This note considers consensus algorithms for double-integrator dynamics. We propose and analyze consensus algorithms for double-integrator dynamics in four cases: 1) with a bounded control input, 2) ...without relative velocity measurements, 3) with a group reference velocity available to each team member, and 4) with a bounded control input when a group reference state is available to only a subset of the team. We show that consensus is reached asymptotically for the first two cases if the undirected interaction graph is connected. We further show that consensus is reached asymptotically for the third case if the directed interaction graph has a directed spanning tree and the gain for velocity matching with the group reference velocity is above a certain bound. We also show that consensus is reached asymptotically for the fourth case if and only if the group reference state flows directly or indirectly to all of the vehicles in the team.
Summary
Petroleum‐based plastics have replaced many natural materials in their former applications. With their excellent properties, they have found widespread uses in almost every area of human ...life. However, the high recalcitrance of many synthetic plastics results in their long persistence in the environment, and the growing amount of plastic waste ending up in landfills and in the oceans has become a global concern. In recent years, a number of microbial enzymes capable of modifying or degrading recalcitrant synthetic polymers have been identified. They are emerging as candidates for the development of biocatalytic plastic recycling processes, by which valuable raw materials can be recovered in an environmentally sustainable way. This review is focused on microbial biocatalysts involved in the degradation of the synthetic plastics polyethylene, polystyrene, polyurethane and polyethylene terephthalate (PET). Recent progress in the application of polyester hydrolases for the recovery of PET building blocks and challenges for the application of these enzymes in alternative plastic waste recycling processes will be discussed.
The high recalcitrance of many synthetic plastics results in their long persistence in the environment and globally in growing amounts of plastic waste. Microbial enzymes are emerging as candidates for the development of biocatalytic plastic recycling processes.
This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler-Lagrange systems. We propose a fundamental consensus algorithm, a consensus ...algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler-Lagrange equations. Due to the fact that the closed-loop interconnected Euler-Lagrange equations using these algorithms are non-autonomous, Matrosov's theorem is used for convergence analysis. It is shown that consensus is reached on the generalised coordinates and their derivatives of the networked Euler-Lagrange systems as long as the undirected communication topology is connected. Simulation results show the effectiveness of the proposed algorithms.
In this paper, distributed cooperative attitude synchronization and tracking problems are considered for multiple rigid bodies with attitudes represented by modified rodriguez parameters. Two ...distributed control laws are proposed and analyzed. The first control law applies a passivity approach for distributed attitude synchronization. The control law guarantees attitude synchronization without the requirement for absolute angular velocity measurements and relative angular velocity measurements between neighboring rigid bodies. The second control law incorporates a time-varying reference attitude, where the reference attitude is allowed to be available to only a subset of the group members under general directed information exchange. The control law guarantees that all rigid bodies track the time-varying reference attitude as long as a virtual leader whose attitude is the time-varying reference attitude has a directed path to all other rigid bodies in the group. Simulation results are presented to demonstrate the effectiveness of the two control laws.
In this paper, we study the consensus problem in multi-vehicle systems, where the information states of all vehicles approach a time-varying reference state under the condition that only a portion of ...the vehicles (e.g., the unique team leader) have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team. We first analyze a consensus algorithm with a constant reference state using graph theoretical tools. We then propose consensus algorithms with a time-varying reference state and show necessary and sufficient conditions under which consensus is reached on the time-varying reference state. The time-varying reference state can be an exogenous signal or evolve according to a nonlinear model. These consensus algorithms are also extended to achieve relative state deviations among the vehicles. An application example to multi-vehicle formation control is given as a proof of concept.
In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. The objective is to minimize the sum of local time-varying cost functions, ...each of which is known to only an individual agent, through local interaction. Here, the optimal point is time varying and creates an optimal trajectory. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. In both cases, a centralized approach is first introduced to solve the optimization problem. Then, this problem is solved in a distributed manner and a discontinuous algorithm based on the signum function is proposed in each case. In the case of single-integrator (respectively, double-integrator) dynamics, each agent relies only on its own position and the relative positions (respectively, positions and velocities) between itself and its neighbors. A gain adaption scheme is introduced in both algorithms to eliminate certain global information requirement. To relax the restricted assumption imposed on feasible cost functions, an estimator based algorithm using the signum function is proposed, where each agent uses dynamic average tracking as a tool to estimate the centralized control input. As a tradeoff, the estimator-based algorithm necessitates communication between neighbors. Then, in the case of double-integrator dynamics, the proposed algorithms are further extended. Two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. To account for interagent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics. It is shown that the center of the agents tracks the optimal trajectory, the connectivity of the agents is maintained, and interagent collision is avoided.
Pragmatic studies of learners' development during study abroad (SA) have mainly focused on English as the target language, whereas limited research has investigated Chinese, particularly over ...extended periods of stay. This study cross-sectionally explores the effect of SA on learners' L2 Chinese requests, with a focus on long SA durations. Data were collected through six role plays from 40 learners in China, who were classified into three groups according to their length of stay (LoS). Fifteen Chinese students were also recruited to provide native speaker data for comparison. The results indicated that, compared with native speakers, learners produced fewer direct but more indirect request strategies and fewer external and internal modifiers. Learners increasingly favoured conventionally indirect request strategies as they studied longer in China, indicating non-target-like development. External modification devices were comparatively easier for learners to acquire, as revealed by similarities in the situational distributions between learners and native speakers and among learner groups. Internal modification posed more difficulties for learners, although their abilities to employ internal modifiers developed with increasing LoS. The effect of SA on learners' pragmatic development is discussed in relation to different natures of pragmatic aspects, LoS, prior L2 proficiency, contact with native speakers, and living arrangements during SA.
•This study investigates the effect of study abroad on learners' L2 Chinese requests.•The study was designed with a focus on longer study abroad (SA) durations.•Learners favoured conventionally indirect requests more as the length of stay extended.•Compared with external modifiers, internal modifiers posed greater difficulties.•The effect of SA duration on learners' pragmatic development is a complex issue.
This paper studies synchronization of coupled second-order linear harmonic oscillators with local interaction. We analyze convergence conditions over, respectively, directed fixed and switching ...network topologies by using tools from algebraic graph theory, matrix theory, and nonsmooth analysis. It is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions. Examples are given to validate the convergence conditions. The theoretical result is also applied to synchronized motion coordination of multi-agent systems as a proof of concept.
The present study longitudinally investigates the cognitive processes of advanced L2 learners engaged in a multimedia task that elicited status-equal and status-unequal refusals in English during ...their study abroad. Data were collected three times by retrospective verbal report from 20 Chinese learners who were studying abroad over the course of one academic year. The results revealed that the learners reported paying increasingly more attention to sociopragmatics in context when they responded to each situation of the task. Furthermore, the study showed the effect of study abroad on the learners' perceptions of the factors affecting their pragmatic productions across the three phases. These effects were reflected by the decrease in pragmatic difficulties and the increase in pragmatic knowledge reported by the learners. This article demonstrates that using the retrospective verbal report at different points during learners' study abroad allows the examination of the changes in the cognitive processes involved in L2 pragmatic production.
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