Adaptive neuro-genetic control of chaos applied to the attitude control problem

Conventional adaptive control techniques have, for the most part, been based on methods for linear or weakly non-linear systems. More recently, neural network and genetic algorithm controllers have started to be applied to complex, non-linear dynamic systems. The control of chaotic dynamic systems poses a series of especially challenging problems. In this paper, an adaptive control architecture using neural networks and genetic algorithms is applied to a complex, highly nonlinear, chaotic dynamic system: the adaptive attitude control problem (for a satellite), in the presence of large, external forces (which left to themselves led the system into a chaotic motion). In contrast to the OGY method, which uses small control adjustments to stabilize a chaotic system in an otherwise unstable but natural periodic orbit of the system, the neuro-genetic controller may use large control adjustments and proves capable of effectively attaining any specified system state, with no a prioriknowledge of the dynamics, even in the presence of significant noise.This work was partly supported by SERC grant 90800355.     

蔡氏混沌系统网络的混沌同步及其保密通信

利用非线性函数耦合混沌同步方法,研究蔡氏混沌系统的同步问题．依据线性系统的稳定性分析准则, 证明耦合系数k = 0:5 时非线性函数耦合混沌系统的同步稳定性,并数值模拟检验其有效性．基于Routh-Hurwitz 稳 定性判据,推导出非线性耦合强度的下限,即k > 0:427．将非线性函数耦合同步方法推广到完全连接网络,证明了 网络同步的稳定性．在此基础上,利用混沌掩盖构造完全连接网络的保密通信系统,并通过数值仿真证明其可行 性．     

离散混沌系统的参数自适应控制

提出多重参数离散混沌系统的参数自适应控制的新方法,利用可调系统与参考模型之间的耦合关系,给出基于系统变量作为观测量的参数自适应控制算法,采用Ｌｙａｐｕｎｏｖ函数方法证明了参数控制系统是渐近稳定的。仿真结果表明文中给出的控制算法具有较快的收敛速度,并讨论了系统参数是非线性形式的一般系统及其不确定的外界噪声扰动对系统的影响。     

Nonlinear Feedback Control for the Lorenz System

The Lorenz system is well known for its ability to produce chaotic motion and the control problem of this system has attracted much attention in recent years. In this paper, control of the Lorenz chaotic systems based on a nonlinear feedback technique is presented. The objective of control is two-fold: one is to drive the system to one of equilibrium points associated with uncontrolled chaotic motion and the other is to let one of the closed-loop system states track a given signal. The controllers designed here are based on exact linearization theory of nonlinear systems and can regulate the closed-loop system states globally to a given point. Finally, illustrative examples show the effectiveness of the proposed design method.     

Powerful and flexible fuzzy algorithm for nonlinear dynamic systemidentification

A new powerful and flexible fuzzy algorithm for nonlinear dynamic system identification is presented. It is based on the identification of the derivative of the system state, instead of the future system state. The membership functions of the underlying static fuzzy model are two-sided Gaussian functions and the learning algorithm is a hybrid-nested routine based on least-squares, quasi-Newton and simplex optimization methods. Moreover, a simple clustering algorithm based on an additional higher level fuzzy model is proposed. The application to the identification of the Mackey-Glass chaotic time series is presented and compared with previous results in terms of maximum error and nondimensional error index. Finally, the application to a test nonlinear dynamic system is presented to show the capabilities of the clustering algorithm. The obtained results show that the proposed algorithm can find wide application in practical problems, such as in nonlinear electronic circuit design     

一类不确定分数阶混沌系统的同步控制

针对一类参数未知,状态不能全部测量的分数阶混沌系统的同步控制问题,结合状态观测器和自适应方法,提出了一种更符合工程实际的新的控制方案,利用分数阶微积分稳定性理论,给出了基于状态观测器的控制律和自适应律。该同步方法理论严格,没有强加在系统上的限制条件,适用范围比较宽,便于实现,并且保留了非线性项,达到同步的时间短。以分数阶R~ssler系统为研究对象,实现了参数未知,状态不能全部测量的分数阶混沌系统同步。理论分析与计算机仿真结果证实了该方法的有效性。     

基于两级算法的混沌控制

提出了一种两级算法,可以解决连续混沌系统的最小能量控制问题,首先,给出一个二次目标函数,同时把混沌系统分解为线性部分和非线性部分.上级算法对混沌系统中的非线性部分进行预估,并把整个原系统表为带有常系数的线性系统;下级算法用极小值原理解决这个典型线性二次最优控制问题,并把解返回到上级算法,上级算法根据下级的解对非线性部分重新预估.这样通过两级间不断的信息交换,最终得到混沌系统的最优控制律.该方法不仅实现了对混沌系统的控制,而且在整个控制过程中保证控制能耗为最小.证明了算法的收敛性和闭环系统的稳定性.对统一混沌系统的仿真结果表明了控制策略的有效性.     

