Observer-based Adaptive Optimal Control for Unknown Singularly Perturbed Nonlinear Systems With Input Constraints

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-time scales dynamic neural network (MTSDNN) observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman (HJB) equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input/output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach.      

Online Adaptive Approximate Optimal Tracking Control with Simplified Dual Approximation Structure for Continuous-time Unknown Nonlinear Systems

This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control problem of continuous-time nonlinear systems with unknown dynamics. The requirement of the complete knowledge of system dynamics is avoided by employing an adaptive identifier in conjunction with a novel adaptive law, such that the estimated identifier weights converge to a small neighborhood of their ideal values. An adaptive steady-state controller is developed to maintain the desired tracking performance at the steady-state, and an adaptive optimal controller is designed to stabilize the tracking error dynamics in an optimal manner. For this purpose, a critic neural network (NN) is utilized to approximate the optimal value function of the Hamilton-Jacobi-Bellman (HJB) equation, which is used in the construction of the optimal controller. The learning of two NNs, i.e., the identifier NN and the critic NN, is continuous and simultaneous by means of a novel adaptive law design methodology based on the parameter estimation error. Stability of the whole system consisting of the identifier NN, the critic NN and the optimal tracking control is guaranteed using Lyapunov theory; convergence to a near-optimal control law is proved. Simulation results exemplify the effectiveness of the proposed method.      

Adaptive Tracking Control for Nonlinear Systems with a Class of Input Nonlinearities

An adaptive tracking control approach is presented for nonlinear systems with a class of input nonlinearities. A generalized model has been developed for a class of non‐smooth nonlinearities that include dead‐zone, backlash and ‘backlash‐like’ hysteresis. By using the developed model and Nussbaum‐gain technique, the problem of input nonlinearity is solved perfectly. The proposed method is available even when the designer is uncertain about the type of input nonlinearities mentioned above, and the knowledge on the bounds of these nonlinearity parameters is not required. Furthermore, it is proved that all closed‐loop signals are bounded and the tracking error converges to a small residual set asymptotically. Two simulation examples are provided to demonstrate the effectiveness of the proposed method.     

Optimal Fixed-Point Tracking Control for Discrete-Time Nonlinear Systems via ADP

Based on adaptive dynamic programming (ADP), the fixed-point tracking control problem is solved by a value iteration (Ⅵ) algorithm. First, a class of discrete-time (DT) nonlinear system with disturbance is considered. Second, the convergence of a Ⅵ algorithm is given. It is proven that the iterative cost function precisely converges to the optimal value, and the control input and disturbance input also converges to the optimal values. Third, a novel analysis pertaining to the range of the discount factor is presented, where the cost function serves as a Lyapunov function. Finally, neural networks (NNs) are employed to approximate the cost function, the control law, and the disturbance law. Simulation examples are given to illustrate the effective performance of the proposed method.      

随机伺服系统自适应二次最优组合控制

本文基于极点在线优化原理和随机过程理论,针对缓时变随机伺服系统提出一种参数自适应和二次性能最优的组合控制.这种控制形式简单、运算量小,能较好地适应系统的时变特性,并保持系统在不同参数与工况下具有最佳跟踪性能.文章讨论了控制的收敛性,并通过仿真和应用实例显示这种控制的有效性及良好的鲁棒性.     

带有输入和状态时滞的高阶非线性前馈系统的自适应控制

本文考虑了一类高阶不确定非线性前馈系统的自适应镇定问题.将高阶非线性进一步放宽到不仅允许状态时滞,而且还具有未知增长率.通过将自适应方法、动态增益控制方法和增加幂次积分器法结合,设计了一个状态反馈控制器.所设计的控制器保证了闭环系统的所有信号有界,平衡点全局稳定,并且原状态收敛到0.     

基于动态投入产出控制系统的最优跟踪

研究动态投入产出系统的最优产出跟踪控制问题。根据实际产出需求,采用鲁棒消费策略,修正产出同时使消费过程中的目标函数达到最优。利用离散广义系统的控制的有关理论实现了产出的最优跟踪控制,并给出了具体的优化消费调整策略。算例表明:这种策略实现了对实际产出的渐近跟踪。     

基于自适应动态规划的一类带有时滞的离散时间非线性系统的最优控制策略

针对一类状态和控制变量均带有时滞的非线性系统的带有二次性能指标函数最优控制问题, 本文提出了一种基于新的迭代自适应动态规划算法的最优控制方案. 通过引进时滞矩阵函数, 应用动态规划理论, 本文获得了最优控制的显式表达式, 然后通过自适应评判技术获得最优控制量. 本文给出了收敛性证明以保证性能指标函数收敛到最优. 为了实现所提出的算法, 本文采用神经网络近似性能指标函数、计算最优控制策略、求解时滞矩阵函数、以及给非线性系统建模. 最后本文给出了两个仿真例子说明所提出的最优策略的有效性.     

Adaptive Fuzzy Dynamic Surface Control of Flexible-Joint Robot Systems With Input Saturation

In this paper, we propose an adaptive fuzzy dynamic surface control (DSC) scheme for single-link flexible-joint robotic systems with input saturation. A smooth function is utilized with the mean-value theorem to deal with the difficulties associated with input saturation. An adaptive DSC design with an auxiliary first-order filter is used to solve the "explosion of complexity" problem. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood around zero. The main advantage of the proposed method is that only one adaptation parameter needs to be updated, which reduces the computational burden significantly. Simulation results demonstrate the feasibility of the proposed scheme and the comparison results show that the improved DSC method can reduce the computational burden by almost two thirds in comparison with the standard DSC method.      

基于状态全反馈的动态迟滞非线性系统自适应控制

该文针对不平滑、多映射动态迟滞非线性系统，提出了一种基于神经网络自适应控制方案。在该方案中，通过利用神经网络来逼近模型误差，避免了目前常用逆模型补偿方案中，需求取复杂逆模型的问题。应用Lyapnov稳定定理，证明了整个闭环系统的跟踪误差及神经网络权值将收敛到零点一个有界邻域内。仿真结果表明，所提出的控制方案能够有效补偿迟滞非线性对系统的影响。     

一类双线性系统的最优跟踪控制问题

针对一类具有二次型性能指标的双线性系统的最优跟踪控制问题,提出了一种通过逐次逼近法设计最优控制律的近似方法。首先将状态向量含有时滞的双线性系统的最优跟踪问题转化为最优调节问题;然后利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题族,得到调节系统的最优控制律,并可以通过截取最优控制序列的有限项得到调节系统的前馈-反馈次优控制律。最后,将最优控制问题转化为最优跟踪问题。仿真结果表明,此方法达到了较好的跟踪效果。     

非线性不确定系统的自适应观测器设计

非线性状态观测器可改善过程控制性能和故障诊断,针对一类参数不确定非线性系统提出了自适应观测器设计方法。通过微分同胚变换,将非线性系统转换为仅依赖原系统输入、输出的自适应观测器规范形式。利用自适应调节器估计未知参数,用构造的观测器实现状态的重构。Lyapunov稳定性理论分析了状态观测误差动态方程的稳定性,用来证明所设计的自适应观测器为全局渐近收敛的,既实现了系统状态的渐近重构又确保了在持续激励条件下未知参数估计以指数快速收敛到真值,并通过仿真试验。仿真结果表明提出方法的有效性。     

Optimal Neuro-Control Strategy for Nonlinear Systems With Asymmetric Input Constraints

In this paper, we present an optimal neuro-control scheme for continuous-time (CT) nonlinear systems with asymmetric input constraints. Initially, we introduce a discounted cost function for the CT nonlinear systems in order to handle the asymmetric input constraints. Then, we develop a Hamilton-Jacobi-Bellman equation (HJBE), which arises in the discounted cost optimal control problem. To obtain the optimal neurocontroller, we utilize a critic neural network (CNN) to solve the HJBE under the framework of reinforcement learning. The CNN’s weight vector is tuned via the gradient descent approach. Based on the Lyapunov method, we prove that uniform ultimate boundedness of the CNN’s weight vector and the closed-loop system is guaranteed. Finally, we verify the effectiveness of the present optimal neuro-control strategy through performing simulations of two examples.      

