Nonlinear controller design based on control Lyapunov functions

利用给定控制李雅普诺夫函数，提出了具有凸输入约束的输入仿射非线性系统的渐近稳定控制器和自适应控制器。针对局部齐次输入仿射非线性系统，利用局部齐次控制李雅普诺夫函数设计了具有局部齐次的全局逆最优控制器。该控制器保证了局部收敛率和扇区裕度。我们已经阐明了局部收敛率和扇区边界在坐标变换下是不变的。我们提出了一种全局逆最优控制器，它在原点的小邻域内是LQ最优的。

We have proposed an asymptotically stabilizing controller and an adaptive controller for input affine nonlinear systems with convex input constraints by using given control Lyapunov functions. We have designed a global inverse optimal controller with local homogeneity for locally homogeneous input affine nonlinear systems by using locally homogeneous control Lyapunov functions. The proposed controller guarantees the local convergence rates and sector margins. We have clarified that local convergence rates and sector margins are invariant under coordinate transformations. We have proposed a global inverse optimal controller that is LQ optimal in a small neighborhood of the origin.