Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach

A policy iteration algorithm of adaptive dynamic programming(ADP) is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then,the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks,the developed optimal tracking control scheme for chaotic systems is verified by a simulation.     

A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

We develop an online adaptive dynamic programming （ADP） based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.     

A novel stable value iteration-based approximate dynamic programming algorithm for discrete-time nonlinear systems

The convergence and stability of a value-iteration-based adaptive dynamic programming(ADP) algorithm are considered for discrete-time nonlinear systems accompanied by a discounted quadric performance index. More importantly than sufficing to achieve a good approximate structure, the iterative feedback control law must guarantee the closed-loop stability. Specifically, it is firstly proved that the iterative value function sequence will precisely converge to the optimum.Secondly, the necessary and sufficient condition of the optimal value function serving as a Lyapunov function is investigated. We prove that for the case of infinite horizon, there exists a finite horizon length of which the iterative feedback control law will provide stability, and this increases the practicability of the proposed value iteration algorithm. Neural networks(NNs) are employed to approximate the value functions and the optimal feedback control laws, and the approach allows the implementation of the algorithm without knowing the internal dynamics of the system. Finally, a simulation example is employed to demonstrate the effectiveness of the developed optimal control method.     

Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances

We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration(PI) is introduced to solve the min-max optimization problem. The off-policy adaptive dynamic programming(ADP) algorithm is then proposed to find the solution of the tracking Hamilton–Jacobi–Isaacs(HJI) equation online only using measured data and without any knowledge about the system dynamics. Critic neural network(CNN), action neural network(ANN), and disturbance neural network(DNN) are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded(UUB) of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.     

Hénon混沌系统广义预测函数控制快速收敛算法

提出一种具有收敛跟踪性能的Hénon混沌系统广义预测函数控制快速算法.基于已有的广义预测函数控制方法,依据混沌系统运动特性和实际中控制量变化趋势选取特殊形式的基函数,避免了控制律中的矩阵求逆计算,并在性能指标函数中引入确定的前馈增益矩阵,实现Hénon混沌系统对参考信号的收敛跟踪.仿真结果验证了该算法的有效性. 关键词： 广义预测控制 预测函数控制 Hénon混沌系统 前馈增益矩阵     

基于模糊滑模的有限时间混沌同步实现

提出了混沌同步有限时间实现问题.应用全程滑模控制技术，选择指数型终端滑模趋近律来设计滑模控制器，以实现一类混沌系统的状态同步.该设计方案针对混沌系统的参数不确定性和外界扰动，引入模糊基函数网络，在线估计不确定性和外部扰动的界值.同时该方案消除了滑模控制的到达阶段，状态始终保持在滑模面上，并能在有限时间内趋近于原点.最后以Duffing系统为例研究验证同步策略的可行性和有效性.     

输入受限的混沌系统同步控制

在混沌系统的同步控制中, 由于混沌系统对初始状态的敏感性, 一旦两个混沌系统的状态初值偏差大, 其状态同步往往需要高幅值的控制律来达到, 这给同步控制实现带来了困难, 并且在同步控制中, 两个混沌系统的初始值通常是未知的. 本文考虑控制输入受限情况下的混沌同步控制问题, 基于符号函数的近似表示式, 将受限的控制输入建模为连续可微的光滑函数, 在每一个采样点将同步控制误差系统近似为局部最优线性模型并设计连续型线性二次型调节器(LQR)最优控制律. 为降低混沌同步控制律的幅值和维持同步系统采样时刻之间的动态, 设计了等价的离散最优控制律, 并通过调整LQR性能加权矩阵值, 确保同步控制信号不会超出其受限的上界. 最后对统一混沌模型下的三种不同混沌系统同步控制进行了仿真研究. 仿真结果验证了方法的有效性. 关键词： 统一混沌模型 符号函数 输入受限 同步控制     

改进的保群算法及其在混沌系统中的应用

混沌系统的跟踪控制是近年来非线性控制领域研究的热点之一. 本文提出了一种基于快速下降控制方法的保群算法, 此方法使受控混沌系统能够快速稳定到相空间的一个不动点; 另外提出一种基于滑模控制方法的保群算法, 此方法使受控混沌系统能够快速跟踪一个确定的运动轨迹. 应用这两种新方法分别对两个经典的混沌系统(Lorenz系统和Duffing系统)进行了相应的数值实验, 实验结果表明这两种方法都具用较高的精度和稳定性.     

Control and synchronization of discrete-time chaotic systems via variable structure control technique

We present an input/output linearization control method incorporated in a discrete-time variable structure control technique to resolve the output tracking problem of a class of discrete-time nonlinear systems. The proposed control scheme is then applied to address the control and synchronization problems associated with the Hénon chaotic systems. Numerical simulations demonstrate the feasibility and robustness of the proposed control strategy.     

具有死区和饱和输入的自适应混沌控制

研究了一类具有死区饱和输入的不确定时滞混沌系统的跟踪问题.基于滑模控制原理，提出了一种自适应控制的新方案.该方法不仅克服了已有结果的设计缺陷，还取消了死区斜率已知和死区对称的假设，并从理论上分析证明了跟踪误差渐近收敛到零.最后，Duffing-Holme系统的仿真结果表明了该方案的有效性.     

