Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set

On Three Generalizations of Contraction

We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC

Network motifs emerge from interconnections that favour stability

The microscopic principles organizing dynamic units in complex networks—from proteins to power generators—can be understood in terms of network ‘motifs’: small interconnection patterns that appear much more frequently in real networks than expected in random networks. When considered as small subgraphs isolated from a large network, these motifs are more robust to parameter variations, easier to synchronize than other possible subgraphs, and can provide specific functionalities. But one can isolate these subgraphs only by assuming, for example, a significant separation of timescales, and the origin of network motifs and their functionalities when embedded in larger networks remain unclear. Here we show that most motifs emerge from interconnection patterns that best exploit the intrinsic stability characteristics at different scales of interconnection, from simple nodes to whole modules. This functionality suggests an efficient mechanism to stably build complex systems by recursively interconnecting nodes and modules as motifs. We present direct evidence of this mechanism in several biological networks

Phase Synchronization Control of Robotic Networks on Periodic Ellipses with Adaptive Network Topologies

This paper presents a novel formation control method for a large number of robots or vehicles described by Euler-Lagrange (EL) systems moving in elliptical orbits. A new coordinate transformation method for phase synchronization of networked EL systems in elliptical trajectories is introduced to define desired formation patterns. The proposed phase synchronization controller synchronizes the motions of agents, thereby yielding a smaller synchronization error than an uncoupled control law in the presence of bounded disturbances. A complex time-varying and switching network topology, constructed by the adaptive graph Laplacian matrix, relaxes the standard requirement of consensus stability, even permitting stabilization on an arbitrary unbalanced graph. The proofs of stability are constructed by robust contraction analysis, a relatively new nonlinear stability tool. An example of reconfiguring swarms of spacecraft in Low Earth Orbit shows the effectiveness of the proposed phase synchronization controller for a large number of complex EL systems moving in elliptical orbits

Adoption of vehicular ad hoc networking protocols by networked robots

This paper focuses on the utilization of wireless networking in the robotics domain. Many researchers have already equipped their robots with wireless communication capabilities, stimulated by the observation that multi-robot systems tend to have several advantages over their single-robot counterparts. Typically, this integration of wireless communication is tackled in a quite pragmatic manner, only a few authors presented novel Robotic Ad Hoc Network (RANET) protocols that were designed specifically with robotic use cases in mind. This is in sharp contrast with the domain of vehicular ad hoc networks (VANET). This observation is the starting point of this paper. If the results of previous efforts focusing on VANET protocols could be reused in the RANET domain, this could lead to rapid progress in the field of networked robots. To investigate this possibility, this paper provides a thorough overview of the related work in the domain of robotic and vehicular ad hoc networks. Based on this information, an exhaustive list of requirements is defined for both types. It is concluded that the most significant difference lies in the fact that VANET protocols are oriented towards low throughput messaging, while RANET protocols have to support high throughput media streaming as well. Although not always with equal importance, all other defined requirements are valid for both protocols. This leads to the conclusion that cross-fertilization between them is an appealing approach for future RANET research. To support such developments, this paper concludes with the definition of an appropriate working plan