Computing the delay margin of the subthalamo-pallidal feedback loop

In the last ten years, several models of basal ganglia dynamics have been proposed in order to explain the abnormal neural oscillations that appear in Parkinson's disease. Recently, Nevado Holgado et al. [1] have shown that a two-dimensional nonlinear model of the subthalamopallidal feedback loop, which interconnects the subthalamic nucleus (STN) and the external part of the globus pallidus (GPe), exhibits oscillations in the beta band when the parameters of the model are those of the pathological state. They proposed, moreover, a simplified model for which the condition for oscillations can be computed analytically. In our work, we consider a slightly more general model of the subthalamopallidal feedback loop, that includes a self-excitation loop of the STN onto itself and allows more general activation functions. It coincides with the model of Wilson and Cowan [2], with the difference that interconnection delays are included and that the refractory period is neglected

A new mixed wheel slip and acceleration control based on a cascaded design

International audienceIn this paper, a new cascaded wheel-slip control strategy based on wheel slip and wheel acceleration measurements is presented. This new algorithm is able to stabilize globally and asymptotically the wheel slip around any prescribed setpoint, both in the stable and unstable regions of the tyre

Recent results on wheel slip control: Hybrid and continuous algorithms

In this talk, a new cascaded wheel-slip control strategy based on wheel slip and wheel acceleration measurements is presented. This new algorithm is able to stabilize globally and asymptotically the wheel slip around any prescribed setpoint, both in the stable and unstable regions of the tyre

Jumps and synchronization in anti-lock brake algorithms

International audienceThe aim of our paper is to provide a new class of anti-lock brake algorithms (that use wheel deceleration logic-based switchings) and a simple mathematical background that explains their behavior. These algorithms extend those proposed in our previous work [6], and consider cases where there might be discontinuities of road characteristics or where it is intended to synchronize the ABS strategies on several wheels of the vehicle

Validity of the phase approximation for coupled nonlinear oscillators: a case study

International audienceMotivated by neuroscience applications, we rigorously derive the phase dynamics of an ensemble of interconnected nonlinear oscillators under the effect of a proportional feedback. We individuate the critical parameters determining the validity of the phase approximation and derive bounds on the accuracy of the latter in reproducing the behavior of the original system. We use these results to study the existence of oscillating phase-locked solutions in the original oscillator model

Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback

International audienceMotivated by the recent development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of mean-field feedback and analyze the robustness of its phase-locking with respect to general inputs. Under standard assumptions, this system can be reduced to a modified version of the Kuramoto model of coupled nonlinear oscillators. In the first part of the paper we present an analytical study on the existence of phase-locked solutions under generic interconnection and feedback configurations. In particular we show that, in general, no oscillating phaselocked solutions can co-exist with any non-zero proportional mean-field feedback. In the second part we prove some robustness properties of phase-locked solutions (namely total stability). Thisgeneral result allows in particular to justify the persistence of practically phase-locked states if sufficiently small feedback gains are applied, and to give explicit necessary conditions on the intensity of a desynchronizing mean-field feedback. Furthermore, the Lyapunov function used in the analysis provides a new characterization of the robust phase-locked configurations in the Kuramoto system with symmetric interconnections

Existence of phase-locking in the Kuramoto system under mean-fi eld feedback

International audienceMotivated by the development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of a proportional mean-fi eld feedback. Under standard assumptions, this system can be reduced to a modi fied version of the Kuramoto model of coupled nonlinear oscillators. In the first part of the paper we show that, in general, no oscillating phase-locked solution can co-exist with any non-zero feedback gain. In the second part we propose a new characterization of phase-locking between Kuramoto oscillators. In particular we derive a fi xed point equation for the Kuramoto system under mean- field feedback and we show how, generically, the "standard" (with zero feedback gain) Kuramoto fixed point equation is locally invertible in terms of the implicit function theorem

Adaptation of hybrid five-phase ABS algorithms for experimental validation

International audienceThe Anti-lock Braking System (ABS) is the most important active safety system for passenger cars, but unfortunately the literature is not really precise about its description, stability and performance. This research improves a five-phase hybrid algorithm based on wheel deceleration and validate it on a tyre-in-the-loop laboratory facility. Five relevant effects are modelled so that the simulation matches the reality. Two methods to deal with the time delays are proposed. It can be verified that the limit cycle of the ABS encircle the optimal braking point without having any tyre parameter a priori known

Hybrid modelling and limit cycle analysis for a class of five-phase ABS algorithms

International audienceThe aim of our paper is to provide a new class of five-phase anti-lock brake algorithms (that use wheel deceleration logic-based switching) and a simple mathematical background that explains their behavior. First, we completely characterize the conditions required for our algorithm to work. Next, we explain how to compute analytically an approximation of the Poincaré map of the system (without using numerical integration) and show how to calibrate the algorithm's parameters to obtain the most efficient limit cycle