Olivier Huber

Bio: Olivier Huber is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topics: Sliding mode control & Discretization. The author has an hindex of 7, co-authored 16 publications receiving 223 citations. Previous affiliations of Olivier Huber include Humboldt University of Berlin & French Institute for Research in Computer Science and Automation.

Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control

Abstract: Discrete-time sliding mode controllers with an implicit discretization of the signum function are considered. With a proper choice of the equivalent part of the control, the resulting controller is shown to be Lyapunov stable with finite-time convergence of the sliding variable to 0. The convergence of the control input, as the sampling period goes to 0, to the continuous-time one is shown. The robustness with respect to matching perturbations is also investigated. The discretization performance in terms of the error order is studied for different discretizations of the equivalent part of the input. Numerical and experimental results illustrate and support the analysis.

An introduction to Siconos

Abstract: In this document, a brief overview of the Siconos Platform is given. One of the goal is to give a flavor on a simple example of the ability of the platform to model and simulate the so-called non smooth dynamical systems (NSDS). In particular, some examples of Lagrangian mechanical systems with contact and friction or electrical circuits with ideal and piecewise linear components (diodes, MOS transistors, \ldots) are commented. Finally, the Siconos software is presented, starting from its architecture to a non exhaustive presentation of its components and functionalities. The aim of this document is not to serve as a reference guide but more as a illustrative introduction document to promote the use of the platform.

Lyapunov Stability Analysis of the Implicit Discrete-Time Twisting Control Algorithm

Abstract: An implicit discrete-time version of the twisting sliding-mode control algorithm is considered. The framework of variational inequalities is used to define the control input values. This provides the foundation for both the analysis of the controller and the numerical computations. The controller is shown to be well-defined and the discrete-time closed-loop system's fixed point is finite-time globally stable in the sense of Lyapunov. The analysis is led in the unperturbed case, and numerical simulations demonstrate the efficiency of the proposed controller when a disturbance acts on the system.

Experimental results on implicit and explicit time-discretization of equivalent-control-based sliding-mode control

Abstract: This chapter presents a set of experimental results concerning the sliding mode control of an electro-pneumatic system. The controller is implemented {\em via} a micro-processor as a discrete-time input. Three discrete-time control strategies are considered for the implementation of the discontinuous part of the sliding mode controller: explicit discretizations with and without saturation, and an implicit discretization (that is very easy to implement as a projection on the interval [-1,1]). While the explicit implementation is known to generate numerical chattering, the implicit one is expected to significantly reduce chattering while keeping the accuracy. The experimental results reported in this work remarkably confirm that the implicit discrete-time sliding mode supersedes the explicit ones, with several important features: chattering in the control input is almost eliminated (while the explicit and saturated controllers behave like high-frequency bang-bang inputs), the input magnitude depends only on the perturbation size and is ``independent'' of the controller gain and sampling time. On the contrary the explicit controller shows obvious chattering for all sampling times, its magnitude increases as the controller gain increases, and it does not reduce when the sampling period augments. The tracking errors are comparable for both methods, though the implicit method keeps the precision when the control gain increases, which is not the case for the explicit one. Introducing a saturation in the explicit controller does not allow to significantly improve the explicit controller behaviour if one does not take care of the saturation width.

Chattering-Free Digital Sliding-Mode Control With State Observer and Disturbance Rejection

Abstract: In this paper, a novel discrete-time implementation of sliding-mode control systems is proposed, which fully exploits the multivaluedness of the dynamics on the sliding surface. It is shown to guarantee a smooth stabilization on the discrete sliding surface in the disturbance-free case, hence avoiding the chattering effects due to the time-discretization. In addition, when a disturbance acts on the system, the controller attenuates the disturbance effects on the sliding surface by a factor h (where h is the sampling period). Most importantly, this holds even for large h . The controller is based on an implicit Euler method and is very easy to implement with projections on the interval [-1, 1] (or as the solution of a quadratic program). The zero-order-hold (ZOH) method is also investigated. First- and second-order perturbed systems (with a disturbance satisfying the matching condition) without and with dynamical disturbance compensation are analyzed, with classical and twisting sliding-mode controllers.

Event-triggered sliding mode control for a class of nonlinear systems

Abstract: Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into a...

Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control

Abstract: Discrete-time sliding mode controllers with an implicit discretization of the signum function are considered. With a proper choice of the equivalent part of the control, the resulting controller is shown to be Lyapunov stable with finite-time convergence of the sliding variable to 0. The convergence of the control input, as the sampling period goes to 0, to the continuous-time one is shown. The robustness with respect to matching perturbations is also investigated. The discretization performance in terms of the error order is studied for different discretizations of the equivalent part of the input. Numerical and experimental results illustrate and support the analysis.