一种基于离散混沌系统的密钥流设计算法

本文设计了一种基于离散混沌系统的密钥流发生器算法．通过把简单混沌系统 与线性系统、分段线性状态反馈函数所形成的混沌系统在阈值化后进行异或运算，使得输出 的密钥流为不可预测性的伪随机序列．分析和仿真结果表明，本算法能有效地抵抗对系统的 预测攻击及统计分析，能够达到密码学上对密钥流的要求．该算法可作为流密码体制中的密 钥流发生器．     

Synchronization of chaotic attractors with different equilibrium points

This paper investigates the synchronization of coupled chaotic systems with many equilibrium points. By addition of an external switching piecewise-constant controller, the system changes to a new one with several independent chaotic attractors in the state space. Then, by addition of a nonlinear state feedback control, the chaos synchronization is presented. This method can be used in many couples of chaotic systems characterized by the same equilibrium point or by two different equilibrium points, even they are the same systems (Lorenz, Jerk, Van der Pol) or two chaotic systems with different structures (Lorenz modified).     

基于预测控制的混沌系统参数微调控制方法

本文将预测控制理论引入混沌系统的控制研究中，提出一种基于预测控制的混沌系统参数微调控制方法，通过对控制参数进行微调，将模型未知时的混沌运动稳定到系统的不稳定不动点处．与现有同类方法相比，本控制系统具有快得多的响应速度，需要较短的时间就能实现混沌系统的控制．本方法能够控制超混沌系统，算法简便，控制算法的收敛性和控制系统的稳定性能够保证，理论分析和仿真实验都表明了本方法的有效性．     

Synchronization of fractional-order uncertain chaotic systems with input nonlinearity

In this paper, sliding mode control has been designed for synchronization of fractional order uncertain chaotic systems with input nonlinearity. First, sliding mode control law has been taken from chaotic state error system which is asymptotically stable. Second, the shown sliding mode control ensures that fractional-order error system is asymptotically stable in the presence of uncertainty and nonlinear input. Simulation results using MATLAB software show that the designed controller is able to synchronize fractional-order chaotic systems in the presence of the mentioned factors.     

Hybrid threshold strategy‐based adaptive tracking control for nonlinear stochastic systems with full‐state constraints

This article focuses on the adaptive tracking control problem for a class of interconnected nonlinear stochastic systems under full‐state constraints based on the hybrid threshold strategy. Different from the existing works, we propose a novel pre‐constrained tracking control algorithm to deal with the full‐state constraint problem. First, a novel nonlinear transformation function and a new coordinate transformation are developed to constrain state variables, which can directly cope with asymmetric state constraints. Second, the hybrid threshold strategy is constructed to provide a reasonable way in balancing system performance and communication constraints. By the use of dynamic surface control technique and neural network approximate technique, a smooth pre‐constrained tracking controller with adaptive laws is designed for the interconnected nonlinear stochastic systems. Moreover, based on the Lyapunov stability theory, it is proved that all state variables are successfully pre‐constrained within asymmetric boundaries. Finally, a simulation example is presented to verify the effectiveness of proposed control algorithm.     

基于非线性观测器设计的混沌同步控制

提出一种基于非线性观测器设计的混沌同步控制方法,给出了一类含有不确定参数混沌系统的观测器实现条件.该控制策略可满足混沌系统中存在一些不确定参数的要求.通过对Lorenz混沌系统的理论分析和数字仿真,证明了其有效性.     

基于复合离散混沌动力系统的序列密码算法

利用复合离散混沌系统的特性,提出了两个基于复合离散混沌系统的序列密码算法.算法的加密和解密过程都是同一个复合离散混沌系统的迭代过程,取迭代的初始状态作为密钥,以明文序列作为复合系统的复合序列,它决定了迭代过程中迭代函数的选择(或明文与密钥),然后将迭代轨迹粗粒化后作为密文.由于迭代对初始条件的敏感性和迭代函数选择的随机性,密钥、明文与密文之间形成了复杂而敏感的非线性关系,而且密文和明文的相关度也很小,从而可以有效地防止密文对密钥和明文信息的泄露.复合离散混沌系统均匀的不变分布还使密文具有很好的随机特性.经分析表明,系统具有很高的安全性.     

一种基于随机密钥及"类标准映射"的图像加密算法

应用离散混吨动力系统设计了一种图像加密／解密算法。该文算法主要特点是：无论从加密／解密算法的设计到密钥的产生都是由不同的混吨动力系统提供的。算法主要包括两部分：(1)采用依赖于随机密钥的非线性迭代变换来完成图像像素替代,其中所用的于密钥由离散混吨系统产生;(2)采用“类标准映射”的强耦合结构来完成图像像素的置换,并且这种置换是依赖于密钥的。替代和置换部分组成了具有良好密码特性的SP网络结构。分析和仿真结果表明,经过这样的替代和置换,算法具有良好的安全性及效率。     

混沌系统的RBF神经网络非线性补偿控制

设计RBF神经网络非线性补偿控制器,提出了混沌系统线性状态反馈的复合控制方法,将可调系统混沌行为镇定到期望目标位置或者变成周期运动.用Lorenz方程作仿真实验,结果证明了该方法的有效性.     

Estimation of nonlinear systems via a Chebyshev approximation approach

This paper proposes to decompose the nonlinear dynamic of a chaotic system with Chebyshev polynomials to improve performances of its estimator. More widely than synchronization of chaotic systems, this algorithm is compared to other nonlinear stochastic estimator such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Chebyshev polynomials orthogonality properties is used to fit a polynomial to a nonlinear function. This polynomial is then used in an Exact Polynomial Kalman Filter (ExPKF) to run real time state estimation. The ExPKF offers mean square error optimality because it can estimate exact statistics of transformed variables through the polynomial function. Analytical expressions of those statistics are derived so as to lower ExPKF algorithm computation complexity and allow real time applications. Simulations under the Additive White Gaussian Noise (AWGN) hypothesis, show relevant performances of this algorithm compared to classical nonlinear estimators.     

Proximal policy optimization-based controller for chaotic systems

Deep reinforcement learning (DRL) algorithms are suitable for modeling and controlling complex systems. Methods for controlling chaos, a difficult task, require improvement. In this article, we present a DRL-based control method that can control a nonlinear chaotic system without any prior knowledge of the system's equations. We use proximal policy optimization (PPO) to train an agent. The environment is a Lorenz chaotic system, and our goal is to stabilize this chaotic system as quickly as possible and minimize the error by adding extra control terms to the chaotic system. Therefore, the reward function accounts for the total triaxial error. The experimental results demonstrated that the trained agent can rapidly suppress chaos in the system, regardless of the system's random initial conditions. A comprehensive comparison of different DRL algorithms indicated that PPO is the most efficient and effective algorithm for controlling the chaotic system. Moreover, different maximum control forces were applied to determine the relationship between the control forces and controller performance. To verify the robustness of the controller, random disturbances were introduced during training and testing, and the empirical results indicated that the agent trained with random noise performed better. The chaotic system has highly nonlinear characteristics and is extremely sensitive to initial conditions, and DRL is suitable for modeling such systems.     

一种适用于复杂系统的智能控制新算法及仿真研究

提出一种基于改进遗传算法的自适应模糊控制 策略,通过优化控制器中非线性量化函数及自适应控制表达式等中的关键参数,得到基于加 权ITAE指标的满意控制．经过大量仿真研究,证明其对多输入多输出系统、混沌系统、滞后 系统等复杂系统的控制有良好效果．     

Control of chaotic dynamical systems using radial basis function network approximators

This paper presents a general control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. For many chaotic systems that can be decomposed into a sum of a linear and a nonlinear part, under some mild conditions the RBFN can be used to well approximate the nonlinear part of the system dynamics. The resulting system is then dominated by the linear part, with some small or weak residual nonlinearities due to the RBFN approximation errors. Thus, a simple linear state-feedback controller can be devised, to drive the system response to a desirable set-point. In addition to some theoretical analysis, computer simulations on two representative continuous-time chaotic systems (the Duffing and the Lorenz systems) are presented to demonstrate the effectiveness of the proposed method.