【作者】 张斌；

【导师】 罗跃生；

【作者基本信息】 哈尔滨工程大学 ， 应用数学， 2018， 硕士

【摘要】 切换系统是由有限个子系统或者动态模型所构成的特殊系统,并且跟其他系统的本质区别就是拥有一个切换规则。当选择一个合适的切换规则,就可以使得切换系统由不稳定变为稳定,性能指标达到最优等性质。所以,切换系统不仅在理论研究中具有重要的意义,而且在实际中也得到了广泛的应用。本文得到了以下四个方面的创新性研究结果:(1)对于抽象性能指标最优化问题的极值条件做了一般化的处理。得到了抽象多元泛函与算子复合的新泛函的一阶变分存在性定理和一阶变分表达式及其泛函达到极值的一个必要性条件。对于线性和非线性切换系统输入的设计做了一个一般化的处理,该结果是一个对于切换系统在相应性能指标达到最优时,输入设计方案的通用理论基础。(2)对一类积分形式的泛函,在由微分方程描述的系统条件下的极值问题,得到了一个取得极值的必要性条件。(3)对线性切换系统在给定二次型性能指标最优条件下的控制器以及切换规则进行了研究。得到几类相应最优控制器的设计方法,并利用设计的最优控制器得到一个最优的切换规则。但是由于得到的控制器是无穷多个,所以未来致力于设计有限个控制器,切换次数有限的切换规则。(4)对一类带有不确定项,非线性时变时滞切换系统进行控制器及其切换规则的设计。利用Lyapunov函数、凸组合技术、线性矩阵不等式的方法给出系统满足鲁棒H_∞性能的切换规则的设计方案和一个关于控制器的矩阵不等式。更多还原

【Abstract】 Switching systems is a special system composed of a limited number of subsystems or dynamic model,and the essential difference with other systems is it has a switching rule.When choosing an appropriate switching rule,the switching system can be made stable from unstable to optimal performance.Therefore,the switching system is not only of great significance in theoretical research,but also in practice has been widely used.This paper obtains the following four aspects of innovative research results:(1)The general conditions for the extreme conditions of the abstract performance index optimization problem are generalized.We obtained the existence theorem of the first order variation functions of the new functional of the abstract multivariate functional and operator complex and a necessary condition for first order variational expressions and their functional extremums.A generalized processing is done for the linear and nonlinear switching systems,the result is a general theoretical basis for the input design scheme when the switching system achieves the optimum performance.(2)For a kind of functional in the form of integrals,we obtain a necessary condition for obtaining the extremum under the extreme conditions of system conditions described by differential equations.(3)The controller and switching rule of linear switching system under the optimal quadratic performance index are studied.Get several kinds of corresponding optimal controller design method,and use the optimal controller to get an optimal switching rule.However,since there are an infinite number of controllers,the future is devoted to designing a limited number of controllers and switching rules with limited switching times.(4)Design of controller and switching rules for a class of switched systems with uncertainties and time-varying delays.The Lyapunov function,convex combination technique and linear matrix inequality are used to give design scheme of the switching rules for the system satisfying the robust H_∞performance and give a matrix inequality about controller.更多还原