Stabilization of nonlinear systems in presence of filtered output via extended high-gain observers

International audienceWe consider the problem of stabilizing a nonlinear system with filtered output. Given an output feedback control law which satisfies a stability requirement, we consider the case in which the necessary output cannot be measured. The measure is rather the output of an auxiliary stable dynamics in cascade with the system. In place of fully redesign the control architecture, we slightly modify the original control law design by adding a disturbance observer and we recover the desired stability property for the system. The disturbance observer is design as an extended high-gain observer

A High-Gain Nonlinear Observer With Limited Gain Power

International audienceIn this note we deal with a new observer for nonlinear systems of dimension n in canonical observability form. We follow the standard high-gain paradigm, but instead of having an observer of dimension n with a gain that grows up to power n, we design an observer of dimension 2n − 2 with a gain that grows up only to power 2

Total stability and integral action for discrete-time nonlinear systems

Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability is well established in the continuous-time nonlinear framework, the same cannot be stated for its discrete-time counterpart. In this paper, we propose the discrete-time parallel of total stability results for continuous-time nonlinear system. This enables the analysis of robustness properties via simple model difference in the discrete-time context. First, we study how existence of equilibria for a nominal model transfers to sufficiently similar ones. Then, we provide results on th

Uniting observers

International audienceWe propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviours for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: one, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behaviour. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented

Multi-pattern output consensus in networks of heterogeneous nonlinear agents with uncertain leader: a nonlinear regression approach

International audienceIn this paper we consider the problem of consensus of a network of heterogeneous nonlinear agents on a family of different desired trajectories generated by an uncertain leader. We design a set of local reference generators and local controllers which guarantees that the agents achieve consensus robustly on all possible trajectories inside this family. The design of the local reference generators is based on the possibility to express the trajectory of the leader as a nonlinear regression law which is parametrized by some constant unknown parameters

Generalized Lyapunov conditions for k-contraction: analysis and feedback design

Recently, the concept of k-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of k-contraction properties has faced significant challenges due to the reliance on complex mathematical objects called matrix compounds. As a result, related control design methodologies have yet to appear in the literature. In this paper, we overcome existing limitations and propose new sufficient conditions for k-contraction which do not rely on matrix compounds. Our design-oriented conditions stem from a strong geometrical interpretation and establish a connection between kcontraction and p-dominance. Notably, these conditions are also necessary in the linear time-invariant framework. Leveraging on these findings, we propose a feedback design methodology for both the linear and the nonlinear scenarios

Emulation-based semiglobal output regulation of minimum phase nonlinear systems with sampled measurements

International audienceWe investigate the semiglobal output regulation of minimum-phase single-input single-output nonlinear systems with sampled measurements. We proceed by emulation. We start by considering a continuous-time regulator, which solves the problem in the absence of sampling. Then, we consider sampled measurements and we model the overall system as a hybrid system. We show that the original continuous-case properties are preserved when the measurements are sampled provided that the maximum allowable transmission interval satisfies a given explicit bound

Chaotic Masking Protocol for Secure Communication and Attack Detection in Remote Estimation of Cyber-Physical Systems

In remote estimation of cyber-physical systems (CPSs), sensor measurements transmitted through network may be attacked by adversaries, leading to leakage risk of privacy (e.g., the system state), and/or failure of the remote estimator. To deal with this problem, a chaotic masking protocol is proposed in this paper to secure the sensor measurements transmission. In detail, at the plant side, a chaotic dynamic system is deployed to encode the sensor measurement, and at the estimator side, an estimator estimates both states of the physical plant and the chaotic system. With this protocol, no additional secure communication links is needed for synchronization, and the masking effect can be perfectly removed when the estimator is in steady state. Furthermore, this masking protocol can deal with multiple types of attacks, i.e., eavesdropping attack, replay attack, and stealthy false data injection attack.Comment: 8 pages, 7 figure

Quantifying the effect of demixing approaches on directed connectivity estimated between reconstructed EEG sources

Electrical activity recorded on the scalp using electroencephalography (EEG) results from the mixing of signals originating from different regions of the brain as well as from artifactual sources. In order to investigate the role of distinct brain areas in a given experiment, the signal recorded on the sensors is typically projected back into the brain (source reconstruction) using algorithms that address the so-called EEG inverse problem. Once the activity of sources located inside of the brain has been reconstructed, it is often desirable to study the statistical dependencies among them, in particular to quantify directional dynamical interactions between brain areas. Unfortunately, even when performing source reconstruction, the superposition of signals that is due to the propagation of activity from sources to sensors cannot be completely undone, resulting in potentially biased estimates of directional functional connectivity. Here we perform a set of simulations involving interacting sources to quantify source connectivity estimation performance as a function of the location of the sources, their distance to each other, the noise level, the source reconstruction algorithm, and the connectivity estimator. The generated source activity was projected onto the scalp and projected back to the cortical level using two source reconstruction algorithms, linearly constrained minimum variance beamforming and Exact' low-resolution tomography (eLORETA). In source space, directed connectivity was estimated using multi-variate Granger causality and time-reversed Granger causality, and compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance