基于非光滑线性Ｌｉｐｓｃｈｉｔｚ连续平面的滑模控制设计

利用Ｆｉｌｉｐｐｏｖ解、Ｃｌａｒｋｅ广义梯度和非光滑Ｌｙａｐｕｎｏｖ稳定理论,对一类滑模面设计为非光滑线性Ｌｉｐｓｃｈｉｔｚ连续平面的二阶系统滑模控制问题进行深入讨论．首先设计控制律,使闭环系统在有限时间内能够到达所设计的滑模面;然后证明系统在滑模面上的运动是渐近稳定的．放宽了对滑模控制中滑模面设计的要求,提高了所提出设计方法的灵活性,有利于改善系统性能．仿真结果验证了所提出设计方法的正确性和有效性．

     

非光滑非线性系统的非光滑连续控制

针对具有非光滑非线性的系统,提出了一种非光滑连续控制方法,通过非光滑建模方法能够快速精确地补偿系统中有害的非光滑非线性,同时通过非光滑连续控制引入一些有益的非光滑非线性以获得快速高精度的控制性能,给出了实验迟滞曲线和建模结果。讨论了该项技术在非光滑非线性控制系统中的应用前景。     

光滑神经网络解决一类线性约束的非Lipschitz优化问题

带有线性不等式约束的非光滑非优化问题被广泛应用于稀疏优化,具有重要的研究价值.为了解决这类问题,提出了一种基于光滑化和微分包含理论的神经网络模型.通过理论分析,证明了所提神经网络的状态解全局存在,轨迹能够在有限时间进入可行域并永驻其中,且任何聚点都是目标优化问题的广义稳定点.最后给出数值实验和图像复原实验验证神经网络在理论和应用中的有效性.与现有神经网络相比,它具有以下优势：初始点可以任意选取;避免计算精确罚因子;无需求解复杂的投影算子.     

非光滑聚合博弈纳什均衡的分布式连续时间算法

本文研究多智能体聚合博弈的分布式算法设计.其中,个体的成本函数具有非光滑性.提出一个连续时间分布式算法,使得每个个体仅利用本地数据及局部的信息交互就能达到纳什均衡.利用李雅普诺夫方法,证明了算法的收敛性.在此基础上,进一步研究了带有耦合不等式约束博弈的广义纳什均衡求解.仿真结果验证了方法的有效性.     

基于特征增强的轻量级无人机目标检测算法

针对无人机航拍图像特征少,小尺寸目标多以及检测任务实时性要求高等问题,本文以YOLOX算法为基础提出基于特征增强的轻量级无人机目标检测算法。首先,设计更加轻量的密集残差网络结构ResNet_G优化模型的主干网络,提升模型对图像特征的利用率,同时降低模型复杂度;其次,提出基于注意力机制的Atrous Spatial Pyramid Pooling(ASPP)模块作为特征增强模块,加强上下文信息关联度以减少丢失小目标特征;最后,使用Focal Loss函数与CDIoU Loss函数,改善负样本对模型权重的影响以提高对密集目标的识别能力。实验结果表明,与原网络相比,改进后算法在VisDrone2021数据集上平均检测精度提升5.08%,参数量减少0.25M,推理时间降低2.21ms。     

基于流形正则化的非光滑非负矩阵分解

经典的非光滑非负矩阵分解方法只能发现数据中的全局统计信息,对于非线性分布数据无能为力,而流形学习方法在探索高维非线性数据集真实几何结构方面具有明显优势。鉴于此,基于流形正则化思想,提出了一种新颖的基于流形正则化的非光滑非负矩阵分解方法。该方法不仅考虑了数据的几何结构,而且对编码系数矩阵和基矩阵同时进行稀疏约束,并将它们整合于单个目标函数中。构造了一个有效的乘积更新算法,并在理论上证明了算法的收敛性。标准数据集上的实验表明了MRnsNMF的有效性。     

