Marco Tulio Angulo

Robust exact uniformly convergent arbitrary order differentiator

An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n-1) times is that its n-th derivative is uniformly bounded by a known constant. The proposed differentiator switches from a newly designed uniform differentiator to the classical High-Order Sliding Mode (HOSM) differentiator. The Uniform part drives the differentiation error trajectories into a compact neighborhood of the origin in a time that is independent of the initial differentiation error. Then, the HOSM differentiator is used to bring the differentiation error to zero in finite-time.

Brief paper: Output-feedback finite-time stabilization of disturbed LTI systems

Semi-global finite-time exact stabilization of linear time-invariant systems with matched disturbances is attained using a dynamic output feedback, provided the system is controllable, strongly observable and the disturbance has a bound affine in the state norm. The novel non-homogeneous high-order sliding-mode control strategy is based on the gain adaptation of both the controller and the differentiator included in the feedback. A robust criterion is developed for the detection of differentiator convergence to turn on the controller at a proper time.

Robust exact finite-time output based control using high-order sliding modes

Linear time-invariant systems with matched perturbations are exactly stabilised in finite time by means of dynamic output-feedback control under the assumptions of a permanent complete vector relative degree and bounded perturbations. The approach makes use of non-homogeneous high-order sliding-mode controllers and differentiators. A criterion of the differentiator convergence is developed for the detection of a proper time of turning on the controller. A gain adaptation strategy is proposed for both controller and differentiator. The performance with noisy discrete sampling is studied.

Output-feedback finite-time stabilization of disturbed feedback linearizable nonlinear systems

A novel methodology for designing multivariable High-Order Sliding-Mode (HOSM) controllers for disturbed feedback linearizable nonlinear systems is introduced. It provides for the finite-time stabilization of the origin of the state-space by using output feedback. Only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required. The control problem is solved in two consecutive steps: firstly, designing an observer based on the measured output and, secondly, designing of a full-state controller computed from a new virtual output with vector relative degree. The introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives. By estimating the required derivatives through the HOSM differentiator, a finite-time convergent observer is constructed.

The differentiation error of noisy signals using the Generalized Super-Twisting differentiator

A method to compute the differentiation error in presence of bounded measurement noise for the family of Generalized Super-Twisting differentiators is presented. The proposed method allows choosing the optimal gain of each differentiator in the family providing the smallest ultimate bound of the differentiation error. In particular, an heuristic formula for the optimal gain of the pure Super-Twisting differentiator is presented.

Design of a prescribed convergence time uniform Robust Exact Observer in the presence of measurement noise

In practice, any observer is expected to have small convergence time and high precision despite the presence of disturbances. Decreasing the convergence time usually requires to increase the overall gain of the observer. However, this also amplifies the effect of the noise and deteriorates the precision. This trade-off is studied in this paper for the Uniform Robust Exact Observer for mechanical systems: an observer with uniform convergence with respect to the initial condition. In addition, a method to compute its gains is presented guaranteeing a prescribed convergence time while keeping the best possible precision under measurement noise. A simulation example comparing the performance of the uniform observer with respect to a linear one is presented.

An exact and uniformly convergent arbitrary order differentiator

An arbitrary order differentiator that, in absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n − 1)-times is that its n-th derivative is uniformly bounded by a known constant. The new differentiator is obtained by combining the HOSM differentiator with an additional part that converges uniformly with respect to the initial conditions.

Fundamental limitations of network reconstruction from temporal data

Inferring properties of the interaction matrix that characterizes how nodes in a networked system directly interact with each other is a well-known network reconstruction problem. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations governing which properties of the interaction matrix (e.g. adjacency pattern, sign pattern or degree sequence) can be inferred from given temporal data of individual nodes remain unknown. Here, we rigorously derive the necessary conditions to reconstruct any property of the interaction matrix. Counterintuitively, we find that reconstructing any property of the interaction matrix is generically as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. Revealing these fundamental limitations sheds light on the design of better network reconstruction algorithms that offer practical improvements over existing methods.

On Robust Output Based Finite-Time Control of LTI systems using HOSMs

Abstract Finite-Time stability of Linear Time Invariant systems with matched perturbations using dynamic output feedback is achieved under the assumptions of well-defined relative degree and a known bound of the perturbations. The approach is based on high order sliding modes, using global controllers and differentiator. A separation criteria that allows to detect the convergence of the differentiator and posterior gain adaptation is presented. Analysis of the performance under noise and sampling is presented.

Mapping the ecological networks of microbial communities

Mapping the ecological networks of microbial communities is a necessary step toward understanding their assembly rules and predicting their temporal behavior. However, existing methods require assuming a particular population dynamics model, which is not known a priori. Moreover, those methods require fitting longitudinal abundance data, which are often not informative enough for reliable inference. To overcome these limitations, here we develop a new method based on steady-state abundance data. Our method can infer the network topology and inter-taxa interaction types without assuming any particular population dynamics model. Additionally, when the population dynamics is assumed to follow the classic Generalized Lotka–Volterra model, our method can infer the inter-taxa interaction strengths and intrinsic growth rates. We systematically validate our method using simulated data, and then apply it to four experimental data sets. Our method represents a key step towards reliable modeling of complex, real-world microbial communities, such as the human gut microbiota.Understanding ecological interactions in microbial communities is limited by lack of informative longitudinal abundance data necessary for reliable inference. Here, Xiao et al. develop a method to infer the interactions between microbes based on their abundances in steady-state samples.