$L_p$-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 $xinmathbb{R}^n$, $uin mathbb{R}$, $J_n$ is the $n$-th Jordan block and $e_n=(0 cdots 0 1)^Tinmathbb{R}^n$. 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 $dot x=J_nx+e_nsigma (k(x)+d)+D$ where $dinmathbb{R}$ and $Dinmathbb{R}^n$.

Observer-Based High Order Sliding Mode Control of Unity Power Factor in Three-Phase AC/DC Converter for Hybrid Electric Vehicle Applications

In this paper, a full-bridge boost power converter topology is studied for power factor control, using output high order sliding mode control. The AC/DC converters are used for charging the battery and super-capacitor in hybrid electric vehicles from the utility. The proposed control forces the input currents to track the desired values, which can controls the output voltage while keeping the power factor close to one. Super-twisting sliding mode observer is employed to estimate the input currents and load resistance only from the measurement of output voltage. Lyapunov analysis shows the asymptotic convergence of the closed loop system to zero. Simulation results show the effectiveness and robustness of the proposed controller.

Adaptive-Gain Second Order Sliding Mode Observer Design for Switching Power Converters

In this paper, a novel adaptive-gain Second Order Sliding Mode (SOSM) observer is proposed for multicell converters by considering it as a class of hybrid systems. The aim is to reduce the number of voltage sensors by estimating the capacitor voltages only from the measurement of load current. The proposed observer is proven to be robust in the presence of perturbations with emph{unknown} boundary. However, the states of the system are only partially observable in the sense of observability rank condition. Due to its switching behavior, a recent concept of $Z(T_N)$ observability is used to analysis its hybrid observability, since its observability depends upon the switching control signals. Under certain condition of the switching sequences, the voltage across each capacitor becomes observable. Simulation results and comparisons with Luenberger switched observer highlight the effectiveness and robustness of the proposed observer with respect to output measurement noise and system uncertainties (load variations).

Adaptive High Order Sliding Mode Observer Based Fault Reconstruction for a Class of Nonlinear Uncertain Systems: Application to PEM Fuel Cell System

This paper focuses on observer based fault reconstruction for a class of nonlinear uncertain systems with Lipschitz nonlinearities. An adaptive-gain Super-Twisting (STW) observer is developed for observing the system states, where the adaptive law compensates the uncertainty in parameters. The inherent equivalent output error injection feature of STW algorithm is then used to reconstruct the fault signal. The performance of the proposed observer is validated through a Hardware-In-Loop (HIL) simulator which consists of a commercial twin screw compressor and a real time Polymer Electrolyte Membrane fuel cell emulation system. The simulation results illustrate the feasibility and effectiveness of the proposed approach for application to fuel cell systems.

Stabilization of perturbed integrator chains using Lyapunov-Based Homogeneous Controllers

In this paper, we present a Lyapunov-based homogeneous controller for the stabilization of a perturbed chain of integrators of arbitrary order $rgeq 1$. The proposed controller is based on homogeneous controller for stabilization of pure integrator chains. The advantages to control the homogeneity degree of the controller are also discussed. A bounded-controller with minimum amplitude of discontinuous control and a controller with fixed-time convergence are synthesized, using control of homogeneity degree, and their performances are shown in simulations. It is demonstrated that the homogeneous arbitrary HOSM controller cite{Levant2001} is a particular case of our controller.

Target-point based path following controller for a car-type vehicle using bounded controls

In this paper, we have studied the control problem of target-point based path following for car-type vehicles. This special path following task arises from the needs of vision based guidance systems, where a given target-point located ahead of the vehicle, in the visual range of the camera, must follow a specified path. A solution to this problem is developed through a non linear transformation of the path following problem into a reference trajectory tracking problem, by modeling the target point as a virtual vehicle. Bounded feedback laws must be then used on the real vehicles angular acceleration and the virtual vehicles velocity, to achieve stability. The resulting controller is globally asymptotically stable with respect and the proof is demonstrated using Lyapunov based arguments and a bootstrap argument. The effectiveness of this controller has been illustrated through simulations.