arXiv subjects

Jorge Cortes

Publications and source records attributed to Jorge Cortes.

At least 91 records · Page 5Linked to original sources

arXiv2015

Asymptotic convergence of constrained primal-dual dynamics

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.

math.OC↗

arXiv2015

Event-Triggered Stabilization of Linear Systems Under Bounded Bit Rates

This paper addresses the problem of exponential practical stabilization of linear time-invariant systems with disturbances using event-triggered control and bounded communication bit rate. We consider both the case of instantaneous communication with finite precision data at each transmission and the case of non-instantaneous communication with bounded communication rate. Given a prescribed rate of convergence, the proposed event-triggered control implementations opportunistically determine the transmission instants and the finite precision data to be transmitted on each transmission. We show that our design exponentially practically stabilizes the origin while guaranteeing a uniform positive lower bound on the inter-transmission and inter-reception times, ensuring that the number of bits transmitted on each transmission is upper bounded uniformly in time, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted earlier. We also characterize the necessary and sufficient average data rate for exponential practical stabilization. Several simulations illustrate the results.

eess.SY↗

arXiv2015

Distributed event-triggered coordination for average consensus on weight-balanced digraphs

This paper proposes a novel distributed event-triggered algorithmic solution to the multi-agent average consensus problem for networks whose communication topology is described by weight-balanced, strongly connected digraphs. The proposed event-triggered communication and control strategy does not rely on individual agents having continuous or periodic access to information about the state of their neighbors. In addition, it does not require the agents to have a priori knowledge of any global parameter. We show that, under the proposed law, events cannot be triggered an infinite number of times in any finite period (i.e., no Zeno behavior), and that the resulting network executions provably converge to the average of the initial agents' states exponentially fast. We also provide weaker conditions on connectivity under which convergence is guaranteed when the communication topology is switching. Simulations illustrate our results.

math.OC↗

arXiv2015

Team-triggered coordination for real-time control of networked cyber-physical systems

This paper studies the real-time implementation of distributed controllers on networked cyber-physical systems. We build on the strengths of event- and self-triggered control to synthesize a unified approach, termed team-triggered, where agents make promises to one another about their future states and are responsible for warning each other if they later decide to break them. The information provided by these promises allows individual agents to autonomously schedule information requests in the future and sets the basis for maintaining desired levels of performance at lower implementation cost. We establish provably correct guarantees for the distributed strategies that result from the proposed approach and examine their robustness against delays, packet drops, and communication noise. The results are illustrated in simulations of a multi-agent formation control problem.

math.OC↗

arXiv2015

Distributed event-triggered communication for dynamic average consensus in networked systems

This paper presents distributed algorithmic solutions that employ opportunistic inter-agent communication to achieve dynamic average consensus. In our solutions each agent is endowed with a local criterion that enables it to determine whether to broadcast its state to its neighbors. Our starting point is a continuous-time distributed coordination strategy that, under continuous-time communication, achieves practical asymptotic tracking of the dynamic average of the time-varying agents' reference inputs. Then, for this algorithm, depending on the directed or undirected nature of the time-varying interactions and under suitable connectivity conditions, we propose two different distributed event-triggered communication laws that prescribe agent communications at discrete time instants in an opportunistic fashion. In both cases, we establish positive lower bounds on the inter-event times of each agent and characterize their dependence on the algorithm design parameters. This analysis allows us to rule out the presence of Zeno behavior and characterize the asymptotic correctness of the resulting implementations. Several simulations illustrate the results.

math.OC↗

arXiv2014

Robust distributed linear programming

This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show that the resulting continuous-time saddle-point algorithm is provably correct but, in general, not distributed because of a global parameter associated with the nonsmooth exact penalty function employed to encode the inequality constraints of the linear program. This motivates the design of a discontinuous saddle-point dynamics that, while enjoying the same convergence guarantees, is fully distributed and scalable with the dimension of the solution vector. We also characterize the robustness against disturbances and link failures of the proposed dynamics. Specifically, we show that it is integral-input-to-state stable but not input-to-state stable. The latter fact is a consequence of a more general result, that we also establish, which states that no algorithmic solution for linear programming is input-to-state stable when uncertainty in the problem data affects the dynamics as a disturbance. Our results allow us to establish the resilience of the proposed distributed dynamics to disturbances of finite variation and recurrently disconnected communication among the agents. Simulations in an optimal control application illustrate the results.

