一类脉冲切换系统的最优控制

研究一类脉冲依赖于状态的脉冲切换系统的最优控制问题.考虑了目标函数的两种情况:当目标函数光滑时,通过将跳跃瞬间转化为一个新的待优化参数,得到了该脉冲切换系统的必要最优性条件;当目标函数不光滑时,利用非光滑分析的知识,得到了广义微分形式的必要最优性条件.算例分析验证了所提出方法的有效性.     

一类脉冲切换系统的最优控制

研究一类脉冲依赖于状态的脉冲切换系统的最优控制问题. 考虑了目标函数的两种情况: 当目标函数光滑时, 通过将跳跃瞬间转化为一个新的待优化参数, 得到了该脉冲切换系统的必要最优性条件; 当目标函数不光滑时, 利用非光滑分析的知识, 得到了广义微分形式的必要最优性条件. 算例分析验证了所提出方法的有效性.     

一类离散线性切换系统的最优控制

研究了一类离散线性切换系统在切换时间、切换次数固定的情况下的二次最优控制问题.利用离散动态规划的方法,将多级决策过程分解成一系列易于求解的单级决策过程,求出最优控制序列和最优切换序列,并给出算法.最后通过一个数值例子来说明所提出的方法的有效性.     

基于切换次序参数化的时滞切换正系统最优控制

考虑时滞线性自治切换正系统,将切换次序参数化作为系统的离散输入,通过系统的等价转换,分析时滞线性自治切换正系统的最优控制问题.利用极小值原理,给出满足性能指标的最优切换次序条件,分析时滞项对性能指标和切换时刻的影响,最后给出数值例子验证结论的有效性.     

一类脉冲切换系统的有限时间稳定性

针对一类具有脉冲现象的非线性切换系统,提出了一种基于有限时间稳定lyapunov函数技术和多Lyapunov函数技术相结合的有限时间稳定性分析方法。该方法首先将非线性系统的有限时间稳定性的概念推广到所考虑的脉冲切换系统。然后,利用有限时间Lyapunov函数技术,确保各个子系统达到有限时间稳定。进一步,给出一个有限时间稳定的非线性比较系统。通过多Lyapunov函数技术,保证原系统的Lyapunov函数值不超过比较系统的状态值,由此得到原脉冲非线性切换系统有限时间稳定的充分条件。最后,一个数值例子说明文中方法的有效性。本文所得的研究结果能应用于生产线控制,交通管理,网络控制等实际系统。     

一类含阶跃干扰的切换系统最优控制

研究了一类含阶跃干扰的切换系统的二次最优控制问题,其中切换系统的切换序列、切换次数固定、采用动态规划方法,利用多级决策和改进的遗传算法来得到最优切换时刻和最优控制输入．最后通过一个数值例子说明了本文方法的有效性．     

一类双向确定性系统最优控制问题的最大值原理

本文讨论了一类双向确定性系统的最优控制问题，我们利用Ｅｋｅｌａｎｄ变分原理，推得了最优控制所满足的最大原理。同时，对线性系统的情况，我们还证明了最大值条件的充分性。     

基于有限时间的一类时滞非线性切换系统滑模控制

研究一类时滞非线性切换系统的有限时间滑模控制问题.针对所研究的系统模型,构造每个子系统对应的积分滑模面,基于滑模控制理论,设计带有状态时滞的滑模控制器使得每个子系统能在有限时间内到达相应的滑模面上,并对系统中存在的非线性项采用Lipschitz条件进行处理.根据多李亚普诺夫函数、平均驻留时间方法以及分割策略引理,给出滑模趋近段和滑模动态有限时间有界的充分条件,并通过对线性矩阵不等式的求解得到控制器增益.最后,通过一个数值仿真例子验证该设计方法的有效性.     

基于控制参数化的切换系统最优控制方法研究

针对一类特殊的混杂系统——切换系统的最优控制问题．利用控制函数参数化方法和时间尺度转化法,将切换系统最优控制问题转化为最优参数选择问题,可利用Miser3．2来求解该问题,这样能有效地简化求解切换系统最优控制的难度,而且算法易于理解,编程易于实现。     

基于控制参数化的切换系统最优控制方法研究

针对一类特殊的混杂系统——切换系统的最优控制问题,利用控制函数参数化方法和时间尺度转化法,将切换系统最优控制问题转化为最优参数选择问题,可利用Miser 3.2来求解该问题,这样能有效地简化求解切换系统最优控制的难度,而且算法易于理解,编程易于实现。     

一类线性连续切换系统的迭代学习控制

针对有限时间区间内执行重复控制任务的线性连续切换系统,考虑基于迭代学习的跟踪控制问题.假设线性切换系统的切换率在时间域内是任意的,提出该类系统的D型迭代学习控制算法.理论分析表明,当学习增益矩阵满足一定的条件时,D型迭代学习控制算法可以保证切换系统的实际输出在整个运行区间上一致收敛于期望输出,实现完全跟踪控制.数值仿真进一步验证了方法的有效性.     

