Adaptive output feedback finite time control for a class of second order nonlinear systems

This paper develops a finite time output feedback based control scheme for a class of nonlinear second order systems. The system representation includes both model uncertainty and uncertain parameters. A finite time parameter estimator is developed. This facilitates the design of a finite time observer based on the well-established step-by-step sliding mode observer design approach. A terminal sliding mode control scheme is then developed using the corresponding state estimates. The methodology is applied to a continuous stirred tank reactor system to validate the effectiveness of the proposed approach

Continuous Uniform Finite Time Stabilization of Planar Controllable Systems

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong $\mathcal{C}^1$ Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers

Finite Time Stabilization of a Double Integrator - Part I: Continuous Sliding Mode-based Position Feedback Synthesis

International audienceThe twisting and supertwisting algorithms, generating important classes of second order sliding modes (SOSM's), are well-recognized for their finite time stability and robustness properties. In the present paper, a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of SOSM's that present the aforementioned attractive features. Thus modified, the twisting and supertwisting algorithms are utilized in the state feedback synthesis and, respectively, velocity observer design, made for the finite time stabilization of a double integrator if only position measurements are available. Performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations

LpL_p-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design

Consider the $n$-th integrator $\dot x=J_nx+\sigma(u)e_n$, where $x\in\mathbb{R}^n$, $u\in \mathbb{R}$, $J_n$ is the $n$-th Jordan block and $e_n=(0\ \cdots 0\ 1)^T\in\mathbb{R}^n$. We provide easily implementable state feedback laws $u=k(x)$ which not only render the closed-loop system globally asymptotically stable but also are finite-gain $L_p$-stabilizing with arbitrarily small gain. These $L_p$-stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite-time stabilization of linear systems. We also provide additional $L_\infty$-stabilization results for the case of both internal and external disturbances of the $n$-th integrator, namely for the perturbed system $\dot x=J_nx+e_n\sigma (k(x)+d)+D$ where $d\in\mathbb{R}$ and $D\in\mathbb{R}^n$