一类非线性离散系统自适应准滑模控制

针对一般非线性离散时间系统的不确定性和扰动抑制问题, 提出一种新的自适应准滑模控制算法. 算法包括两部分, 其一是基于紧格式动态线性化模型的自适应准滑模控制器设计, 其中动态线性化方法中“伪偏导数”的估计算法仅依赖于系统I/O 实时量测值. 其二是采用径向基神经网络估计器来估计系统的综合不确定性. 理论分析证明了系统的BIBO稳定性. 仿真结果验证了所提算法的有效性.     

离散非线性零和博弈的事件驱动最优控制方案

在求解离散非线性零和博弈问题时,为了在有效降低网络通讯和控制器执行次数的同时保证良好的控制效果,本文提出了一种基于事件驱动机制的最优控制方案.首先,设计了一个采用新型事件驱动阈值的事件驱动条件,并根据贝尔曼最优性原理获得了最优控制对的表达式.为了求解该表达式中的最优值函数,提出了一种单网络值迭代算法.利用一个神经网络构建评价网.设计了新的评价网权值更新规则.通过在评价网、控制策略及扰动策略之间不断迭代,最终获得零和博弈问题的最优值函数和最优控制对.然后,利用Lyapunov稳定性理论证明了闭环系统的稳定性.最后,将该事件驱动最优控制方案应用到了两个仿真例子中,验证了所提方法的有效性.     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

非线性主动悬架系统自适应最优控制

针对非线性主动悬架系统多性能指标综合优化问题,提出一类自适应最优控制方法.首先,通过引入一阶低通滤波操作,利用系统输入输出构建结构简单且调节参数少的一类未知非线性动态估计器,在线估计系统未知非线性动态;其次,构建包含乘驾舒适度、悬架行程空间及输入能耗的性能指标函数,采用单层神经网络对最优性能指标函数进行在线逼近,并得到新的哈密尔顿函数;为实现在线求解,构建一类新的基于参数估计误差信息的自适应律,在线更新神经网络权值并计算最优控制律;最后,理论分析闭环系统稳定性和收敛性,并通过专业软件Carsim与Matlab/Simulink搭建的联合仿真平台给出的对比仿真结果,验证所提出方法可有效解决主动悬架系统多目标性能优化控制问题,提升主动悬架系统综合性能.     

一类非线性离散系统的直接自适应模糊控制

针对一类含延迟非线性离散系统,提出了一种直接自适应模糊控制器设计的新方案．将系统用T-S模糊模型来表示,并基于并行分布补偿(PDC)基本思想设计了一种具有未知参数的模糊控制器,同时采用梯度下降算法对该控制器的参数进行在线辨识．通过输入到状态稳定(ISS)方法,证明了系统输出和参考输出的误差有界且满足一定的平均性能．仿真表明本方法的有效性．     

非线性离散奇异摄动系统的组合优化控制方法的合理性分析

分析一类非线性离散奇异摄动系统的降阶组合优化控制器的合理性, 即降阶组合控制器与原始高阶优化控制器之间的关系. 基于快、慢子系统的解耦, 分别对快、慢子系统设计子优化控制器, 并进一步提出作用于原高阶系统的组合优化控制器. 对原高阶系统设计传统高阶优化控制器, 提出组合优化控制器近似等于传统高阶优化控制器的充分条件. 最后通过仿真验证了所得到结论的正确性.

     

Adaptive control of a class of discrete-time MIMO nonlinear systems with uncertain couplings

In this article, adaptive control is investigated for a class of discrete-time multi-input-multi-output nonlinear systems in block-triangular form with uncertain couplings of delayed states among subsystems. Future states prediction is carried out to facilitate adaptive control design and auxiliary outputs are introduced to develop a novel compensation mechanism for the uncertain nonlinear couplings. By using Lyapunov method and ordering signals growth rate, it is rigorously proved that all the signals in the whole closed-loop systems are globally bounded and the output tracking errors asymptotically converge to zeros. The effectiveness of the proposed control is demonstrated in the simulation study.     

A novel optimal tracking control scheme for a class of discrete-time nonlinear systems using generalised policy iteration adaptive dynamic programming algorithm

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm, called generalised policy iteration ADP algorithm, is developed to solve optimal tracking control problems for discrete-time nonlinear systems. The idea is to use two iteration procedures, including an i-iteration and a j-iteration, to obtain the iterative tracking control laws and the iterative value functions. By system transformation, we first convert the optimal tracking control problem into an optimal regulation problem. Then the generalised policy iteration ADP algorithm, which is a general idea of interacting policy and value iteration algorithms, is introduced to deal with the optimal regulation problem. The convergence and optimality properties of the generalised policy iteration algorithm are analysed. Three neural networks are used to implement the developed algorithm. Finally, simulation examples are given to illustrate the performance of the present algorithm.     

A new neural network-based approach for self-tuning control of nonlinear SISO discrete-time systems

This article presents a new neural network-based approach for self-tuning control of nonlinear single-input single-output (SISO) discrete-time dynamic systems. According to the approach, a neural network ARMAX (NN-ARMAX) model of the system is identified and continuously updated, using an online training algorithm. Control design is accomplished by solving an optimal discrete-time linear quadratic tracking problem using an observer-type linear state-space Kalman innovation model, which is built from the parameters of a local linear version of the NN-ARMAX model. The state-feedback control law is implemented using the Kalman state, which is calculated without estimating the noise covariance properties. The proposed control approach is shown to be very effective and outperforms the self-tuning control approach based on a linear ARMAX model on two simulation examples.     

A new adaptive scheme for a class of discrete-time nonlinear systems

A new adaptive control scheme for discrete-time systems is proposed. The objective is the tracking of the trajectory. Global boundedness convergence and boundedness are obtained for a certain subclass of nonlinear systems.     

基于单网络ADP的一类未知非线性系统的近似最优控制

针对一类未知的连续非线性系统,提出一个基于单网络近似动态规划(ADP)的近似最优控制方案。该方案通过设计一个新型的递归神经网络(RNN)辨识器放松了系统模型需已知或部分已知的要求,并利用一个神经网络(NN)近似系统的性能指标函数消除了常规ADP方法中的控制网络。通过Lyapunov理论分析严格证明了闭环系统内所有信号一致最终有界,并且所获得的性能指标函数和控制输入分别收敛到最优性能指标函数和最优控制输入的小邻域内。仿真结果验证了所提出控制方案的有效性。     

受扰非线性离散系统的前馈反馈最优控制

利用逐次逼近法研究含外部扰动的非线性离散系统的线性二次型前馈反馈最优控制问题.首先将系统的最优控制问题转化为非线性两点边值问题族.其次,构造了该问题族的由精确线性项和非线性补偿项组成的解序列,并证明了解序列一致收敛到系统的最优解.最后,通过截取最优控制序列解中非线性补偿项的有限项,得到系统的前馈反馈次优控制(FFSOC)律及设计算法.仿真算例表明,该算法容易实现,且对抑制外部扰动的鲁棒性优于经典的反馈次优控制(FSOC).     

一类非线性离散时间系统的模糊辨识

对一类非线性离散时间系统提出了模糊辨识方法,此方法用与未知参数向量成线性关系的模糊逻辑系统作为辨识模型,并通过自适应学习律对此模糊逻辑系统中的未知参数进行自适应调节,文中证明了此方法可使辨识误差收敛到原点的一个邻域内。仿真结果验证了此方法的有效性。     

Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach

In this paper, a finite-horizon neuro-optimal tracking control strategy for a class of discrete-time nonlinear systems is proposed. Through system transformation, the optimal tracking problem is converted into designing a finite-horizon optimal regulator for the tracking error dynamics. Then, with convergence analysis in terms of cost function and control law, the iterative adaptive dynamic programming (ADP) algorithm via heuristic dynamic programming (HDP) technique is introduced to obtain the finite-horizon optimal tracking controller which makes the cost function close to its optimal value within an ?-error bound. Three neural networks are used as parametric structures to implement the algorithm, which aims at approximating the cost function, the control law, and the error dynamics, respectively. Two simulation examples are included to complement the theoretical discussions.     

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.     

Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE

In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.     

Observer-based synergetic adaptive neural network control for a class of discrete-time nonlinear systems with dead-zone

In this paper, the observer-based synergetic adaptive neural network control method is designed for a class of discrete-time systems with dead-zone. A macro-variable is introduced by a synergetic approach to control theory and neural networks are utilised to estimate unmeasured states and unknown functions in the system. Furthermore, by employing an adaptive design procedure and Lyapunov stability theory, the closed-loop system stability is guaranteed, and the desired system performance is achieved simultaneously. Finally, some simulation results are given to prove the validity of the developed control method.     

Discrete-time optimal control for stochastic nonlinear polynomial systems

This paper presents a solution to the discrete-time optimal control problem for stochastic nonlinear polynomial systems over linear observations and a quadratic criterion. The solution is obtained in two steps: the optimal control algorithm is developed for nonlinear polynomial systems by considering complete information when generating a control law. Then, the state estimate equations for discrete-time stochastic nonlinear polynomial system over linear observations are employed. The closed-form solution is finally obtained substituting the state estimates into the obtained control law. The designed optimal control algorithm can be applied to both distributed and lumped systems. To show effectiveness of the proposed controller, an illustrative example is presented for a second degree polynomial system. The obtained results are compared to the optimal control for the linearized system.     

未知饱和控制系统有穷域最优控制

针对带有饱和执行器且局部未知的非线性连续系统的有穷域最优控制问题,设计了一种基于自适应动态规划(ADP)的在线积分增强学习算法,并给出算法的收敛性证明.首先,引入非二次型函数处理控制饱和问题.其次,设计一种由常量权重和时变激活函数构成的单一网络,来逼近未知连续的值函数,与传统双网络相比减少了计算量.同时,综合考虑神经网络产生的残差和终端误差,应用最小二乘法更新神经网络权重,并且给出基于神经网络的迭代值函数收敛到最优值的收敛性证明.最后,通过两个仿真例子验证了算法的有效性.     

离散时间非线性系统的数据驱动无模型自适应迭代学习控制

本文基于迭代域的动态线性化方法,提出了一类单入单出离散时间非线性系统的数据驱动无模型自适应迭代学习控制方案.无模型自适应迭代学习控制本质上属于一种数据驱动控制方法,仅利用被控对象的输入输出数据即可实现控制方案的设计.理论分析表明无模型自适应迭代学习控制方案可以保证最大学习误差的单调收敛性.数值仿真和快速路交通控制应用验证了无模型自适应迭代学习控制方案的有效性.