Randomized Constraints Consensus for Distributed Robust Linear Programming

In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under time-varying, asynchronous and directed communication topology. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check-in a randomized setup-the robust feasibility (and hence optimality) of the candidate optimal point, and (ii) an optimization step in which they exchange their candidate bases (minimal sets of active constraints) with neighbors and locally solve an optimization problem whose constraint set includes: a sampled constraint violating the candidate optimal point (if it exists), agent's current basis and the collection of neighbor's basis. As main result, we show that if a processor successfully performs the verification step for a sufficient number of communication rounds, it can stop the algorithm since a consensus has been reached. The common solution is-with high confidence-feasible (and hence optimal) for the entire set of uncertainty except a subset having arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm on a multi-core platform in which the nodes communicate asynchronously.Comment: Accepted for publication in the 20th World Congress of the International Federation of Automatic Control (IFAC

Randomized algorithms for control of uncertain systems with application to hand disk drives

Ph.DDOCTOR OF PHILOSOPH

Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.Comment: 18 pages, Submitted for publication to IEEE Transactions on Automatic Contro

Robust Stabilization of Resource Limited Networked Control Systems Under Denial-of-Service Attack

In this paper, we consider a class of denial-of-service (DoS) attacks, which aims at overloading the communication channel. On top of the security issue, continuous or periodic transmission of information within feedback loop is necessary for the effective control and stabilization of the system. In addition, uncertainty---originating from variation of parameters or unmodeled system dynamics---plays a key role in the system's stability. To address these three critical factors, we solve the joint control and security problem for an uncertain discrete-time Networked Control System (NCS) subject to limited availability of the shared communication channel. An event-triggered-based control and communication strategy is adopted to reduce bandwidth consumption. To tackle the uncertainty in the system dynamics, a robust control law is derived using an optimal control approach based on a virtual nominal dynamics associated with a quadratic cost-functional. The conditions for closed-loop stability and aperiodic transmission rule of feedback information are derived using the discrete-time Input-to-State Stability theory. We show that the proposed control approach withstands a general class of DoS attacks, and the stability analysis rests upon the characteristics of the attack signal. The results are illustrated and validated numerically with a classical NCS batch reactor system.Comment: Accepted for IEEE CDC 201

A Statistical Learning Theory Approach for Uncertain Linear and Bilinear Matrix Inequalities

In this paper, we consider the problem of minimizing a linear functional subject to uncertain linear and bilinear matrix inequalities, which depend in a possibly nonlinear way on a vector of uncertain parameters. Motivated by recent results in statistical learning theory, we show that probabilistic guaranteed solutions can be obtained by means of randomized algorithms. In particular, we show that the Vapnik-Chervonenkis dimension (VC-dimension) of the two problems is finite, and we compute upper bounds on it. In turn, these bounds allow us to derive explicitly the sample complexity of these problems. Using these bounds, in the second part of the paper, we derive a sequential scheme, based on a sequence of optimization and validation steps. The algorithm is on the same lines of recent schemes proposed for similar problems, but improves both in terms of complexity and generality. The effectiveness of this approach is shown using a linear model of a robot manipulator subject to uncertain parameters.Comment: 19 pages, 2 figures, Accepted for Publication in Automatic

Randomized Constraints Consensus for Distributed Robust Mixed-Integer Programming

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check---in a randomized fashion---the robust feasibility of a candidate optimal point, and (ii) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached), so that candidate optimal solutions are consensual. The common solution is proven to be---with high confidence---feasible and hence optimal for the entire set of uncertainty except a subset having an arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multi-core platform in which the nodes communicate asynchronously.Comment: Submitted for publication. arXiv admin note: text overlap with arXiv:1706.0048

Optimal Network Topology for Effective Collective Response

Natural, social, and artificial multi-agent systems usually operate in dynamic environments, where the ability to respond to changing circumstances is a crucial feature. An effective collective response requires suitable information transfer among agents, and thus is critically dependent on the agents' interaction network. In order to investigate the influence of the network topology on collective response, we consider an archetypal model of distributed decision-making---the leader-follower linear consensus---and study the collective capacity of the system to follow a dynamic driving signal (the "leader") for a range of topologies and system sizes. The analysis reveals a nontrivial relationship between optimal topology and frequency of the driving signal. Interestingly, the response is optimal when each individual interacts with a certain number of agents which decreases monotonically with the frequency and, for large enough systems, is independent of the size of the system. This phenomenology is investigated in experiments of collective motion using a swarm of land robots. The emergent collective response to both a slow- and a fast-changing leader is measured and analyzed for a range of interaction topologies. These results have far-reaching practical implications for the design and understanding of distributed systems, since they highlight that a dynamic rewiring of the interaction network is paramount to the effective collective operations of multi-agent systems at different time-scales