Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

/pdf/consensus-and-cooperation-in-networked-multi-agent-systems-5ame7z72ny.pdf

Consensus and Cooperation in Networked Multi-Agent Systems

Data Mining Practical Machine Learning Tools and Techniques

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

/pdf/an-overview-of-recent-progress-in-the-study-of-distributed-1xnb6e12se.pdf

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

System Identification I

/pdf/optimal-coordinated-maneuvers-for-three-dimensional-aircraft-10ugouyotx.pdf

Optimal coordinated maneuvers for three dimensional aircraft conflict resolution

We investigate the connections between compression learning and scenario based optimization.We ﬁrst show how to strengthen, or relax the consistency assumption at the basis of compressionlearning and study the learning and generalization properties of the algorithm involved. We thenconsider diﬀerent constrained optimization problems aﬀected by uncertainty represented by meansof scenarios. We show that the issue of providing guarantees on the probability of constraint viola-tion reduces to a learning problem for an appropriately chosen algorithm that enjoys compressionlearning properties. The compression learning perspective provides a unifying framework for sce-nario based optimization and allows us to revisit the scenario approach and the probabilisticallyrobust design, a recently developed technique based on a mixture of randomized and robust op-timization, and to extend the guarantees on the probability of constraint violation to cascadingoptimization problems. Keywords: Compression learning, consistent algorithms, randomized optimization, scenarioapproach, statistical learning theory.1. IntroductionOptimal decision making in the presence of uncertainty is important for the eﬃcient and eco-nomic operation of systems aﬀected by endogenous, or exogenous uncertainties. One approach todeal with uncertainty is through robust optimization. In this case a decision is made such that theconstraints are satisﬁed for all admissible values of the uncertainty [2]. Tractability of the developedtechniques relies heavily on the geometry of the uncertainty set. On the other hand, chance con-strained optimization allows for constraint violation but with an a-priori speciﬁed probability [3],[4]. In [5], [6], diﬀerent approximations to chance constrained optimization problems are proposed

On the connection between compression learning and scenario based optimization

In this paper, an optimal coordinated motion planning problem is formulated where multiple agents have to reach given destination positions starting from given initial positions, subject to constraints on the admissible formation patterns. Solutions to the problem are reinterpreted as distance minimizing geodesies on a certain manifold with boundary. A geodesic on this manifold that possesses conjugate points will not be distance-minimizing beyond its first conjugate point. We study a particular instance of the problem, where a number of initially aligned agents tries to switch positions by rotating around their common centroid. We characterize analytically the complete set of conjugate points of a geodesic that naturally arises as a candidate solution. This allows us to prove that the geodesic does not correspond to an optimal coordinated motion when the angle of rotation exceeds a threshold that decreases to zero as the number of agents increases. Moreover, infinitesimal perturbations that improve the performance of the geodesic after it passes the conjugate points are characterized by a family of orthogonal polynomials.

/pdf/interesting-conjugate-points-in-formation-constrained-5g7nv80nhb.pdf

Interesting conjugate points in formation constrained optimal multi-agent coordination

We address constraint-coupled optimization for a system composed of multiple cooperative agents communicating over a time-varying network. We propose a distributed proximal minimization algorithm that is guaranteed to converge to an optimal solution of the optimization problem, under suitable convexity and connectivity assumptions. The performance of the introduced algorithm is shown on a numerical example of a charging scheduling problem for a fleet of plug-in electric vehicles.

A Distributed Dual Proximal Minimization Algorithm for Constraint-Coupled Optimization Problems

Reportedly, standard identi cation algorithms do not guarantee the controllability of the estimated system. In this paper, a penalized least squares (PLS) identi cation criterion is proposed to overcome this di culty. The criterion is shown to provide estimated systems which exhibit an uniform controllability property through time. Moreover, the Lai and Wei upper bound for the least squares estimation error ([1], Theorem 1) is still valid for PLS. This ensures a safe use of the proposed method in adaptive control applications. The e ectiveness of the method is illustrated by a general adaptive stability result valid for PLS-based certainty-equivalent adaptive control schemes.

Maria Prandini

Papers

Optimal coordinated maneuvers for three dimensional aircraft conflict resolution

On the connection between compression learning and scenario based optimization

Interesting conjugate points in formation constrained optimal multi-agent coordination

A Distributed Dual Proximal Minimization Algorithm for Constraint-Coupled Optimization Problems

A penalized identification criterion for securing controllability in adaptive control.