不确定性区域系统的鲁棒控制

区域模型已经成功应用于模拟生物医学和药物代谢动力学系统中。针对一类具有参数不确定性的正定区域系统,对其质量控制的反馈稳定性提出了一种新的正定鲁棒控制律,该控制律基于李亚普诺夫稳定性理论并且闭环系统满足全局渐进稳定性。通过术后病人神经肌肉阻滞控制的具体实例对其质量控制的性能进行了分析,并通过仿真与其他控制律的性能进行了比较。     

一类双线性系统的最优跟踪控制问题

针对一类具有二次型性能指标的双线性系统的最优跟踪控制问题,提出了一种通过逐次逼近法设计最优控制律的近似方法。首先将状态向量含有时滞的双线性系统的最优跟踪问题转化为最优调节问题;然后利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题族,得到调节系统的最优控制律,并可以通过截取最优控制序列的有限项得到调节系统的前馈-反馈次优控制律。最后,将最优控制问题转化为最优跟踪问题。仿真结果表明,此方法达到了较好的跟踪效果。     

非线性离散时间系统的自适应模糊补偿控制

针对一类非线性离散时间系统,提出一种自适应模糊逻辑补偿控制方案.控制律由跟踪控制律和逼近误差补偿控制律两部分组成,利用模糊逻辑系统对系统参数扰动和外界干扰进行自适应补偿,由模糊滑模控制律实现对模糊逻辑系统逼近误差的进一步补偿.所设计的控制器可保证闭环系统一致最终有界.将该控制器用于月球探测车动态转向系统中,仿真结果表明了该方法的有效性.     

Leader-following consensus control of second-order nonlinear multi-agent systems with applications to slew rate control

This paper addresses the distributed leader-following consensus control of second-order strict-feedback nonlinear multi-agent systems. By employing mean value theorem, variable separation technique, and backstepping methodology, a fully distributed adaptive control law is designed using only local relative state information. The proposed control law solves the leader-following consensus problem for any directed communication graph that contains a spanning tree with the root node being the leader agent. The application to hovercraft slew rate control system is given to verify the effectiveness of the theoretical results.     

Micro tracking and positioning using off-the-shelf servopneumatics

Conventional pneumatic systems do not exhibit significant heat or magnetic fields and present high force to volume ratios. They are, however, typically confined to simple motion tasks owing to their control complexity. Leveraging on a sliding mode based control strategy, the authors have shown in previous works that good tracking and positioning results can be achieved using off-the-shelf servopneumatics. This paper extends the previously mentioned works by applying a modified version of the control law to a new experimental setup comprising different valves and actuators and a better resolution encoder. The modification of the control law involves the use of a new boundary layer thickness variation law, different from the one previously used. Experimental results show that the modified control law leads to very accurate motion control. The positioning error from a control perspective is only limited by the encoder resolution, 1 μm, in any position of the piston stroke and when carrying loads of 3 kg and 8 kg, without any controller retuning. Good results in the micrometer range are also obtained when tracking sinusoidal and triangular references.     

时滞系统在高速网络下的最优扰动抑制

研究在含有控制时滞与测量时滞的系统在高速通讯网络下最优扰动抑制问题. 首先建立在高速通讯网络下含有控制时滞与测量时滞系统的离散化数学模型, 利用模型转换将时滞系统转化为形式上的无时滞系统. 然后通过求解离散Riccati方程和Stein方程设计含有状态反馈、扰动前馈和控制记忆项的最优控制律, 前馈项和控制记忆项分别补偿了扰动和控制时滞对系统性能的影响. 通过构造降维扰动状态观测器, 设计了含扰动前馈、输出反馈及 控制记忆项的动态控制律, 解决了前馈补偿器的物理不可实现问题. 仿真实例验证了所设计的最优控制律的有效性.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

离散变结构控制系统的比例—等速—变速控制

提出离散变结构控制系统的变速趋近律和比例一等速－变带控制策略,以变速趋近律为到达条件,可产生扇形切换区,并可期待原点的稳定性。将变速趋近律和指数趋近组合使用,可形成一种新的控制策略,它克服了两种趋近律的缺点,保留了其优点,使系统性能得以改善。     

一类不确定脉冲型混杂系统的保代价控制

针对混合代价函数,研究了参数不确定脉冲型混杂系统的保代价控制问题,给出了混杂状态反馈保代价控制律的设计方法,由此得到的控制律既能使系统闭环鲁棒渐近稳定,又可使系统的闭环混合代价指标在对象参数摄动的范围内不超过确定的上界.本文提出的控制律不仅包含连续时间动态,也包含离散事件动态,而且其离散事件动态行为不需要与被控系统的离散事件动态行为一致,因此设计时不要求被控系统的每个连续时间子系统都具有可控性.仿真结果表明所提设计方法是可行有效的.     

具有控制时滞的离散系统的无抖振滑模控制

研究含时滞的线性离散系统的变结构控制问题. 首先将之简化为不含时滞项的线性离散系统. 然后对简化系统提出一种新的无抖振滑动模态控制算法. 该算法使滑模控制分为两个阶段,当系统轨迹在滑模某邻域以外时, 利用传统的到达控制律使系统状态轨迹单调趋近滑模面; 当系统轨迹进入该邻域内, 无抖振控制律使其轨迹一步到达滑模面. 该控制律有效地削除了由离散系统解轨迹的不连续性产生的抖振现象. 仿真结果表明了这种方法的有效性.     

Robust constrained control of piecewise affine systems through set‐based reachability computations

This article addresses finite‐horizon robust control of a piecewise affine system affected by uncertainty and characterized by different affine dynamics (modes) associated with a polyhedral partition of the state space. The goal is to design a static state‐feedback control law that maintains the state of the system within given—possibly time‐varying—sets, subject to actuation constraints. The proposed approach rests on two phases: a reference mode sequence with a sufficiently large robustness level is determined first, and then a tracking state‐feedback control law defined on the reach sets of the controlled system is designed to counteract uncertainty and maintain the reach sets within the reference sequence. If this is not possible and the reach sets split over different modes, then, further reference mode sequences and tracking controllers are computed. The designed state‐feedback control law is represented through a collection of controllers defined on precomputed reach sets of the closed‐loop control system. Performance of the approach is shown on some numerical examples.     

一类非线性系统的广义预测控制研究

针对一类难以线性化的单输入单输出非线性离散系统,就其实际输出信号跟踪参考输出信号的控制问题,研究了它的广义预测控制律设计方法。在系统数学模型非线性项的系数多项式满足一定条件的情况下,通过适当的数学处理,使问题的本质归结为求解线性差分系统的一组Diophantine方程,从而解出了非线性系统广义预测控制律表达式中的各个系数多项式,并给出了广义预测控制律的具体解析形式。通过仿真实例验证了所提出设计方法的正确性和有效性。     

Robust global stabilization of a class of uncertain feedforward nonlinear systems

The problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered. The control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small. With respect to previous works on the subject the design procedure is able to deal with uncertain (possibly time-varying) parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system. The small gain theorem for nonlinear systems which are input to state stable “with restrictions” is shown to be a key tool for designing a state feedback saturated control law.     

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances. The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms. Based on the internal model principle, a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances. According to the sensitivity approach, the optimal tracking control law for the ith nonlinear subsystem can be obtained. The optimal tracking control law for the nonlinear large-scale systems can be obtained. A numerical simulation shows that the method is effective.     

非线性相似组合大系统最优控制的逐次逼近过程

研究一类仿射非线性相似组合大系统关于二次型性能指标的最优控制问题．首先通过模型简化,将非线性相似组合大系统化为若干个准解耦的子系统;然后利用非线性系统最优控制的逐次逼近设计方法,将求解高阶强耦合的非线性两点边值问题简化为求解一族解耦的线性两点边值问题序列．该线性两点边值问题序列的解一致收敛于非线性相似组合大系统的最优控制,得到的最优控制律由线性最优控制的解析项与非线性补偿序列的极限项组成．通过截取最优控制非线性补偿序列的有限次逼近值．得到了非线性组合大系统的次优控制律．     

一类关联时滞系统的分散稳定化控制器设计

应用Lyapunov稳定性理论,提出一类关联时滞系统能用分散线性状态反馈镇定的充分条件,进而证明了该条件等价于子系统级上N个带参数的代数Riccati矩阵方程的正定解的存在性,并利用这些正定解矩阵给出了相应的稳定化分散控制器。应用所提出的方法,可望得到具有更小反馈增益参数的分散稳定化控制律。     

基于滚动优化的对偶控制策略

考虑具有未知参数的随机系统的最优控制问题.提出了一种新的基于滚动优化的对偶控制算法.在动态规划泛函方程中,用Kalman滤波对系统的状态进行估计;用线性化方法对阶段损失函数中的后验概率进行近似,然后,用滚动优化策略对控制与学习之间的耦合关系进行解耦.从而获得了原不可解泛函方程的解析递推表达式和一个易于实施的控制律的解析解.用一个例子说明了控制律的性能,仿真结果表明:该控制律具有良好的对偶性质,在学习和控制之间实现了较好的平衡.     

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper studies the technique of the composite nonlinear feedback (CNF) control for a class of cascade nonlinear systems with input saturation. The objective of this paper is to improve the transient performance of the closed-loop system by designing a CNF control law such that the output of the system tracks a step input rapidly with small overshoot and at the same time maintains the stability of the whole cascade system. The CNF control law consists of a linear feedback control law and a nonlinear feedback control law. The linear feedback law is designed to yield a closed-loop system with a small damping ratio for a quick response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system when the system output approaches the target reference to reduce the overshoot. The result has been successfully demonstrated by numerical and application examples including a flight control system for a fighter aircraft.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.