共查询到18条相似文献,搜索用时 328 毫秒
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通过Lyapunov函数设计反馈控制器使得非线性仿射控制系统全局渐进稳定是一种有效的方法. 为了使得反馈控制器具有连续性, Sontag提出控制Lyapunov函数应具有小控制性, 即要求在原点连续反馈控制器存在, 该条件在实际中无法应用. 针对这一问题本文提出了聚点条件来保证反馈控制器具有连续性, 该条件直接对选择的控制Lyapunov函数进行检验, 并且聚点条件还是必要的; 文章将控制Lyapunov函数的严格不等式放宽为非严格的不等式, 提出非严格控制Lyapunov函数, 利用LaSalle定理得到: 采用满足聚点条件的非严格控制Lyapunov函数来设计连续反馈控制器, 非线性仿射控制系统是全局渐进稳定, 扩大了控制Lyapunov函数的寻找范围; 最后通过对一种带摩擦的弹簧系统进行验证. 相似文献
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不确定非线性切换系统的鲁棒H∞控制 总被引:1,自引:0,他引:1
讨论了一类不确定非线性切换系统的鲁棒H∞控制问题.首先,基于多Lyapunov函数方法,设计状态反馈控制器以及切换律,使得对于所有允许的不确定性.相应的闭环系统渐近稳定又具有指定的L2-增益.该问题可解的充分条件以一组含有纯量函数的偏微分不等式形式给出,此偏微分不等式较一般Hamilton-Jacobi不等式更具可解性.所提出的方法不要求任何一个子系统渐近稳定.接着作为应用,借助混杂状态反馈策略讨论了非切换不确定非线性系统的鲁棒H∞控制问题.最后通过一个简单例子说明了控制设计方法的可行性. 相似文献
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针对一类状态/输入受限的不确定严格反馈非仿射非线性系统跟踪控制问题,提出一种鲁棒自适应backstepping控制策略.在保证系统精度的前提下,对状态/输入受限的非仿射系统进行Taylor级数在线展开,得到其仿射形式;为保证系统复合扰动在线准确逼近,提出基于投影算子的递归扰动模糊神经网络干扰观测器(RPFNNDO);在考虑不确定系统存在状态受限和输入饱和等因素下,结合障碍Lyapunov函数、tanh函数及Nussbaum函数,利用backstepping方法设计控制器,并采用Lyapunov稳定理论分析闭环系统稳定性.应用于无人机航迹控制的仿真结果验证了所提方法的有效性. 相似文献
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针对具有量化输入饱和及输出受限的非线性非仿射系统,提出固定时间自适应神经网络跟踪控制方法.引入中值定理解决系统具有非仿射结构的问题;基于反步法,使用Barrier Lyapunov函数约束系统输出,并利用RBF神经网络逼近未知函数;根据固定时间控制理论设计输入信号,该输入信号由滞后量化器量化,以降低控制信号的通信速率,并保证该系统在满足量化输入饱和及输出受限的条件下,系统可以在固定时间内跟踪上期望信号,且该系统收敛时间与初始状态无关.最后通过Matlab仿真软件验证所设计控制器的有效性. 相似文献
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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。 相似文献
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This paper addresses the stabilization problems for nonlinear affine systems. First of all, the explicit feedback controller is developed for a nonlinear multiple-input affine system by assuming that there exists a control Lyapunov function. Next, based upon the homogeneous property, sufficient conditions for the continuity of the derived controller are developed. And then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems. It is shown that under some homogeneous assumptions on control Lyapunov functions and the interconnection term, the cascaded system can be globally stabilized. Finally, some interesting results of finite-time stabilization for nonlinear affine systems are also obtained. 相似文献
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The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. Stabilizing control laws may not be robust to this type of uncertainty, especially if cancellation of nonlinearities is used in the design. By exploiting a connection between robustness and optimality, “domination redesign” of the control Lyapunov function (CLF) based Sontag's formula has been shown to possess robustness to static and dynamic input uncertainties. In this paper we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a CLF which is suitable for domination redesign. 相似文献
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For the problem of stabilization of nonlinear systems linear in unknown constant parameters, we introduce the concept of an adaptive control Lyapunov function (aclf) and use Sontag's constructive proof of Artstein's theorem to design an adaptive controller. In this framework the problem of adaptive stabilization of a nonlinear system is reduced to the problem of nonadaptive stabilization of a modified system. To illustrate the construction of aclf's we give an adaptive backstepping lemma which recovers our earlier design. 相似文献
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Emmanuel Moulay 《Automatica》2008,44(11):2981-2984
In this paper, we provide an explicit homogeneous feedback control with the requirement that a control Lyapunov function exists for an affine control system and satisfies an homogeneous condition. We use a modified version of the Sontag formula to achieve our main goal. Moreover, we prove that the existence of an homogeneous control Lyapunov function for an homogeneous affine system leads to an homogeneous closed-loop system by using the previous feedback control. 相似文献
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讨论三维仿射非线性控制系统,在具有零和一对共轭纯虚数特征值的临界状态下的局部光滑镇定性.首先,应用非奇异线性状态变换和时间尺度变换,将系统转化成标准形式.之后,运用形式级数法的思想和扩展正则判别函数法,构造多组线性方程组,给出确定光滑控制律和闭环系统李雅普诺夫函数的一种方法,从而得到该标准化系统局部光滑镇定的充分条件.示例说明该方法是有效的. 相似文献
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This paper focuses on an adaptive practical preassigned finite‐time control problem for a class of unknown pure‐feedback nonlinear systems with full state constraints. Two new concepts, called preassigned finite‐time function and practical preassigned finite‐time stability, are defined. In order to achieve the main result, the pure‐feedback system is first transformed into an affine strict‐feedback nonlinear system based on the mean value theorem. Then, an adaptive preassigned finite‐time controller is obtained based on a modified barrier Lyapunov function and backstepping technique. Finally, simulation examples are exhibited to demonstrate the effectiveness of the proposed scheme. 相似文献
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This paper investigates external stability of Caputo fractional‐order nonlinear control systems. Following the idea of a traditional Lyapunov function method, we point out the problems that would appear when applying it for fractional external stability. These problems are shown to be solvable by employing results on smoothness of solutions, but this method generalized for Caputo fractional‐order nonlinear control systems requires strong conditions to be imposed on vector field functions and inputs. To further explore the fractional external stability, diffusive realizations and Lyapunov‐like functions are taken into consideration. Specifically, a Caputo fractional‐order nonlinear control system with certain assumptions proves to be equivalent to its diffusive realization; a Lyapunov‐like function based on the realization exhibits properties useful to prove the external stability. As expected, this Lyapunov‐like method has weaker requirements. Finally, it is applied to the external stabilization of a Caputo fractional‐order Chua's circuits with inputs. 相似文献