math.OC↗

arXiv2014

Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment

This paper considers the economic dispatch problem for a network of power generating units communicating over a strongly connected, weight-balanced digraph. The collective aim is to meet a power demand while respecting individual generator constraints and minimizing the total generation cost. We design a distributed coordination algorithm consisting of two interconnected dynamical systems. One block uses dynamic average consensus to estimate the evolving mismatch in load satisfaction given the generation levels of the units. The other block adjusts the generation levels based on the optimization objective and the estimate of the load mismatch. Our convergence analysis shows that the resulting strategy provably converges to the solution of the dispatch problem starting from any initial power allocation, and therefore does not require any specific procedure for initialization. We also characterize the algorithm robustness properties against the addition and deletion of units (capturing scenarios with intermittent power generation) and its ability to track time-varying loads. Our technical approach employs a novel refinement of the LaSalle Invariance Principle for differential inclusions, that we also establish and is of independent interest. Several simulations illustrate our results.

math.OC↗

arXiv2014

Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.

math.OC↗

arXiv2014

Distributed bargaining in dyadic-exchange networks

This paper considers dyadic-exchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents obtain similar benefits from collaborating), or Nash (both stable and balanced) outcomes. We design provably-correct continuous-time algorithms to find each of these classes of outcomes in a distributed way. Our algorithmic design to find Nash bargaining solutions builds on the other two algorithms by having the dynamics for finding stable outcomes feeding into the one for finding balanced ones. Our technical approach to establish convergence and robustness combines notions and tools from optimization, graph theory, nonsmooth analysis, and Lyapunov stability theory and provides a useful framework for further extensions. We illustrate our results in a wireless communication scenario where single-antenna devices have the possibility of working as 2-antenna virtual devices to improve channel capacity.

math.OC↗

arXiv2014

Distributed linear programming with event-triggered communication

We consider a network of agents whose objective is for the aggregate of their states to converge to a solution of a linear program in standard form. Each agent has limited information about the problem data and can communicate with other agents at discrete time instants of their choosing. Our main contribution is the synthesis of a distributed dynamics and a set of state-based rules, termed triggers, that individual agents use to determine when to opportunistically broadcast their state to neighboring agents to ensure asymptotic convergence to a solution of the linear program. Our technical approach to the algorithm design and analysis overcomes a number of challenges, including establishing convergence in the absence of a common smooth Lyapunov function, ensuring that the triggers are detectable by agents using only local information, accounting for asynchronism in the state broadcasts, and ruling out various causes of arbitrarily fast state broadcasting. Various simulations illustrate our results.

math.OC↗

arXiv2014

Dynamic Average Consensus under Limited Control Authority and Privacy Requirements

This paper introduces a novel continuous-time dynamic average consensus algorithm for networks whose interaction is described by a strongly connected and weight-balanced directed graph. The proposed distributed algorithm allows agents to track the average of their dynamic inputs with some steady-state error whose size can be controlled using a design parameter. This steady-state error vanishes for special classes of input signals. We analyze the asymptotic correctness of the algorithm under time-varying interaction topologies and characterize the requirements on the stepsize for discrete-time implementations. We show that our algorithm naturally preserves the privacy of the local input of each agent. Building on this analysis, we synthesize an extension of the algorithm that allows individual agents to control their own rate of convergence towards agreement and handle saturation bounds on the driving command. Finally, we show that the proposed extension additionally preserves the privacy of the transient response of the agreement states and the final agreement value from internal and external adversaries. Numerical examples illustrate the results.

math.OC↗

arXiv2012

Distributed continuous-time convex optimization on weight-balanced digraphs

This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge, on any strongly connected weight-balanced digraph, to the set of minimizers of a sum of convex differentiable functions with globally Lipschitz gradients. Our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results.

math.OC↗

arXiv2012

Distributed convergence to Nash equilibria in two-network zero-sum games

This paper considers a class of strategic scenarios in which two networks of agents have opposing objectives with regards to the optimization of a common objective function. In the resulting zero-sum game, individual agents collaborate with neighbors in their respective network and have only partial knowledge of the state of the agents in the other network. For the case when the interaction topology of each network is undirected, we synthesize a distributed saddle-point strategy and establish its convergence to the Nash equilibrium for the class of strictly concave-convex and locally Lipschitz objective functions. We also show that this dynamics does not converge in general if the topologies are directed. This justifies the introduction, in the directed case, of a generalization of this distributed dynamics which we show converges to the Nash equilibrium for the class of strictly concave-convex differentiable functions with locally Lipschitz gradients. The technical approach combines tools from algebraic graph theory, nonsmooth analysis, set-valued dynamical systems, and game theory.

math.OC↗

arXiv2011

Distributed strategies for generating weight-balanced and doubly stochastic digraphs

Weight-balanced and doubly stochastic digraphs are two classes of digraphs that play an essential role in a variety of cooperative control problems, including formation control, distributed averaging, and optimization. We refer to a digraph as doubly stochasticable (weight-balanceable) if it admits a doubly stochastic (weight-balanced) adjacency matrix. This paper studies the characterization of both classes of digraphs, and introduces distributed algorithms to compute the appropriate set of weights in each case.

math.OC↗

arXiv2010

Biological control networks suggest the use of biomimetic sets for combinatorial therapies

Cells are regulated by networks of controllers having many targets, and targets affected by many controllers, but these "many-to-many" combinatorial control systems are poorly understood. Here we analyze distinct cellular networks (transcription factors, microRNAs, and protein kinases) and a drug-target network. Certain network properties seem universal across systems and species, suggesting the existence of common control strategies in biology. The number of controllers is ~8% of targets and the density of links is 2.5% \pm 1.2%. Links per node are predominantly exponentially distributed, implying conservation of the average, which we explain using a mathematical model of robustness in control networks. These findings suggest that optimal pharmacological strategies may benefit from a similar, many-to-many combinatorial structure, and molecular tools are available to test this approach.

q-bio.MN↗

arXiv2009

Systems approaches and algorithms for discovery of combinatorial therapies

Effective therapy of complex diseases requires control of highly non-linear complex networks that remain incompletely characterized. In particular, drug intervention can be seen as control of signaling in cellular networks. Identification of control parameters presents an extreme challenge due to the combinatorial explosion of control possibilities in combination therapy and to the incomplete knowledge of the systems biology of cells. In this review paper we describe the main current and proposed approaches to the design of combinatorial therapies, including the empirical methods used now by clinicians and alternative approaches suggested recently by several authors. New approaches for designing combinations arising from systems biology are described. We discuss in special detail the design of algorithms that identify optimal control parameters in cellular networks based on a quantitative characterization of control landscapes, maximizing utilization of incomplete knowledge of the state and structure of intracellular networks. The use of new technology for high-throughput measurements is key to these new approaches to combination therapy and essential for the characterization of control landscapes and implementation of the algorithms. Combinatorial optimization in medical therapy is also compared with the combinatorial optimization of engineering and materials science and similarities and differences are delineated.

q-bio.QM↗

arXiv2009

Discontinuous Dynamical Systems: A tutorial on solutions, nonsmooth analysis, and stability

This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control, nonsmooth mechanics, and robotic manipulation. Independently of the particular application, one always faces similar questions when dealing with discontinuous dynamical systems. The most basic one is the notion of solution. We begin by introducing the notions of Caratheodory, Filippov and sample-and-hold solutions, discuss existence and uniqueness results for them, and examine various examples. We also give specific pointers to other notions of solution defined in the literature. Once the notion of solution has been settled, we turn our attention to the analysis of stability of discontinuous systems. We introduce the concepts of generalized gradient of locally Lipschitz functions and proximal subdifferential of lower semicontinuous functions. Building on these notions, we establish monotonic properties of candidate Lyapunov functions along the solutions. These results are key in providing suitable generalizations of Lyapunov stability theorems and the LaSalle Invariance Principle. We illustrate the applicability of these results in a class of nonsmooth gradient flows.

math.DS↗

arXiv2008

Nonholonomic systems on Lie algebroids

This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2

math-ph↗