Finite-time event-triggered control for a class of cascade switched affine nonlinear systems

This paper is concerned with the finite-time boundedness (FTB) problem of a class of cascade switched affine nonlinear systems. In order to avoid unnecessary waste of network communication and Zeno behavior, a dynamical event-triggered scheme is proposed, which is more general than some existing event-triggered schemes with a common parameter matrix. By using the average dwell time method and multiple Lyapunov function technologies, sufficient conditions for the existence of controller gains are first proposed such that the closed-loop system is finite-time bounded with a finite-time disturbance attenuation performance. It is also proved that the Zeno phenomenon is excluded. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Data-driven optimal control of switched linear autonomous systems

In this paper, a novel data-driven optimal control approach of switching times is proposed for unknown continuous-time switched linear autonomous systems with a finite-horizon cost function and a prescribed switching sequence. No a priori knowledge on the system dynamics is required in this approach. First, some formulas based on the Taylor expansion are deduced to estimate the derivatives of a cost function with respect to the switching times using system state data. Then, a data-driven optimal control approach based on the gradient decent algorithm is designed, taking advantage of the derivatives to approximate the optimal switching times. Moreover, the estimation errors are analysed and proven to be bounded. Finally, simulation examples are illustrated to validate the effectiveness of the approach.     

A polynomial approach for optimal control of switched nonlinear systems

Optimal control problems for switched nonlinear systems are investigated. We propose an alternative approach for solving the optimal control problem for a nonlinear switched system based on the theory of moments. The essence of this method is the transformation of a nonlinear, nonconvex optimal control problem, that is, the switched system, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high‐performance numerical computing. Consequently, we propose to convexify the control variables by means of the method of moments obtaining semidefinite programs. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust stabilizing control laws for a class of second-order switched systems

For a class of second-order switched systems consisting of two linear time-invariant (LTI) subsystems, we show that the so-called conic switching law proposed previously by the present authors is robust, not only in the sense that the control law is flexible (to be explained further), but also in the sense that the Lyapunov stability (resp., Lagrange stability) properties of the switched system are preserved in the presence of certain kinds of vanishing perturbations (resp., nonvanishing perturbations). The analysis is possible since the conic switching laws always possess certain kinds of “quasi-periodic switching operations”. We also propose for a class of nonlinear second-order switched systems with time-invariant subsystems a switching control law which locally exponentially stabilizes the entire nonlinear switched system, provided that the conic switching law exponentially stabilizes the linearized switched systems (consisting of the linearization of each nonlinear subsystem). This switched control law is robust in the sense mentioned above.     

一类切换线性奇异系统的H∞控制

研究一类由任意有限多个奇异子系统组成的切换奇异系统的状态反馈和动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换策略.分别采用矩阵变换和消元法,将矩阵不等式分别转化为一组线性矩阵不等式(LMIs).数值算例说明了所提方法的有效性和可行性.     

一类非线性切换系统任意切换采样控制设计

本文针对一类具有非严格反馈形式的非线性切换系统,在输出只在采样点可获得的情况下,提出了一种基于模糊采样观测器的自适应输出反馈控制方法.该方法降低了现有任意切换控制研究结果中因共同控制思想导致的控制器设计的保守性,避免了迭代过程对虚拟控制的反复求导引发的计算爆炸现象及控制器高增益的弊端.切换的自适应律突显了每个子系统的特...     

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

In this paper, the adaptive control problem for a class of switched nontriangular nonlinear systems is investigated, which allows the control gains to vanish at some points. Neither the triangular structure nor the solvability of the adaptive control problem is required for each subsystem. A key point of this work is to solve the adaptive control problem of switched nontriangular nonlinear systems with vanishing control gains by the dual design of the controllers and switching signals. To this end, firstly, a hysteresis‐type control gains‐dependent switching law is designed, which makes the control gain of the active subsystem not vanish and thus the associated designed control input can enter into the active subsystem. Moreover, the designed switching law guarantees a dwell time between any adjacent switching instants, which rules out the Zeno behavior. Secondly, when the adaptive control problem of each subsystem is unsolvable, a sufficient condition ensuring the solvability of the adaptive control problem of switched nontriangular nonlinear systems is developed even if no control input can enter into subsystems at some points. Finally, the effectiveness of the proposed result is illustrated by two examples.