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Context. The transition from left-hand to right-hand polarized Alfv\'en waves depends on the wavenumber, the ratio of kinetic to magnetic pressure $\beta$, temperature anisotropy, and ion composition of the plasma. Along with the temperature anisotropy, the electron-to-proton temperature ratio $T_e/T_p$ is of great relevance for the characterization of the thermal properties of a plasma. This ratio varies significantly between different space plasma environments. Thus, studying how variations on this ratio affect the polarisation properties of electromagnetic waves becomes highly relevant for our understanding of the dynamics of space plasmas. Aim. We present an extensive study on the effect of the thermal properties of electrons on the behaviour and characteristics of Alfv\'enic waves in fully kinetic linear theory, as well as on the transition from electromagnetic ion-cyclotron (EMIC) to kinetic Alfv\'en waves (KAW). Method. We solve the fully kinetic dispersion relation for oblique electromagnetic waves of the Alfv\'en branch in a homogenous Maxwellian electron-proton plasma. We quantify the effect of the thermal properties of electrons by varying the electron-to-proton temperature ratio for different configurations of the propagation angle, $\beta_p=8\pi nkT_p/B^2$, and wavenumber. Results. We show that the temperature ratio $T_e/T_p$ has strong and non-trivial effects on the polarisation of the Alfv\'enic modes, especially at kinetic scales and $\beta_e+\beta_p>0.5$. We conclude that electron inertia plays an important role in the kinetic scale physics of the KAW in the warm plasma regime, and thus cannot be excluded in hybrid models for computer simulations., Comment: 13 pages, 7 figures

The expanding solar wind plasma ubiquitously exhibits anisotropic non-thermal particle velocity distributions. Typically, proton Velocity Distribution Functions (VDFs) show the presence of a core and a field-aligned beam. Novel observations made by Parker Solar Probe (PSP) in the innermost heliosphere have revealed new complex features in the proton VDFs, namely anisotropic beams that sometimes experience perpendicular diffusion. This phenomenon gives rise to VDFs that resemble a "hammerhead". In this study, we use a 2.5D fully kinetic simulation to investigate the stability of proton VDFs with anisotropic beams observed by PSP. Our setup consists of a core and an anisotropic beam populations that drift with respect to each other. This configuration triggers a proton-beam instability from which nearly parallel fast magnetosonic modes develop. Our results demonstrate that before this instability reaches saturation, the waves resonantly interact with the beam protons, causing significant perpendicular heating at the expense of the parallel temperature. Furthermore, the proton perpendicular heating induces a hammerhead-like shape in the resulting VDF. Our results suggest that this mechanism probably contribute to producing the observed hammerhead distributions.

This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed optimization often lead to conservative performance, characterized by slow convergence or even divergence if parameters are not properly chosen. In this work, we propose a systems theory tool based on the port-Hamiltonian formalism to design algorithms for consensus optimization programs. Moreover, we propose the Mixed Implicit Discretization (MID), which transforms the continuous-time port-Hamiltonian system into a discrete time one, maintaining the same convergence properties regardless of the step size parameter. The consensus optimization algorithm enhances the convergence speed without worrying about the relationship between parameters and stability. Numerical experiments demonstrate the method's superior performance in convergence speed, outperforming other methods, especially in scenarios where conventional methods fail due to step size parameter limitations.

The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This paper develops a first-order differentiator with the following combination of properties: robustness to measurement noise, exactness in the absence of noise, optimal worst-case differentiation error, and Lipschitz continuous output where the output's Lipschitz constant is a tunable parameter. This combination of advantageous properties is not shared by any existing differentiator. Both continuous-time and sample-based versions of the differentiator are developed and theoretical guarantees are established for both. The continuous-time version of the differentiator consists in a regularized and sliding-mode-filtered linear adaptive differentiator. The sample-based, implementable version is then obtained through appropriate discretization. An illustrative example is provided to highlight the features of the developed differentiator.

In networked control applications, event-triggering mechanisms (ETMs) reduce the communication load while ensuring performance guarantees. However, the design of ETMs is becoming increasingly complex, particularly for decentralized multi-agent and consensus setups, where the condition used to trigger communication might incorporate the agent's local information and the information received from neighbors. This typically results in ad-hoc solutions, which may only work for the consensus protocols under consideration. In this work, we aim to safely incorporate neural networks in the ETM to provide a general and flexible solution while ensuring guaranteed performance. To decouple the stability analysis of the consensus protocol from the abstraction of the neural network in the ETM, we first derive design criteria for the consensus and ETM pair, which allow independent analysis of each element under mild constraints. As a result, we propose NN-ETM, a novel ETM featuring a neural network, which provides an all-purpose solution to optimize communication in consensus problems while preserving the stability guarantees of the consensus protocol.