基于l1-非凸非光滑函数的图像恢复方法

针对有整齐边界且加性噪声满足均匀、椒盐、拉普拉斯等非高斯分布的图像,根据逐步拟合及变量转换思想,提出一种基于l1-非凸、非光滑函数的逐步非凸图像恢复方法。根据原始非凸、非光滑函数建立一组拟合函数,获得原始问题的优良初始值,利用变量转换解决l1-非凸、非光滑函数的非可微性问题。实验结果表明,该方法恢复的图像效果较好,峰值信噪比较高。     

不确定非线性系统的非光滑控制及应用

针对一类具有严格反馈结构形式的不确定非线性系统,研究非光滑鲁棒控制问题。在一定的假设条件下,基于backstepping设计方法,设计鲁棒非光滑控制律,证明闭环系统的鲁棒稳定性。将所得结果应用于飞行器的末制导问题,设计非光滑末制导律,并进行数值仿真研究。仿真结果说明了方法的有效性。     

基于非光滑观测器的间隙三明治系统状态估计

在工业领域, 机械传动系统、液压系统等往往含有间隙特性, 这类系统可以用带间隙的三明治系统描述. 本文针对带间隙的三明治系统特点, 构建了一种非光滑观测器以对系统状态进行估计. 首先根据带间隙三明治系统的特点, 采用分离原理, 建立了描述系统特性的非光滑状态空间方程. 据此构造了能够随系统工作区间变化而自动切换的非光滑观测器, 给出了相应的收敛定理及其证明. 最后通过伺服液压系统的例子, 分别比较了非光滑观测器和传统的观测器对状态的跟踪效果, 比较结果表明非光滑观测器对于带间隙三明治系统状态变量估计的准确性要优于传统的观测器.     

非连续Lur’e时滞网络的有限时间聚类同步与自适应控制

本文主要研究一类由非恒同非连续Lur’e系统耦合而成复杂动态网络的自适应有限时间聚类同步问题.首先,通过引入Filippov微分包含理论和测度选择定理,本文设计了一类有效的牵制反馈控制器,该控制器只控制当前聚类中与其他聚类有直接连接的部分节点.为了有效节省控制成本,本文基于反馈控制强度设计了一类自适应更新定律以获取实现网络同步的最优控制强度.其次,利用有限时间稳定性理论和Lyapunov稳定性定理,本文得到时变时滞耦合和非线性耦合Lur’e网络实现有限时间聚类同步的判定条件,并给出该网络达到聚类同步的收敛时间估计.最后,通过一个算例仿真验证了本控制方案和同步判据的有效性及正确性.     

New approaching condition for sliding mode control design with Lipschitz switching surface

In this paper, we concern the approaching condition of sliding mode control (SMC) with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov’s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov’s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output (SISO) systems, of which the switching surface is designed Lipschitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.     

基于自稳定域和相依锥判据的一类二阶不确定系统的控制设计

针对一类二阶不确定系统,构造了以线性Lipschitz曲面作为边界的自稳定域,并依此设计控制律,利用Filippov解与空间非光滑曲面的相依锥判据,证明在该控制律的作用下系统轨迹将在有限时间到达所设计的自稳定域边界并进入其内部,从而系统轨迹将收敛到原点.所得结果放宽了对自稳定域边界光滑性的要求,提高了设计的灵活性.仿真结果验证了设计的正确性和有效性.     

Adaptive control design for a class of nonsmooth nonlinear systems with matched and linearly parameterized uncertainty

This paper presents an adaptive control design for a class of nonsmooth nonlinear systems with matched uncertainty, which is linearly parameterized with a known discontinuous function. The design framework is based on the concept of the Filippov solution as the classical Lyapunov theory for smooth systems cannot be applied to establish the stability of the adaptive control system due to the presence of the discontinuity. It is proved that as an adaptive control system, the global Lyapunov stability with the convergence of the state of the controlled system to the origin can be achieved by evaluating the monotonicity of the Lyapunov function in the state space, particularly on the discontinuous surface, while the uniqueness of the solution of the closed‐loop system is not necessarily guaranteed. Some interesting numerical examples are demonstrated with simulation results. Copyright © 2008 John Wiley & Sons, Ltd.     

Sliding mode control design via piecewise smooth Lipschitz surfaces based on contingent cone criteria

In order to improve flexibility of sliding mode control (SMC) for a class of nonlinear systems, a new control design method is proposed in this paper. The sliding surface is extended to be a generic Lipschitz continuous surface instead of a smooth one, with which different characteristics of sliding motion may be realized. Due to the nonsmoothness of the sliding surface, the control design problem is discussed in the framework of Filippov’s differential inclusion, by analyzing the geometric properties of the nonsmooth surface. Discontinuous control laws are presented based on new contingent cone criteria, which steer all of the trajectories of the closed-loop system to reach the piecewise smooth sliding surface in finite time.     

Sliding mode control based on a modified linear control input

In this study, we explain and demonstrate a design method of sliding mode control based on a modified linear control input. In the proposed method, the optimal gain matrix is derived such that it does not depend on the plant parameters. We confirmed the robustness of the proposed method by applying input-side disturbances and plant parameter deviations to plants and the effectiveness of the proposed method by performing a DC motor position control experiment     

Sliding mode control design based on Ackermann's formula

The sliding mode control methods are developed to design systems which have the desired dynamic behavior and are robust with respect to perturbations. It is shown that the discontinuity plane for sliding mode control may be found in an explicit form using Ackermann's formula. Two design procedures are derived. First, static controllers are designed to enforce sliding modes with the desired dynamic properties after a finite-time interval. Then, dynamic controllers are designed that exhibit the desired dynamic properties during the entire control process     

基于二重积分滑动面的Buck变换器滑模研究

利用状态空间平均方法建立了Buck变换器的数学模型,该模型考虑了电容和电感的串联等效电阻,仿真结果与电路模型的仿真结果基本一致,其准确性较高;基于该数学模型,分别设计了PID控制和PWM滑模控制,滑模控制基于二重积分滑动面,并利用了电流信息。仿真结果表明,在负载突变情况下,基于二重积分滑动面的PWM滑模电流控制具有更好的动态响应特性和稳态误差调节特性。     

Sliding mode control design based on the state-dependent Riccati equation: theoretical and experimental implementation

In this paper, a suboptimal sliding mode control method is derived from combination of the sliding mode control (SMC) and the state-dependent Riccati equation (SDRE) technique, applied for a class of nonlinear closed-loop systems. One of the distinguished features of this control method is its robustness towards uncertainty. Due to lack of optimality in SMC method, in this paper, a robust and suboptimal method is presented by considering the SDRE in design of the sliding surface in two types of: algebraic and integral sliding surfaces. In addition, due to the use of the state-dependent differential Riccati equation in the integral form of sliding surface, proposed method is able to provide a robust attitude with desired finite-time control option. The sensitivity of various percentage of uncertainty in the physical structure of the system is studied and control strategies for general manipulators are provided. The proposed control structure was implemented on Scout robot theoretically and practically by the LabVIEW software; and the results were compared by considering the uncertainty in its structure. In comparison with conventional SMC, the proposed method reduced the required time to reach the sliding surface almost 50%.     

On the variable structure control approach with sliding modes to robust finite-time consensus problems: A methodological overview based on nonsmooth analysis

When controlling cyber–physical systems via consensus algorithms, the robustness issue is of paramount importance because of model mismatching and/or disturbances that generally modify the Laplacian flow dynamics associated to the overall network, compromising the possibility to achieve any expected, orchestrated emergent behavior. To face this issue, the Variable Structure Control (VSC) approach has recently been shown to be an effective tool in designing control protocols over networks, providing robustness and often yielding finite-time convergence. Moreover, VSC further enables the decoupling of simultaneous control objectives where reaching a consensus state is only part of a more complex task, for instance as it happens in distributed optimization. Thus motivated, this paper overviews, from a tutorial perspective, some selected recent advances in the application of VSC with Sliding Modes to design robust consensus controllers in both the leader-less and the leader-following settings. Efforts are also made to unify the notation and to discuss the theoretical foundations of the nonsmooth analysis tools at the basis of their design for a wide readership unfamiliar with these problems and formal tools. To this aim, examples supporting the treatment, and numerical simulations, are given and discussed in detail. Finally, hints for future investigations along with some current open problems are provided.