随机系统统计特征控制算法研究

发布时间：2018-07-08 21:20

本文选题：随机系统 + 统计特征　；参考：《西安理工大学》2016年博士论文

【摘要】：世界充满不确定性,从量子系统到一般的工业系统,无不如此。随机系统控制理论经历了半个多世纪的研究,在均值、方差这两个低阶统计特征控制方面已经取得了一系列理论成果,并广泛应用于航空航天、工业生产等实际工程领域。然而,现有的随机控制方法存在着两个方面的问题:一是仅针对外部干扰噪声或测量噪声的不确定性进行处理,无法同时兼顾系统参数本身的不确定性,而系统的数学模型是对实际过程的近似,一些情况下必然存在着参数的不确定性;二是受控系统的结构往往限定为线性系统,这样仅通过均值、方差这两个低阶统计特征的控制就能够实现系统的整体性能,而对于非线性系统来说,仅仅均值和方差并不足以表征系统的完整特征。显然,传统的随机控制理论已经无法很好的满足当前的控制需求。本文针对存在不确定参数线性随机系统的低阶统计特征控制以及非线性随机系统的完全统计特征控制进行了深入研究,并将部分研究成果应用于车辆悬架控制系统。主要研究内容如下:1、针对随机系统存在多个子模型的情况,把大系统的分解-协调思想引入到多模型控制中,以各子模型的后验概率作为协调变量,将多个子模型的控制律进行融合归一,利用归一后的模型对系统进行控制,获得一种新的低阶统计特征控制策略。采用融合模型控制方法,能够在系统的控制过程中减少模型切换导致的响应抖动影响,有效改善控制过程的平滑性。2、针对系统参数发生飘移且变化量服从高斯分布的系统,提出一种次优低阶统计特征控制方法。该方法基于对性能指标跟踪与参数辨识的双重考虑,把系统输出的最小方差和系统参数的估计协方差矩阵融入到衡量控制优劣的性能指标中进行综合分析,设计出一种具有学习和控制权衡效果的次优对偶控制策略。3、针对非线性随机系统,研究了矩逼近完全统计特征控制问题。首先假设对系统施行干预的控制律为状态响应的多项式反馈,同时把动态方程中的非线性函数进行泰勒展开。然后导出了随机状态响应各阶矩的递推方程,该方程的解为控制增益的函数。最后,为使被控制的概率密度函数形状具有期望的形式,构造了一个优化问题,并通过梯度法搜索出最优控制增益,实现了完全统计特征的有效控制。4、进一步研究了非线性随机系统完全统计特征精确控制问题。通过把概率密度函数展开为多项式以及指数多项式的方法,研究了几种分析途径,成功推导出稳态概率密度函数和随机系统控制增益的关系。尤其是通过把概率密度函数展开为指数多项式的方法,推导出指数函数泰勒展开系数与待求反馈控制增益间的一一精确对应关系。然后,根据目标概率密度函数的不同情况,分别给出了采用本方法的跟踪控制策略。5、针对一类具备半主动式悬架系统的越野车辆,应用本文提出的融合思想的多模型低阶统计特征控制方法进行悬架系统的控制研究。首先建立半主动式悬架系统控制动力学模型,在此基础上得到其对应的连续时间状态方程,并对其进行离散化处理。然后分别针对车辆重载和轻载情况建立了不同的运行模型,设计出对应的控制器。仿真分析展示了该方法的有效性。最后,对全文进行了概括性总结,并指出有待进一步研究和完善的问题。
[Abstract]:The world is full of uncertainty, from quantum systems to general industrial systems. The theory of stochastic system control has gone through more than half a century of research. A series of theoretical results have been obtained in the two low order statistical characteristics control of mean and variance, and it is widely used in practical engineering fields such as aerospace, industrial production and so on. There are two problems in the existing stochastic control methods: one is to deal with the uncertainty of the external interference noise or the measurement noise, and the uncertainty of the system parameters can not be taken into account at the same time. The mathematical model of the system is similar to the actual process. In some cases, the uncertainty of the parameters is inevitable; two is the uncertainty of the parameters. The structure of a controlled system is often limited to a linear system, so that the overall performance of the system can be achieved only through the control of the two low order statistical characteristics of mean and variance, but for nonlinear systems, only the mean and variance are not sufficient to characterize the complete characteristics of the system. It is obvious that the traditional stochastic control theory is not very good. In order to meet the current control requirements, this paper studies the low order statistical characteristics control of the linear stochastic systems with uncertain parameters and the complete statistical characteristics control of the nonlinear stochastic systems. Some research results are applied to the vehicle suspension control system. The main contents are as follows: 1, there are many random systems. In the case of the sub model, the decomposition coordination idea of large system is introduced into the multi model control, and the posterior probability of each sub model is used as the coordination variable. The control law of the multiple sub models is fused, and the system is controlled by the model after the normalization, and a new low order statistical characteristic control strategy is obtained. The fusion model control is adopted. The method can reduce the effect of response jitter caused by model switching in the process of system control and effectively improve the smoothness of the control process. A suboptimal low order statistical feature control method is proposed for the system with which the system parameters are floating and the change quantity obeys Gauss distribution. This method is based on the performance index tracking and parameter identification. In the double consideration, the minimum variance of the system output and the estimated covariance matrix of the system parameters are integrated into the performance index of the control and control. A suboptimal dual control strategy,.3, which has the effect of learning and control, is designed. The moment approximation complete statistical feature control is studied for the nonlinear stochastic system. First, it is assumed that the control law for the intervention of the system is a polynomial feedback of the state response, and the nonlinear function in the dynamic equation is carried out by Taylor expansion. Then the recursive equation of the random state response of each order moment is derived, and the solution of the equation is a function of controlling the gain. Finally, the shape of the controlled probability density function is made to have the shape of the controlled probability density function. In the form of expectation, an optimization problem is constructed, and the optimal control gain is searched by the gradient method. The effective control.4 for complete statistical characteristics is realized. The exact control problem of the complete statistical characteristics of a nonlinear stochastic system is further studied. By expanding the probability density function into a polynomial and an exponential polynomial, a few studies are made. The relationship between the steady-state probability density function and the control gain of the stochastic system is derived successfully. In particular, the exact relation between the exponential function Taylor expansion coefficient and the feedback control gain is derived by expanding the probability density function as an exponential polynomial. Then, the probability density function of the target is based on the probability density function of the target. The tracking control strategy.5 using this method is given in different situations. For a class of off-road vehicles with semi-active suspension system, the multi model low order statistical feature control method proposed in this paper is used to control the control of suspension system. First, a semi-active suspension system control dynamic model is established. On the basis of it, the corresponding continuous time state equation is obtained and discretized. Then different running models are established for heavy load and light load, and the corresponding controller is designed. The simulation analysis shows the effectiveness of the method. Finally, a general summary of the full text is summarized, and it is pointed out that it needs to be further studied. Study and improve the problem.
【学位授予单位】：西安理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP273

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