基于高斯伪谱方法的混沌系统最优控制

针对混沌系统最优控制问题,提出一种基于高斯伪谱方法的数值求解新算法. 首先在勒让德-高斯点上构造Lagrange插值多项式并近似表示混沌系统最优控制中的状态变量和控制变量;接着将连续空间的最优控制问题转化为非线性规划问题;然后通过序列二次规划（SQP）算法获得最优解;最后对三个典型混沌系统的仿真实验结果表明,新方法能有效和快速地实现混沌系统的最优控制. 关键词： 混沌系统 最优控制 高斯伪谱法 非线性规划     

Fuzzy model based adaptive synchronization of uncertain chaotic systems: Robust tracking control approach

This Letter presents fuzzy model-based robust tracking control for the adaptive synchronization of uncertain chaotic systems. Fuzzy model and adaptive algorithm are employed to present the unknown chaotic systems. H^∞ and sliding mode control are combined to construct a robust tracking controller. The incorporated H^∞ controller can attenuate the external disturbance and approximation error to any prescribed level. The proposed scheme guarantees that all the variables are bounded and the tracking error is compensated.     

Distributed Consensus Tracking Control of Chaotic Multi-Agent Supply Chain Network: A New Fault-Tolerant,Finite-Time,and Chatter-Free Approach

Over the last years, distributed consensus tracking control has received a lot of attention due to its benefits, such as low operational costs, high resilience, flexible scalability, and so on. However, control methods that do not consider faults in actuators and control agents are impractical in most systems. There is no research in the literature investigating the consensus tracking of supply chain networks subject to disturbances and faults in control input. Motivated by this, the current research studies the fault-tolerant, finite-time, and smooth consensus tracking problems for chaotic multi-agent supply chain networks subject to disturbances, uncertainties, and faults in actuators. The chaotic attractors of a supply chain network are shown, and its corresponding multi-agent system is presented. A new control technique is then proposed, which is suitable for distributed consensus tracking of nonlinear uncertain systems. In the proposed scheme, the effects of faults in control actuators and robustness against unknown time-varying disturbances are taken into account. The proposed technique also uses a finite-time super-twisting algorithm that avoids chattering in the system’s response and control input. Lastly, the multi-agent system is considered in the presence of disturbances and actuator faults, and the proposed scheme’s excellent performance is displayed through numerical simulations.     

OPTIMAL TRACKING OF PARAMETER DRIFT IN A CHAOTIC SYSTEM: EXPERIMENT AND THEORY

We present a method of optimal tracking for chaotic dynamical systems with a slowly drifting parameter. The net drift in the parameter is assumed to be small: this makes detecting and tracking the drift more difficult. The method relies on the existence of underlying deterministic behavior in the dynamical system, yet neither requires a system model nor develops one. We begin by describing an experimental study where a heuristic optimality criterion gave good tracking performance: the tracking method there was based on maximizing smoothness and overall variation in the drift observer, which was found by solving an eigenvalue problem. We then develop a theory, based on simplifying assumptions about the chaotic dynamics, to explain the success of the tracking method for chaotic systems. For signals from deterministic systems that are sufficiently complex in a sense that we make precise, typical drift observers provide poor tracking performance and require the drift to be particularly slow. In contrast, our theory shows that the optimality criterion seeks out a special drift observer that both provides better tracking performance and allows the drift to be appreciably faster. For periodic or quasiperiodic systems (no chaos), good tracking is easily achievable and the present method is irrelevant. For stochastic systems (no determinism), the optimal tracking method does not asymptotically improve tracking performance. Exhaustive numerical simulations of a simple drifting chaotic map, first without and then with stochastic forcing, show agreement with theoretical predictions of tracking performance and validate the theory.     

广义Hénon混沌系统的自适应双模控制与同步

提出一种广义Hénon映射的自适应双模控制与同步方法.广义Hénon映射的混沌吸引子比Hénon映射的混沌吸引子更复杂,控制与同步困难,对于保密通信来说具有更高的安全性.该方法采用自适应双模控制,实现了广义Hénon映射的追踪控制与同步,提高了受控系统抑制参数摄动和随机扰动的能力,改善系统的鲁棒性.仿真结果验证了该方法的有效性.     

Hénon混沌系统广义预测控制无静差快速算法

提出了一种具有无静差跟踪性能的Hénon混沌系统广义预测控制快速算法.采用改进的时变遗忘因子递推最小二乘方法辨识混沌系统,通过在常规广义预测控制性能指标函数中引入前馈增益矩阵与柔化矩阵,并将MP神经元网络与BP算法相结合在线调整柔化因子,实现系统对参考信号的无静差快速跟踪.该算法避免了矩阵求逆计算,能够很好地跟踪参考信号.仿真结果验证了该方法的有效性. 关键词： 广义预测控制 Hénon混沌系统 前馈增益矩阵 柔化矩阵     

一类离散时间广义系统的迭代学习控制

针对一类离散时间广义系统,提出了一种离散迭代学习控制算法.首先,通过非奇异变换将离散时间广义系统分解为正常离散状态方程和代数方程的形式.然后,利用上一次迭代学习获得的前一时刻误差和当前时刻误差来修正上一次的控制量,从而获得下一次迭代学习的新控制量,并对算法的收敛性进行了理论证明,给出了算法收敛的充分条件.研究结果表明,所提算法能够在有限时间区间内实现系统状态对期望状态的完全跟踪.最后,通过仿真算例进一步验证了所提算法的有效性.     

一类参数未知混沌系统的追踪控制与参数辨识

针对一类参数未知的混沌系统,提出一种追踪控制方法,基于Lyapunov稳定性理论,设计了追踪控制器和参数自适应控制律,实现了混沌系统的追踪控制和未知参数的辨识.以统一混沌系统为例进行了数值模拟,结果表明了该方法的有效性. 关键词： 混沌系统 追踪控制 参数辨识     

Adaptive synchronization of uncertain chaotic systems via switching mechanism

This paper deals with the problem of synchronization for a class of uncertain chaotic systems.The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error,with unknown growth rate.A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system.Based on the Lyapunov approach,the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities.To demonstrate the efficiency of the proposed scheme,the well-known chaotic system namely Chua’s circuit is considered as an illustrative example.