Robust Adaptive Attitude Control for Non-rigid Spacecraft With Quantized Control Input

In this paper,an adaptive backstepping control scheme is proposed for attitude tracking of non-rigid spacecraft in the presence of input quantization,inertial uncertainty and external disturbance.TThe control signal for each actuator is quantized by sector-bounded quantizers,including the logarithmic quantizer and the hysteresis quantizer.By describing the impact of quantization in a new affine model and introducing a smooth function and a novel form of the control signal,the influence caused by input quantization and external disturbance is properly compensated for.Moreover,with the aid of the adaptive control technique,our approach can achieve attitude tracking without the explicit knowledge of inertial parameters.Unlike existing attitude control schemes for spacecraft,in this paper,the quantization parameters can be unknown,and the bounds of inertial parameters and disturbance are also not needed.In addition to proving the stability of the closed-loop system,the relationship between the control performance and design parameters is analyzed.Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems. Unlike existing optimal state feedback control, the control input of the optimal parallel control is introduced into the feedback system. However, due to the introduction of control input into the feedback system, the optimal state feedback control methods can not be applied directly. To address this problem, an augmented system and an augmented performance index function are proposed firstly. Thus, the general nonlinear system is transformed into an affine nonlinear system. The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically. It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function. Moreover, an adaptive dynamic programming (ADP) technique is utilized to implement the optimal parallel tracking control using a critic neural network (NN) to approximate the value function online. The stability analysis of the closed-loop system is performed using the Lyapunov theory, and the tracking error and NN weights errors are uniformly ultimately bounded (UUB). Also, the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals. Finally, the effectiveness of the developed optimal parallel control method is verified in two cases.      

连续时间系统的自适应鲁棒控制及应用

本文针对未知SISO系统,采用自适应与鲁棒控制相结合的方法,提出一种按球域切换的自适应鲁棒控制规律,证明了全局稳定性和渐近调节的可实现性.该算法已用于水轮机转速调节,现场实验结果说明了理论的正确性.     

Adaptive Inverse Control of Excitation System with Actuator Uncertainty

In this paper, we present a new approach of designing adaptive inverse controller for synchronous generator excitation system containing nonsmooth nonlinearities in actuator device. The proposed controller considers not only the dynamics of generator but also nonlinearities in actuator. To address such a challenge, support vector machines (SVM) is adopted to identify the plant and to construct the inverse controller. SVM networks, used to compensate nonlinearities in synchronous generator as well as in actuator, are adjusted online by an adaptive law via back propagation (BP) algorithm. To guarantee convergence and for fast learning, adaptive learning rate and convergence theorem are developed. Simulation results are given, showing satisfactory control performance and illustrate the potential of the proposed adaptive inverse controller as useful for practical purpose.     

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks (NNs) tracking controller is proposed for a class of single-input/singleoutput (SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real (SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.      

一类带死区输入的非线性不确定系统滑模自适应控制

研究一类参数不确定和带有未知死区的非线性系统滑模自适应控制问题。将死区分解为两部分,被控系统中有两类不确定性的系统参数,一类是常值的未知系统参数;另一类是时变的未知系统参数和部分未知的死区。采用滑模控制和自适应控制相结合的方式,第一类不确定性可以由自适应控制来处理,而第二类不确定性可以由滑模控制来处理,即滑模自适应控制器。为了消除滑模控制所带来的抖振,引入边界层。采用’Lyapunov函数证明了系统的稳定性。仿真实验表明方法的可行性。     

基于数据ADP算法的一类带有执行器饱和的未知离散时间系统最优跟踪控制

针对一类带有执行器饱和的未知动态离散时间非线性系统, 提出了一种新的最优跟踪控制方案. 该方案基于迭代自适应动态规划算法, 为了实现最优控制, 首先建立了未知系统动态的数据辨识器. 通过引入M网络, 获得了稳态控制的精确表达式. 为了消除执行器饱和的影响, 提出了一个非二次的性能指标函数. 然后提出了一种迭代自适应动态规划算法获得最优跟踪控制的解, 并给出了收敛性分析. 为了实现最优控制方案, 神经网络被用来构建数据辨识器、计算性能指标函数、近似最优控制策略和求解稳态控制. 仿真结果验证了本文所提出的最优跟踪控制方法的有效性.