforward and feedback level. The feedforward level contains motion coordination, force distribution of external forces, creation of internal forces, and an additional loop adding the elastic displacements due to the applied forces to the planned robot positions. The feedback level is organized in the form of an active compliance control law. For adjusting the controller to the, in general, unknown flexible behaviour, which in practice is the main problem of the controller design, a quasi-static model of the system is derived for different contact cases of the object and a procedure is presented, which by use of this model is capable of determining the compliance of the considered system and therefore of adjusting the controller. Experiments with two puma-type robots have been conducted to show the applicability of the self-adjusting control strategy. The task has been to grasp and move an unconstrained object. It is shown, that the system can adjust the control parameters to the unknown system compliance and that the control performance is improved considerably.