Heteroclinic Cycles in a Class of 3-Dimensional Piecewise Affine Systems

This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems

This paper investigates the problem of robust H-infinity state estimation for a class of uncertain discretetime piecewise affine systems where state space instead of measurable output space partitions are assumed so that the filter implementation may not be synchronized with plant state trajectory transitions. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, two different approaches are developed to the robust filtering design for the underlying piecewise affine systems. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Robust Stabilization of Discrete-time Constrained Singular Piecewise-affine Systems with Norm-bounded Uncertainties

In this paper,the problem of designing robust H-infinity output feedback controller and l2-gain controller are investigated for a class of discrete-time singular piecewise-affine systems with input saturation and state constraints. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques,the H-infinity stabilization condition is established and the l2-gain controller is investigated,and meanwhile,the input saturation disturbance tolerance condition is proposed. Under energy bounded disturbance,the domain of attraction is well estimated and the l2-gain controller is designed in some restricted region. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Meanwhile,by using the corresponding optimization methods,the domain of attraction and the disturbance tolerance level is maximized,and the H-infinity performance γ is minimized.Finally,numerical examples are given to illustrate the effectiveness of the proposed design methods.

Heteroclinic cycles in a new class of four-dimensional discontinuous piecewise affine systems

It is a huge challenge to give an existence theorem for heteroclinic cycles in the high-dimensional discontinuous piecewise systems（DPSs）. This paper first provides a new class of four-dimensional（4 D） two-zone discontinuous piecewise affine systems（DPASs）, and then gives a useful criterion to ensure the existence of heteroclinic cycles in the systems by rigorous mathematical analysis. To illustrate the feasibility and efficiency of the theory, two numerical examples, exhibiting chaotic behaviors in a small neighborhood of heteroclinic cycles, are discussed.

Robust observer-based control for uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present a novel robust observer-based controller design method for discrete-time piecewise affine systems with norm-bounded uncertainties. The key ideas are to construct a piecewise quadratic Lyapunov function to guarantee the stability of the closed-loop systems, approximate polytopic operating regions by ellipsoids, and use the singular value decomposition technique to treat the constraint of matrix equality. It is shown that the suggested control method can be formulated as linear matrix inequalities that are numerically feasible with commer- cially available software. A numerical example is also given to verify the proposed approach.

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered H∞state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed H∞performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler's lemma, the event-triggered H∞observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the event-triggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.

Non-Zenoness of piecewise affine dynamical systems and affine complementarity systems with inputs

In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.

Piecewise output feedback control for affine systems with disturbances based on linear temporal logic specifications

In the paper,we investigate the problem of finding a piecewise output feedback control law for an uncertain affine system such that the resulting closed-loop output satisfies a desired linear temporal logic (LTL) specification.A two-level hierarchical approach is proposed to solve the problem in a triangularized output space.In the lower level,we explore whether there exists a robust output feedback control law to make the output starting in a simplex either remains in it or leaves via a specific facet.In the higher level,for the triangularization,we construct the transition system according to the reachability relationship obtained in the lower level and search for feasible paths that meet the LTL specification.The control approach is then applied to solve a motion planning problem.

GLOBAL INPUT-TO-STATE STABILIZATION WITH QUANTIZED FEEDBACK FOR DISCRETE-TIME PIECEWISE AFFINE SYSTEMS WITH TIME DELAYS

In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems （PWA） with time delays are considered. Both feedback with time delays and feedback without time delays are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are adopted. The theorems for global input-to-state stabilization with quantized feedback of discrete PWA systems with time delays are

基于模糊聚类的PWA系统的模型辨识

针对一类分段仿射结构的离散时间混杂系统,其模型辨识可等价成对系统数据的分类、分类边界的优化及分类数据的线性回归问题．利用改进的G－K模糊聚类算法,克服聚类迭代过程出现的非数值解问题:以综合性能指标最优确定最佳的子模型个数,从而获得最佳的分类数据;以隶属度为权值,采用加权最小二乘算法提高子模型辨识精度;通过聚类中心最短法则确定两两相邻的子数据集,利用支持向量机思想,构造出一个标准的二次规划问题,得到凸多面体的方程系数．仿真结果验证了该方法的有效性和实用性．

DC/DC变换器的PWA模型及预测控制

利用υ步离散法,得到变换器输入控制变量与状态变量之间的直接映射关系,基于混杂系统理论分析系统的动态方程,建立其分段仿射模型。在此模型的基础上,结合非线性预测控制算法,通过模型预测系统的输出,利用反馈校正误差,给出二次型性能指标的优化计算方法,并由此设计预测控制器。最后,以Buck功率变换器为研究对象,通过与峰值电流控制算法的仿真结果进行比较,验证模型的正确性以及控制器设计的有效性。

基于收缩序列集的约束PWA系统鲁棒预测控制

针对一类有附加有界扰动的约束离散时间分段仿射系统,提出了一种具有鲁棒稳定性保证的模型预测控制方法。通过多参数规划采用一步预测时域法离线计算具有收缩性质的鲁棒可稳定集系列,把它们作为优化问题的稳定约束,并选择一个鲁棒正不变集作为终端约束,使得优化问题的可行性即保证了系统的鲁棒稳定性。仿真实例表明提出的控制方法可使系统渐近稳定到鲁棒正不变集。

基于微粒群优化算法的非线性系统PWA多模型建模

针对复杂非线性系统,将微粒群优化(PSO)算法与多模型建模相结合,设计了一种基于PSO算法的非线性系统分段仿射(PWA)多模型建模算法。该算法将PWA多模型建模问题转化为混合整数二次规划(MIQP)问题,并基于PSO算法对其进行优化求解。在求解的过程中,采用分层优化求解方法,有效降低优化问题的维数,减小了陷入局部最优的概率,并通过仿真验证了该算法的有效性。

分段仿射模型在智能车辆混合控制的应用研究

针对智能车辆混合动力学控制问题,首先采用分段仿射模型(PWA)非线性逼近车辆主要部件的系统特性,将智能车辆纵向动力学转化为计算混合逻辑动力学(MLD)模型,在此基础上提出了混合模型预测控制(HMPC)策略。通过求解混合整数二次规划(MIQP)问题,设计了能够计算智能车辆纵向工作模式(二进制控制输入),以及节气门开口度和制动压力(连续控制输入)在自动调速过程中切换顺序的控制器。最后通过仿真对比模拟分析,验证了所设计的混合控制器在典型工况下具有良好的纵向速度调节控制性能。

基于数据驱动的混杂系统建模与优化控制研究

针对一类非线性、多变量的工业过程,提出了一种基于数据驱动的多输入多输出混杂系统模型辨识方法和基于多参数规划的实时非线性预测控制方法。该方法采用高维数据空间的聚类划分方法,成功实现了MIMO形式的分段仿射含输入自回归(PWARX)模型的辨识;利用混杂系统的HYSDEL建摸语言及其编译器工具,将得到的MIMO-PWARX模型转化成非线性的分段仿射(PWA)模型,采用多参数规划的方法,设计基于PWA模型的预测控制器。该方法实现了从过程数据中挖掘出系统的混杂模型的信息,自动生成复杂过程的PWA模型,并实现了实时的非线性预测控制。最后利用该方法成功实现了四容水箱非线性多输入多输出过程模型的在线控制,得到较好的控制效果。