This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. The ellipsoids are defined as time-varying positive definite matrices. On the other hand, given an undirected network, each node is equipped with one of these ellipsoids. The solution is based on a novel distributed reformulation of the original centralized semi-definite outer L\"owner-John program, characterized by a non-separable objective function and global constraints. We prove finite-time convergence to the global minima of the centralized problem in the static case and finite-time bounded tracking error in the dynamic case. Moreover, we prove boundedness of estimation in the tracking of the global optimum and robustness in the estimation against time-varying inputs. As a by-product, the proposed algorithm extends min/max dynamic consensus algorithms to positive definite matrices. We illustrate the properties of the algorithm with different simulated examples, including a distributed estimation showcase where our proposal is integrated into a distributed Kalman filter to surpass the state-of-the-art in mean square error performance., Comment: This work is currently under review

This work is devoted to the problem of distributed target tracking when a team of robots detect the target through a variable perception-latency mechanism. A reference for the robots to track is constructed in terms of a desired formation around the estimation of the target position. However, it is noted that due to the perception-latency, classical estimation techniques have smoothness issues which prevent asymptotic stability for the formation control. We propose a near-optimal smooth-output estimator which circumvents this issue. Moreover, local estimations are fused using novel dynamic consensus techniques. The advantages of the proposal as well as a comparison with a non-smooth optimal alternative are discussed through simulation examples., Comment: This is the accepted version an already published manuscript. See journal reference for details

Target tracking is a popular problem with many potential applications. There has been a lot of effort on improving the quality of the detection of targets using cameras through different techniques. In general, with higher computational effort applied, i.e., a longer perception-latency, a better detection accuracy is obtained. However, it is not always useful to apply the longest perception-latency allowed, particularly when the environment doesn't require to and when the computational resources are shared between other tasks. In this work, we propose a new Perception-LATency aware Estimator (PLATE), which uses different perception configurations in different moments of time in order to optimize a certain performance measure. This measure takes into account a perception-latency and accuracy trade-off aiming for a good compromise between quality and resource usage. Compared to other heuristic frame-skipping techniques, PLATE comes with a formal complexity and optimality analysis. The advantages of PLATE are verified by several experiments including an evaluation over a standard benchmark with real data and using state of the art deep learning object detection methods for the perception stage., Comment: This is the accepted version an already published manuscript. See journal reference for details

In robotic systems, perception latency is a term that refers to the computing time measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a compromise between perception latency, precision for the overall robotic system, and computational resource usage referred to here as the latency-precision trade-off. In this work, we analyze a robot model given by a linear system, a zero-order hold controller, and measurements taken by several perception mode possibilities with different noise levels. We show that the analysis of this system is reduced to studying an equivalent switching system. Our goal is to schedule perception modes such that stability is attained while optimizing a cost function that models the latency-precision trade-off. Our solution framework comprises three main tools: the construction of perception scheduling policy candidates, admissibility verification for policy candidates, and optimal strategies based on admissible policies., Comment: This is the accepted version of an already published manuscript. See journal reference

Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user, regardless of the initial condition. Furthermore, such a class of controllers has been shown to maintain a prescribed-time convergence in the presence of disturbances even if the disturbance bound is unknown. However, such properties require a time-varying gain that becomes singular at the terminal time, which limits its application to scenarios under quantization or measurement noise. This chapter presents a methodology to design a broader class of controllers, called predefined-time controllers, with a prescribed convergence-time bound. Our approach allows designing robust predefined-time controllers based on time-varying gains while maintaining uniformly bounded time-varying gains. We analyze the condition for uniform Lyapunov stability under the proposed time-varying controllers., Comment: This is a preprint of the chapter: "Designing controllers with predefined convergence-time bound using bounded time-varying gains", published in Sliding-Mode Control and Variable-Structure Systems, Springer Nature Switzerland AG 2023. The final authenticated version is available online at: https://doi.org/10.1007/978-3-031-37089-2_3

Distributed sensor networks have gained interest thanks to the developments in processing power and communications. Event-triggering mechanisms can be useful in reducing communication between the nodes of the network, while still ensuring an adequate behaviour of the system. However, very little attention has been given to continuous-time systems in this context. In this work, we propose a strategy for distributed state estimation in sensor networks, based on average dynamic consensus of the continuous measurements. While communication between nodes is discrete and heavily reduced due to the event-triggering mechanism, our method ensures that the nodes are still able to produce a continuous estimate of the global average measurement and the state of the plant, within some tuneable error bounds., Comment: This work has been accepted for presentation at the 22nd IFAC World Congress 2023

Context. Spacecraft measurements have shown Kinetic Alfv\'en Waves propagating in the terrestrial magnetosphere at lower wavenormal angles than predicted by linear Vlasov theory of electron-proton plasmas. To explain these observations, it has been suggested that the abundant heavy ion populations in this region may have strong, non-trivial effects that allow Alfv\'enic waves to acquire right-handed polarization at lower angles with respect to the background magnetic field, as in the case of typical electron-proton plasma. Aims. We study the dispersion properties of Alfv\'enic waves in plasmas with stationary phase-space distribution functions with different heavy ion populations. Our extensive numerical analysis has allowed us to quantify the role of the heavy ion components on the transition from the left-hand polarized electromagnetic ion-cyclotron (EMIC) mode to the right-hand polarized kinetic Alfv\'en wave (KAW) mode. Methods. We used linear Vlasov-Maxwell theory to obtain the dispersion relation for oblique electromagnetic waves. The dispersion relation of Alfv\'en waves was obtained numerically by considering four different oxygen ion concentrations ranging between 0.0 and 0.2 for all propagation angles, as a function of both the wavenumber and the plasma beta parameter. Results. The inclusion of the heavy O+ ions is found to considerably reduce the transition angle from EMIC to KAW both as a function of the wave number and plasma beta. With increasing O+ concentrations, waves become more damped in specific wavenumber regions. However, the inclusion of oxygen ions may allow weakly damped KAW to effectively propagate at smaller wave-normal angles than in the electron-proton case, as suggested by observations., Comment: 11 pages, 8 figures

The outer Lowner-John method is widely used in sensor fusion applications to find the smallest ellipsoid that can approximate the intersection of a set of ellipsoids, described by positive definite covariance matrices modeling the quality of each sensor. We propose a distributed algorithm to solve this problem when these matrices are defined over the network's nodes. This is of particular significance as it is the first decentralized algorithm capable of computing the covariance intersection ellipsoid by combining information from the entire network using only local interactions. The solution is based on a reformulation of the centralized problem, leading to a local protocol based on exact dynamic consensus tools. After reaching consensus, the protocol converges to an outer Lowner-John ellipsoid in finite time, and to the global optimum asymptotically. Formal convergence analysis and numerical experiments are provided to validate the proposal's advantages., Comment: This is the accepted version of the manuscript: "Distributed outer approximation of the intersection of ellipsoids," Rodrigo Aldana-Lopez, Eduardo Sebastian, Rosario Aragues, Eduardo Montijano and Carlos Sagues, in IEEE Control Systems Letters, 2023, DOI: 10.1109/LCSYS.2023.3280259

Visual object tracking under challenging conditions of motion and light can be hindered by the capabilities of conventional cameras, prone to producing images with motion blur. Event cameras are novel sensors suited to robustly perform vision tasks under these conditions. However, due to the nature of their output, applying them to object detection and tracking is non-trivial. In this work, we propose a framework to take advantage of both event cameras and off-the-shelf deep learning for object tracking. We show that reconstructing event data into intensity frames improves the tracking performance in conditions under which conventional cameras fail to provide acceptable results., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this contribution is published in ROBOT2022: Fifth Iberian Robotics Conference

According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty cannot be tolerated under sampling, not even if sampling could become infinitely frequent as the deadline is approached, unless the sampling strategy were designed according to the growth of the control action. Robustness under model uncertainty is analyzed and the amount of uncertainty that can be tolerated under sampling is quantified in order to formulate the least restrictive prescribed-time control problem that is practically implementable. Some solutions to this problem are given for a scalar system. Moreover, either under a-priori knowledge of bounds for initial conditions, or if the strategy can be selected after the first measurement becomes available, it is shown that the real, practically achievable objectives can also be reached with linear time-invariant control and uniform sampling. These derivations serve to yield insight into the real advantages that implementation of prescribed-time controllers may have., Comment: Accepted for presentation at the IFAC World Congress 2023

The electron firehose instabilities are among the most studied kinetic instabilities, especially in the context of space plasmas, whose dynamics is mainly controlled by collisionless wave-particle interactions. This paper undertakes a comparative analysis of the aperiodic electron firehose instabilities excited either by the anisotropic temperature or by the electron counter-beaming populations. Two symmetric counter-beams provide an effective kinetic anisotropy similar to the temperature anisotropy of a single (non-drifting) population, with temperature along the magnetic field direction larger than that in perpendicular direction. Therefore, the counter-beaming plasma is susceptible to firehose-like instabilities (FIs), parallel and oblique branches. Here we focus on the oblique beaming FI, which is also aperiodic when the free energy is provided by symmetric counter-beams. Our results show that, for relative small drifts or beaming speeds ($U$), not exceeding the thermal speed ($\alpha$), the aperiodic FIs exist in the same interval of wave-numbers and the same range of oblique angles (with respect to the magnetic field direction), but the growth rates of counter-beaming FI (CBFI) are always higher than those of temperature anisotropy FI (TAFI). For $U/\alpha > 1$, however, another electrostatic two-stream instability (ETSI) is also predicted, which may have growth rates higher than those of CBFI, and may dominate in that case the dynamics., Comment: 19 pages, 6 figures, 2 tables, accepted for publication in The Astrophysical Journal

This work addresses the problem of distributed formation tracking for a group of follower holonomic mobile robots around a reference signal. The reference signal is comprised of the geometric center of the positions of multiple leaders. This work's main contribution is a novel Modulated Distributed Virtual Observer (MDVO) for the reference signal. Moreover, the proposed MDVO is based on an exact dynamic consensus algorithm with a prescribed convergence time. In addition, we provide simulation examples showcasing two different application scenarios for the proposal., Comment: Please cite the publisher's version. For the publisher's version and full citation details see: https://doi.org/10.1109/LCSYS.2022.3181784

Prescribed-time algorithms based on time-varying gains may have remarkable properties, such as regulation in a user-prescribed finite time that is the same for every nonzero initial condition and that holds even under matched disturbances. However, at the same time, such algorithms are known to lack robustness to measurement noise. This note shows that the lack of robustness of a class of prescribed-time algorithms is of an extreme form. Specifically, we show the existence of arbitrarily small measurement noises causing considerable deviations, divergence, and other detrimental consequences. We also discuss some drawbacks and trade-offs of existing workarounds as motivation for further analysis.

This article addresses the problem of average consensus in a multi-agent system when the desired consensus quantity is a time varying signal. Recently, the EDCHO protocol leveraged high order sliding modes to achieve exact consensus under a constrained set of initial conditions, limiting its applicability to static networks. In this work, we propose REDCHO, an extension of the previous protocol which is robust to mismatch in the initial conditions, making it suitable to use cases in which connection and disconnection of agents is possible. The convergence properties of the protocol are formally explored. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation examples showing the benefits of REDCHO against other methods in the literature., Comment: This is the preprint version of the accepted Manuscript: Rodrigo Aldana-Lopez, Rosario Aragues, Carlos Sagues, REDCHO: Robust Exact Dynamic Consensus of High Order, Automatica, Volume 141, 2022, ISSN 0005-1098

This article addresses the problem of average consensus in a multi-agent system when the desired consensus quantity is a time varying signal. Although this problem has been addressed in existing literature by linear schemes, only bounded steady-state errors have been achieved. Other approaches have used first order sliding modes to achieve zero steady-state error, but suffer from the chattering effect. In this work, we propose a new exact dynamic consensus algorithm which leverages high order sliding modes, in the form of a distributed differentiator to achieve zero steady-state error of the average of time varying reference signals in a group of agents. Moreover, our proposal is also able to achieve consensus to high order derivatives of the average signal, if desired. An in depth formal study on the stability and convergence for EDCHO is provided for undirected connected graphs. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation scenarios., Comment: This is the preprint version of the accepted Manuscript: Rodrigo Aldana-Lopez, Rosario Aragues, Carlos Sagues, EDCHO: High order exact dynamic consensus, Automatica, Volume 131, 2021, ISSN 0005-1098. Please cite the publisher's version

There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their $(n+1)$-th time derivative, the existing design methodologies yield a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time-varying gains to design arbitrary-order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded time-varying gains. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how time-varying gains offer a general and flexible methodology to design algorithms with a predefined UBST., Comment: This is the preprint version of the accepted manuscript with DOI: 10.1002/rnc.6315. Please cite the publisher's version. For the publisher's version and full citation details, see: https://doi.org/10.1002/rnc.6315. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions

This paper proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and derivative bounds. A tight bound on the worst-case accuracy, i.e., the worst-case differentiation error, is derived, which is the best among all causal differentiators and is moreover shown to be obtained after a fixed number of sampling steps. Comparisons with the accuracy of existing high-gain and sliding-mode differentiators illustrate the obtained results., Comment: Please cite the publisher's version. For the publisher's version and full citation details see: https://doi.org/10.1109/LCSYS.2021.3087542

There is a growing interest in differentiation algorithms that converge in fixed time with a predefined Upper Bound on the Settling Time (UBST). However, existing differentiation algorithms are limited to signals having an $n$-th order Lipschitz derivative. Here, we introduce a general methodology based on time-varying gains to circumvent this limitation, allowing us to design $n$-th order differentiators with a predefined UBST for the broader class of signals whose $(n+1)$-th derivative is bounded by a function with bounded logarithmic derivative. Unlike existing methods whose time-varying gain tends to infinity, our approach yields a time-varying gain that remains bounded at convergence time. We show how this last property maintains exact convergence using bounded gains when considering a compact set of initial conditions and improves the algorithm's performance to measurement noise., Comment: Please cite the publisher's version. For the publisher's version and full citation details, see: https://doi.org/10.1016/j.automatica.2023.110995

As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a consistent but exact discretization of the considered class of predefined-time stable systems, whereas in the perturbed case, the consistent discretization preserves the predefined-time stability property. All the results are validated through simulations and compared with the conventional explicit Euler scheme, highlighting the advantages of this proposal.

Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still lack a general methodology to design these algorithms for high-order perturbed systems when we additionally need to impose a user-defined upper-bound on their settling time, especially for systems with perturbations. Here, we fill this gap by introducing a methodology to redesign a class of asymptotically, finite- and fixed-time stable systems into non-autonomous fixed-time stable systems with a user-defined upper-bound on their settling time. Our methodology redesigns a system by adding time-varying gains. However, contrary to existing methods where the time-varying gains tend to infinity as the origin is reached, we provide sufficient conditions to maintain bounded gains. We illustrate our methodology by building fixed-time online differentiators with user-defined upper-bound on their settling time and bounded gains.

This paper presents a method for online trajectory planning in known environments. The proposed algorithm is a fusion of sampling-based techniques and model-based optimization via quadratic programming. The former is used to efficiently generate an obstacle-free path while the latter takes into account the robot dynamical constraints to generate a time-dependent trajectory. The main contribution of this work lies on the formulation of a convex optimization problem over the generated obstacle-free path that is guaranteed to be feasible. Thus, in contrast with previously proposed methods, iterative formulations are not required. The proposed method has been compared with state-of-the-art approaches showing a significant improvement in success rate and computation time. To illustrate the effectiveness of this approach for online planning, the proposed method was applied to the fluid autonomous navigation of a quadcopter in multiple environments consisting of up to two hundred obstacles. The scenarios hereinafter presented are some of the most densely cluttered experiments for online planning and navigation reported to date. See video at https://youtu.be/DJ1IZRL5t1Q

This paper presents an autonomous navigation framework for reaching a goal in unknown 3D cluttered environments. The framework consists of three main components. First, a computationally efficient method for mapping the environment from the disparity measurements obtained from a depth sensor. Second, a stochastic method to generate a path to a given goal, taking into account field of view constraints on the space that is assumed to be safe for navigation. Third, a fast method for the online generation of motion plans, taking into account the robot's dynamic constraints, model, and environmental uncertainty and disturbances. To highlight the contribution with respect to the available literature, we provide a qualitative and quantitative comparison with the state of the art methods for reaching a goal and for exploration in unknown environments, showing the superior performance of our approach. To illustrate the effectiveness of the proposed framework, we present experiments in multiple indoors and outdoors environments running the algorithm fully on board and in real-time, using a robotic platform based on the Intel Ready to Fly drone kit, which represents the implementation in the most frugal platform for navigation in unknown cluttered environments demonstrated to date. Open source code is available at:~\url{https://github.com/IntelLabs/autonomousmavs}. The video of the experimental results can be found at~\url{https://youtu.be/Wq0e7vF6nZM}., Comment: This is the preprint version of the accepted Manuscript: DOI. 10.1002/rob.21959. Please cite the publisher's version. For the publisher's version and full citation details see: https://doi.org/10.1002/rob.21959