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.     

基于ADP算法的带时滞及饱和的非线性系统最优控制

针对控制时滞及带饱和的一类离散时间非线性系统的最优控制问题,通过重构性能指标函数和对应的系统变换,处理了性能指标函数中的控制耦合项;继而引入一个合适的泛函,解决了控制带饱和问题.给出了一个新的性能指标函数,利用迭代自适应动态规划(ADP)算法获得最优控制.为实现该算法,采用神经网络逼近函数来求解最优控制问题.仿真结果验证了方法的有效性.     

非线性离散时间系统带ε误差限的自适应动态规划

为了获得非线性离散时间系统的最优控制策略,基于自适应动态规划的原理,提出了一种带误差限的自适应动态规划方法.对于一个任意的状态,用一个有限长度的控制序列近似最优控制序列,使性能指标与最优性能指标的误差在一个较小的范围内.选取一个非线性离散时间系统对算法的性能进行数值实验,结果验证了该算法的有效性,用较少的计算代价获得了近似最优的控制策略.     

基于迭代神经动态规划的数据驱动非线性近似最优调节

利用数据驱动控制思想,建立一种设计离散时间非线性系统近似最优调节器的迭代神经动态规划方法.提出针对离散时间一般非线性系统的迭代自适应动态规划算法并且证明其收敛性与最优性.通过构建三种神经网络,给出全局二次启发式动态规划技术及其详细的实现过程,其中执行网络是在神经动态规划的框架下进行训练.这种新颖的结构可以近似代价函数及其导函数,同时在不依赖系统动态的情况下自适应地学习近似最优控制律.值得注意的是,这在降低对于控制矩阵或者其神经网络表示的要求方面,明显地改进了迭代自适应动态规划算法的现有结果,能够促进复杂非线性系统基于数据的优化与控制设计的发展.通过两个仿真实验,验证本文提出的数据驱动最优调节方法的有效性.     

基于自适应最优控制的有限时间微分对策制导律

针对固定末端时刻拦截机动目标的制导系统,本文首先构建了非线性有限时间微分对策框架,将导弹拦截非线性系统的最优问题转化为一般非线性系统的最优控制问题,并通过自适应动态规划算法(adaptive dynamic programming, ADP)获得近似最优值函数与最优控制策略.为了有效实现该算法,本文利用一个具有时变权值和激活函数的评价网络来逼近Hamilton-Jacobi-Isaacs(HJI)方程的解,并在线更新.通过李雅普诺夫法来证明本文提出的控制策略可保证闭环微分对策系统稳定性和评价网络权值近似误差的有界性.最后给出一个非线性导弹拦截目标系统的仿真例子验证了该方法的可行性和有效性.     

一类非线性奇异摄动系统的近似最优控制

针对一类非线性奇异摄动系统,基于自适应动态规划算法提出了一种新型的近似最优控制设计方法.该方法基于奇异摄动系统的快、慢Hamilton-Jacobi-Bellman(HJB)方程,从初始性能指标开始,通过神经网络的近似和控制律与性能指标的逐步更新迭代,最终收敛到最优的性能指标,而不用直接求解复杂的HJB方程.同时给出了...     

动态规划最优控制在非线性系统中的应用

应用一种新的自适应动态最优化方法(ADP),在线实现对非线性连续系统的最优控制。首先应用汉密尔顿函数（Hamilton-Jacobi-Bellman, HJB）求解系统的最优控制,并应用神经网络BP算法对汉密尔顿函数中的性能指标进行估计,进而得到非线性连续系统的最优控制。同时引进一种新的自适应算法,基于参数误差,在线实现对系统进行动态最优求解,而且通过李亚普诺夫方法对参数收敛情况也进行详细的分析。最后,用仿真结果来验证所提出的方法的可行性。     

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.     

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。     

未固定初始状态的ε误差限最优控制

为有效控制离散非线性系统,使系统控制策略能够应对状态域的所有初始状态,在近似动态规划方法的基础上,提出一个未固定初始状态的带ε误差限的离散非线性系统优化控制算法。研究初始状态对离散系统控制策略的影响,确定在初始状态域边界上寻找最优初始点的方法。所求控制策略使初始状态域的所有性能指标函数在最大迭代步数内收敛,使性能指标与最优性能指标保持在精度ε内。为了易于实现算法,使用神经网络来近似性能指标函数和最优控制策略。结合实例,对该算法进行仿真分析,分析结果表明了算法的有效性。     

Finite horizon optimal control of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming

In this paper, we aim to solve the finite horizon optimal control problem for a class of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming (ADP) approach. A new ε-optimal control algorithm based on the iterative ADP approach is proposed which makes the performance index function converge iteratively to the greatest lower bound of all performance indices within an error according to ε within finite time. The optimal number of control steps can also be obtained by the proposed ε-optimal control algorithm for the situation where the initial state of the system is unfixed. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the ε-optimal control algorithm. Finally, a simulation example is given to show the results of the proposed method.     

An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games

In this paper, a new iterative adaptive dynamic programming (ADP) method is proposed to solve a class of continuous-time nonlinear two-person zero-sum differential games. The idea is to use the ADP technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero-sum differential games. If the saddle point does not exist, the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum. Stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved. Two simulation examples are given to illustrate the performance of the proposed method.     

Dual iterative adaptive dynamic programming for a class of discrete-time nonlinear systems with time-delays

In this paper, a new dual iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for a class of nonlinear systems with time-delays in state and control variables. The idea is to use the dynamic programming theory to solve the expressions of the optimal performance index function and control. Then, the dual iterative ADP algorithm is introduced to obtain the optimal solutions iteratively, where in each iteration, the performance index function and the system states are both updated. Convergence analysis is presented to prove the performance index function to reach the optimum by the proposed method. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the dual iterative ADP algorithm. Simulation examples are given to demonstrate the validity of the proposed optimal control scheme.     

Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound

In this paper, we aim to solve the finite-horizon optimal control problem for a class of non-linear discrete-time switched systems using adaptive dynamic programming(ADP) algorithm. A new ε-optimal control scheme based on the iterative ADP algorithm is presented which makes the value function converge iteratively to the greatest lower bound of all value function indices within an error according to ε within finite time. Two neural networks are used as parametric structures to implement the iterative ADP algorithm with ε-error bound, which aim at approximating the value function and the control policy, respectively. And then, the optimal control policy is obtained. Finally, a simulation example is included to illustrate the applicability of the proposed method.     

Optimal Constrained Self-learning Battery Sequential Management in Microgrid Via Adaptive Dynamic Programming

This paper concerns a novel optimal self-learning battery sequential control scheme for smart home energy systems. The main idea is to use the adaptive dynamic programming (ADP) technique to obtain the optimal battery sequential control iteratively. First, the battery energy management system model is established, where the power efficiency of the battery is considered. Next, considering the power constraints of the battery, a new non-quadratic form performance index function is established, which guarantees that the value of the iterative control law cannot exceed the maximum charging/discharging power of the battery to extend the service life of the battery. Then, the convergence properties of the iterative ADP algorithm are analyzed, which guarantees that the iterative value function and the iterative control law both reach the optimums. Finally, simulation and comparison results are given to illustrate the performance of the presented method.      

Stable iterative adaptive dynamic programming algorithm with approximation errors for discrete-time nonlinear systems

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. When the iterative control law and iterative performance index function in each iteration cannot be accurately obtained, it is shown that the iterative controls can make the performance index function converge to within a finite error bound of the optimal performance index function. Stability properties are presented to show that the system can be stabilized under the iterative control law which makes the present iterative ADP algorithm feasible for implementation both on-line and off-line. Neural networks are used to approximate the iterative performance index function and compute the iterative control policy, respectively, to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.     

Neural-network-based approach to finite-time optimal control for a class of unknown nonlinear systems

This paper proposes a novel finite-time optimal control method based on input–output data for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. In this method, the single-hidden layer feed-forward network (SLFN) with extreme learning machine (ELM) is used to construct the data-based identifier of the unknown system dynamics. Based on the data-based identifier, the finite-time optimal control method is established by ADP algorithm. Two other SLFNs with ELM are used in ADP method to facilitate the implementation of the iterative algorithm, which aim to approximate the performance index function and the optimal control law at each iteration, respectively. A simulation example is provided to demonstrate the effectiveness of the proposed control scheme.     

Policy Iteration for Optimal Control of Discrete-Time Time-Varying Nonlinear Systems

Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems, in this paper, a new iterative adaptive dynamic programming algorithm, which is the discrete-time time-varying policy iteration (DTTV) algorithm, is developed. The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance. The admissibility of the iterative control law is analyzed. The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution. To implement the algorithm, neural networks are employed and a new implementation structure is established, which avoids solving the generalized Bellman equation in each iteration. Finally, the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm, where the mass and pendulum bar length are permitted to be time-varying parameters. The effectiveness of the developed method is illustrated by numerical results and comparisons.