【作者】 贺冰丽；

【导师】 李俊民；

【作者基本信息】 西安电子科技大学 ， 运筹学与控制论， 2011， 硕士

【摘要】 由于实际系统基本都是非线性的,研究有参数不确定性的非线性系统的自适应控制,无论在理论上还是在实际应用中都具有重要的意义.在处理未知定常参数不确定性动态系统的控制问题时,自适应控制成为人们所公认的最有效的方法之一,因为自适应控制能够在线调节控制增益或系统参数,以适应外界环境变化或外界干扰等因素的影响,从而当时间趋于无穷时,实现跟踪误差的渐近收敛.但是对于参数估计来说,只能满足其有界性.而人们总是希望参数估计最好能收敛到其真值,通常在假设持续激励条件下或通过构造系统的强Lyapunov函数(正定、径向无界、导数负定)就可以实现这一目标.近二十年来,混沌控制与同步问题已成为非线性科学领域的热点问题之一,而且在保密通信、信息工程和生命科学等方面显示出巨大的应用前景.自适应控制方法在处理参数不确定性混沌系统的控制与同步问题中也得到了广泛的应用.基于Lyapunov稳定性理论,本文主要从自适应控制的角度来研究一类严格反馈非线性系统中参数的收敛性和(超)混沌系统的同步问题.主要工作概括如下:第一,针对一类严格反馈非线性系统,应用Backstepping方法和调节函数法设计系统的控制律和自适应律,在适当的持续激励条件下,构造一个显式、全局的强Lyapunov函数证明了闭环系统的所有信号全局一致有界且跟踪误差和参数估计误差均渐近收敛于零.最后通过数值仿真验证了设计方案的可行性和有效性.第二,针对两个参数完全未知的不同超混沌系统,基于Lyapunov稳定性理论,设计了相应的控制器和参数自适应律,使得驱动系统和响应系统实现了混合投影同步.最后通过数值仿真验证其有效性.第三,针对两个带有未知的周期时变参数的不同混沌系统,应用自适应学习控制方法,根据Lyapunov-Krasovskii泛函稳定性理论,构造了微分-差分混合参数学习律和自适应学习控制律,使得两个不同混沌系统的状态误差范数的平方在一个周期区间上的积分意义下实现了渐近同步.该方法成功地应用于Lorenz系统和Chen系统的函数投影同步,最后通过数值仿真验证了该方法的有效性.更多还原

【Abstract】 The practical systems are almost nonlinear, therefore, the study of adaptive control of nonlinear with uncertain parameters are of great significance both in theory and in practical application. Adaptive control is considered as one of the most effective approaches when solving the control problem of uncertain dynamics with unkonwn constant parameters, because adaptive control can adjust control gains or system parameters online to adapt to the affection factors of environmental changes or disturbance, ect. Hence, asymptotic convergence of tracking error is obtained when time approaches to infinite. However, for estimation of parameters, only boundedness can be guaranteed. It is always hoped that estimation of parameter can converge to its true value, this target can be realized by constructing strong Lyapunov functions (positive definite, radially unbounded and its derivative is negative definite) of systems. During the last two decades, chaos control and synchronization has become one of the hot topics in nonlinear science field, and exhibits wide-scope potential application in various disciplines such as secure communication, information engineering and life science and so on. Adaptive control approach has been widely used to dealing with control and synchronization of chaotic systems with uncertain parameters.Based on Lyapunov stability theory,this dissertation considers the parameters convergence properties of strict-feedback nonlinear systems and synchronization of (hyper)chaotic systems from an adaptive control viewpoint. The main contributions included in the dissertation are summarized as follows.Firstly, a strict-feedback nonlinear systems is developed. The design of both the control and the update laws are based on Backstepping techniques and tuning function schemes. Under an appropriate persistency of excitation condition, it is shown that all the closed-loop signals are globally uniformly bounded and both convergence of the tracking error and parameter estimation error to zero asymptotically, by constructing an explicit, global, strong Lyapunov function. The feasibility and effectiveness of the proposed method is illustrated with a simulation example.Secondly, based on Lyapunov stability theory, control laws and parameter update laws are designed for two different hyperchaotic systems with fully uncertain parameters, the states of the drive system and the response system are ultimately asymptotically hybrid projective synchronization. Simulation results are presented to show the feasibility and effectiveness of the proposed methodAt last, a learning control approach is applied to the function projective synchronization of different chaotic systems with unknown periodically time-varying parameters. According to Lyapunov-Krasovskii functional stability theory, a differential-difference mixed-type parametric learning laws and an adaptive learning control laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The approach is successfully applied to the functional projective synchronization between Lorenz system and Chen system. Numerical simulations results are presented to verify the effectiveness of the proposed approach.更多还原