一类线性切换系统的鲁棒状态反馈镇定

考虑一类标称系统存在共同Lyapunov函数的切换系统的鲁棒镇定问题。在不确定性不满足匹配条件下,设计出鲁棒状态反馈控制器,并在给定的切换策略下,确保闭环系统在其平衡点处渐近稳定。仿真结果表明所设计控制器是有效的。     

基于反步法非线性纯反馈系统的控制器设计

针对由于非线性纯反馈系统存在非仿射性结构使得用以往的坐标变换难以设计出控制器的问题,提出了一种新的坐标变换,并引入了一阶控制输入的辅助系统来处理非线性纯反馈系统。首先,结合新提出的坐标变换,计算出新状态方程;然后,基于反步法在每一步中设计出正定的Lyapunov函数;最后,通过设计虚拟控制器和实际的辅助控制器使得Lyapunov的导数负定,这样从理论上解决了非线性纯反馈系统的跟踪问题。仿真实验表明所设计的辅助控制器能使得纯反馈闭环系统所有状态信号有界,控制输出能跟踪到给定信号,跟踪误差渐近地趋于稳定,从而达到要求。     

一类不确定切换模糊组合系统的分散鲁棒镇定

提出一种切换模糊组合系统模型并讨论其鲁棒控制问题.分别利用单Lyapunov函数方法和多Lyapunov函数方法设计出分散切换律和控制器,给出了系统在分散切换律和分散控制器作用下的矩阵不等式可镇定条件.仿真结果表明了该设计方法的有效性.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

一类受扰动脉冲切换系统鲁棒指数镇定

提出一类具有边界范数有界扰动的脉冲切换系统在任意切换条件下鲁棒指数镇定问题。应用Lyapunow直接法,导出这类受扰动脉冲切换系统指数稳定的充分条件并且给出线性时不变状态反馈控制律使该受扰动脉冲切换系统指数镇定,最后,给出数值示例说明所得到的结果是有效的。     

一类非线性离散切换系统基于观测器的指数镇定

对一类离散非线性切换系统, 考虑了基于观测器的指数镇定问题. 借助微分中值定理(DMVT), 将非线性切换系统转化为线性参数(LPV)切换系统. 当状态变量不完全可获得时, 基于多Lyapunov函数方法, 给出系统在基于观测器的输出反馈控制器下指数镇定的充分条件. 所设计的滞后切换规则能够避免产生滑动模态. 并且将结果推广到系统方程含有不确定性的情况. 最后, 仿真例子说明了设计方法的有效性.     

基于切换系统的独立微电网稳定控制设计

独立微电网是一个复杂的非线性系统,为解决典型光储柴独立微电网在能源约束下存在控制单元切换的问题,提出将非线性切换系统理论应用到主从控制下的主控单元切换问题上。首先,当主从控制下的储能系统和柴油发电机分别作为主控单元时,将它们视为两个子系统,建立非线性切换系统模型。然后,应用多Lyapunov函数法分析切换系统的稳定性,同时利用backstepping方法分别设计子系统的非线性控制器,保留系统的非线性特征。最后,采用美国国家能源实验室开发的仿真软件中的硬充电策略作为切换策略,保证切换过程中系统的稳定性。通过MATLAB仿真证明了所设计方法的有效性。     

一类不确定非线性系统的鲁棒镇定器设计

本文研究了输入线性出现在状态方程中的一类不确定非线性系统的鲁棒镇定问题，通过状态坐标变换和具有反馈的输入变换将不确定非经恶性循环系统线性化，基于Lyapunov第二法，对不确定性满足匹配条件和不满足匹配条件时，给出参数不确定性非线性系统的鲁棒镇定规律，并给出计算实例。     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

约束非线性系统切换鲁棒预测控制

采用“分段蕴含”(PWE)方法, 用一组线性变参数模型(LPV)近似约束非线性系统, 降低模型近似的保守性. 对每个LPV模型引入参数Lyapunov函数, 得到稳定的控制律, 并施加于非线性系统. 当检测到LPV模型发生切换时, 根据可行域的离线设计方法确定适当的切换律, 使系统按照设定的规则切换, 保证切换后的初始状态可行. 在文章最后给出了基于切换策略的控制算法的可行性和稳定性. 与传统非线性预测控制相比, 基于切换策略的鲁棒预测控制方法保守性更低, 计算量更小.     

Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.     

Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems

Stabilization of uncertain sampled-data strict-feedback systems is addressed. The stability study is carried out on the Euler approximation of the exact discretized model of the plant. Firstly, a class of state-feedback controllers is developed that guarantees an input-to-state stability property for the closed-loop system. Additionally, assuming some hypotheses on the uncertain terms hold, a practical asymptotic stability property is ensured by designing an appropriate class of controllers.     

Adaptive control of nonlinear systems with nonlinear parameterization

An adaptive feedback regulation scheme is proposed for a class of single input nonlinear systems, with nonlinear parameterizations. A proof of local regulation is given. The results are validated through a simulation study.     

Robust stabilization of switched discrete-time systems with actuator saturation

This paper studies the robust stabilization problem of switched discrete-time linear systems subject to actuator saturation. New switched saturation-dependent Lyapunov functions are exploited to design a robust stabilizing state feedback controller that maximizes an estimation of the domain of attraction. The design problem of controller （coefficient matrices） is then reduced to an optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to show the effectiveness of the proposed method.     

切换系统基于反演递推法的鲁棒自适应控制

切换系统的稳定控制问题是一个重要的研究问题。基于李雅普诺夫函数的方法是研究切换系统稳定性的重要手段,但是有约束非线性系统的李亚普诺夫函数构造仍是一个难题(特别是对带有不确定性的非线性系统)。针对一类带有不确定性的严格反馈型切换非线性系统,利用反演递推法(backstepping)设计了子系统的基于李亚普诺夫函数的鲁棒自适应控制器,并证明了子闭环系统的稳定性,同时设计适当的切换律保证了整个闭环系统的稳定性。其中系统的未知不确定性及外界干扰不要求线性增长速度,并由模糊系统在线逼近。结果表明所提出方法的有效性。     

Global stabilization of MIMO minimum-phase nonlinear systems without strict triangular conditions

An extension of backstepping to a class of multivariable minimum-phase nonlinear systems is proposed. The systems are assumed to be in a special interlaced form which includes a lower triangular form as a special case. The extension involves the recursive application of backstepping and augmentation.     

Stochastic nonlinear stabilization — II: Inverse optimality

After considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper, in this second part, we address the classical question of when is a stabilizing (in probability) controller optimal and show that for every system with a stochastic control Lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional. Then we return to the problem from Part I and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin.