The Hegselmann-Krause (HK) model was first introduced in the field of opinion dynamics to describe the opinion evolution of individuals who interact with others and whose opinions are influenced by those of the people around them [1]. In the HK model, the individuals update their opinions over time by taking the average of the opinions of all their neighbors whose opinions are close enough to their own. This closeness is determined by a bounded confidence threshold, such that agents influence each other's opinion only if their opinions lay within the confidence threshold. Though initially proposed in the context of opinion dynamics, the HK model captures a fundamental self-organizing mechanism in complex systems. Beyond its original application, it has also been adopted as a basic game learning algorithm [2, 3] and has found widespread use in diverse fields, including demand response programs in smart grids [4] and hybrid energy storage management [5]. Among the many properties, one of the interesting features of the model is that it can be synchronized by random noise. This phenomenon, also known as "noise-induced order" in self-organizing systems, was first found in some simulation studies [6-8]. Then the analysis of the phenomenon was considered based on some noisy HK-type models.

Gradient descent (GD) and stochastic gradient descent (SGD) have been widely used in a large number of application domains. Therefore, understanding the dynamics of GD and improving its convergence speed is still of great importance. This paper carefully analyzes the dynamics of GD based on the terminal attractor at different stages of its gradient flow. On the basis of the terminal sliding mode theory and the terminal attractor theory, four adaptive learning rates are designed. Their performances are investigated in light of a detailed theoretical investigation, and the running times of the learning procedures are evaluated and compared. The total times of their learning processes are also studied in detail. To evaluate their effectiveness, various simulation results are investigated on a function approximation problem and an image classification problem.

Reference path following is a key component in the functioning of almost all engineered autonomous agents. Among several path following guidance methods in existing literature, vector-field-based guidance approach has got wide attention because of its simplicity and guarantee of stability under a broad class of scenarios. However, the usage of same cross-track-error-dependent structure of desired vector field in most of the existing literature irrespective of instantaneous cross-track error and course angle of unmanned vehicle makes it quite restrictive in attaining faster convergence and also leads to infeasibly high turn rate command for many scenarios. To this end, this paper presents a novel switched vector field-based guidance for following a general reference path, in which the structure of the desired vector field depends on instantaneous cross-track-error and vehicle's course angle. While the developed method ensures faster convergence, it also ensures that the guidance command always stays within a realistic threshold satisfying its curvature constraint, thus making it more real-life implementable for autonomous vehicles with kino-dynamic constraints. Theoretical analysis for convergence of the developed guidance scheme is presented. Possibilities of undesirable chattering at phase transitions are also eliminated. Numerical simulation studies are presented to validate the satisfactory performance of the developed algorithm.

This paper proposes a new distributed finite-time differentiator (DFD) for multi-agent systems (MAS) under directed graph, which extends the differentiator algorithm from the centralized case to the distributed case by only using relative/absolute position information. By skillfully constructing a Lyapunov function, the finite-time stability of the closed-loop system under DFD is proved. Inspired by the duality principle of control theory, a distributed continuous finite-time output consensus algorithm extended from DFD for a class of leader-follower MAS is provided, which not only completely suppresses disturbance, but also avoids chattering. Finally, several simulation examples are given to verify the effectiveness of the DFD.

Arbitrary pattern formation (\textsc{Apf}) is a well-studied problem in swarm robotics. To the best of our knowledge, the problem has been considered in two different settings: one in a euclidean plane and another in an infinite grid. This work deals with the problem in an infinite rectangular grid setting. The previous works in literature dealing with the \textsc{Apf} problem in an infinite grid had a fundamental issue. These deterministic algorithms use a lot of space in the grid to solve the problem, mainly to maintain the asymmetry of the configuration or to avoid a collision. These solution techniques cannot be useful if there is a space constraint in the application field. In this work, we consider luminous robots (with one light that can take three colors) to avoid symmetry, but we carefully designed a deterministic algorithm that solves the \textsc{Apf} problem using the minimal required space in the grid. The robots are autonomous, identical, and anonymous, and they operate in Look-Compute-Move cycles under a fully asynchronous scheduler. The \textsc{Apf} algorithm proposed in \cite{BOSE2020} by Bose et al. can be modified using luminous robots so that it uses minimal space, but that algorithm is not move-optimal. The algorithm proposed in this paper not only uses minimal space but is also asymptotically move-optimal. The algorithm proposed in this work is designed for an infinite rectangular grid, but it can be easily modified to work on a finite grid as well.

We propose the following general method for scaling learning algorithms to arbitrarily large data sets. Consider the model Mii learned by the algorithm using ni examples in step i (ii (nl, ...,nm)), and the model Moo that would be learned using in(cid:173) finite examples. Upper-bound the loss L(Mii' M oo) between them as a function of ii, and then minimize the algorithm's time com(cid:173) plexity f(ii) subject to the constraint that L(Moo, Mii) be at most f with probability at most 8. We apply this method to the EM algorithm for mixtures of Gaussians. Preliminary experiments on a series of large data sets provide evidence of the potential of this approach.

This paper develops a provably stable sensor-driven controller for path-following applications of robots with unicycle kinematics, one specific class of which is the wheeled mobile robot (WMR). The sensor measurement is converted to a scalar value (the score) through some mapping (the score function); the latter may be designed or learned. The score is then mapped to forward and angular velocities using a simple rule with three parameters. The key contribution is that the correctness of this controller only relies on the score function satisfying monotonicity conditions with respect to the underlying state -- local path coordinates -- instead of achieving specific values at all states. The monotonicity conditions may be checked online by moving the WMR, without state estimation, or offline using a generative model of measurements such as in a simulator. Our approach provides both the practicality of a purely measurement-based control and the correctness of state-based guarantees. We demonstrate the effectiveness of this path-following approach on both a simulated and a physical WMR that use a learned score function derived from a binary classifier trained on real depth images.

This work presents an safe and efficient methodology for autonomous indoor exploration with aerial robots using Harmonic Potential Fields (HPF). The challenge of applying HPF in complex 3D environments rests on high computational load involved in solving the Laplace equation. To address this issue, the proposed solution utilizes the Fast Multiple accelerated Boundary Element Method with boundary values controlled to ensure both safety and convergence. The methodology is validated through simulations, which demonstrate its properties of efficiency, safety and convergence.

This paper puts forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials. This is indeed possible, provided that one is willing to navigate trade-offs between optimality, level of exposure to unsafe events, and the maximum detection time of unsafe actions. We illustrate this concept in two complementary settings. We first focus on the canonical multi-armed bandit problem and study the intrinsic trade-offs of learning safety in the presence of uncertainty. Under mild assumptions on sufficient exploration, we provide an algorithm that provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines. We then consider the problem of finding optimal policies for a Markov Decision Process (MDP) with almost sure constraints. We show that the action-value function satisfies a barrier-based decomposition which allows for the identification of feasible policies independently of the reward process. Using this decomposition, we develop a Barrier-learning algorithm, that identifies such unsafe state-action pairs in a finite expected number of steps. Our analysis further highlights a trade-off between the time lag for the underlying MDP necessary to detect unsafe actions, and the level of exposure to unsafe events. Simulations corroborate our theoretical findings, further illustrating the aforementioned trade-offs, and suggesting that safety constraints can speed up the learning process.