Distributed sampled-data control of nonholonomic multi-robot systems with proximity networks

This paper considers the distributed sampled-data control problem of a group of mobile robots connected via distance-induced proximity networks. A dwell time is assumed in order to avoid chattering in the neighbor relations that may be caused by abrupt changes of positions when updating information from neighbors. Distributed sampled-data control laws are designed based on nearest neighbour rules, which in conjunction with continuous-time dynamics results in hybrid closed-loop systems. For uniformly and independently initial states, a sufficient condition is provided to guarantee synchronization for the system without leaders. In order to steer all robots to move with the desired orientation and speed, we then introduce a number of leaders into the system, and quantitatively establish the proportion of leaders needed to track either constant or time-varying signals. All these conditions depend only on the neighborhood radius, the maximum initial moving speed and the dwell time, without assuming a prior properties of the neighbor graphs as are used in most of the existing literature.Comment: 15 pages, 3 figure

Random Broadcast Based Distributed Consensus Clock Synchronization for Mobile Networks

Clock synchronization is a crucial issue for mobile ad hoc networks due to the dynamic and distributed nature of these networks. In this paper, employing affine models for local clocks, a random broadcast based distributed consensus clock synchronization algorithm is proposed. In the absence of transmission delays, we theoretically prove the convergence of the proposed scheme, which is further illustrated by numerical results. In addition, it is concluded from simulations that the proposed scheme is scalable and robust to transmission delays as well as different accuracy requirements

Optimization and Analysis of Distributed Averaging with Short Node Memory

In this paper, we demonstrate, both theoretically and by numerical examples, that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node's two previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighbouring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors' values, and carry out a theoretical analysis of the improvement in convergence rate that can be obtained using this acceleration methodology. For a chain topology on n nodes, this leads to a factor of n improvement over the one-step algorithm, and for a two-dimensional grid, our approach achieves a factor of n^1/2 improvement, in terms of the number of iterations required to reach a prescribed level of accuracy

Computable Performance Analysis of Recovering Signals with Low-dimensional Structures

The last decade witnessed the burgeoning development in the reconstruction of signals by exploiting their low-dimensional structures, particularly, the sparsity, the block-sparsity, the low-rankness, and the low-dimensional manifold structures of general nonlinear data sets. The reconstruction performance of these signals relies heavily on the structure of the sensing matrix/operator. In many applications, there is a flexibility to select the optimal sensing matrix among a class of them. A prerequisite for optimal sensing matrix design is the computability of the performance for different recovery algorithms. I present a computational framework for analyzing the recovery performance of signals with low-dimensional structures. I define a family of goodness measures for arbitrary sensing matrices as the optimal values of a set of optimization problems. As one of the primary contributions of this work, I associate the goodness measures with the fixed points of functions defined by a series of linear programs, second-order cone programs, or semidefinite programs, depending on the specific problem. This relation with the fixed-point theory, together with a bisection search implementation, yields efficient algorithms to compute the goodness measures with global convergence guarantees. As a by-product, we implement efficient algorithms to verify sufficient conditions for exact signal recovery in the noise-free case. The implementations perform orders-of-magnitude faster than the state-of-the-art techniques. The utility of these goodness measures lies in their relation with the reconstruction performance. I derive bounds on the recovery errors of convex relaxation algorithms in terms of these goodness measures. Using tools from empirical processes and generic chaining, I analytically demonstrate that as long as the number of measurements are relatively large, these goodness measures are bounded away from zeros for a large class of random sensing matrices, a result parallel to the probabilistic analysis of the restricted isometry property. Numerical experiments show that, compared with the restricted isometry based performance bounds, our error bounds apply to a wider range of problems and are tighter, when the sparsity levels of the signals are relatively low. I expect that computable performance bounds would open doors for wide applications in compressive sensing, sensor arrays, radar, MRI, image processing, computer vision, collaborative filtering, control, and many other areas where low-dimensional signal structures arise naturally

CONVERGENCE OF A CLASS OF MULTI-AGENT SYSTEMS IN PROBABILISTIC FRAMEWORK

Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors (e.g., synchronization) of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents ’ trajectories (or on the closed-loop dynamic neighborhood graphs), which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs