5,194 research outputs found
Distributed abstract optimization via constraints consensus: theory and applications
No full textDistributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract optimization programs are a generalization of linear programs that captures numerous geometric optimization problems. We propose novel constraints consensus algorithms for distributed abstract programs with guaranteed finite-time convergence to a global optimum. The algorithms rely upon solving local abstract programs and exchanging the solutions among neighboring processors. The proposed algorithms are appropriate for networks with weak time-dependent connectivity requirements and tight memory constraints. We show how the constraints consensus algorithms may be applied to suitable target localization and formation control problems
COMMENTO SISTEMATICO ALL'ART. 2643 NEL COMMENTARIO A CURA DI G. CIAN
No full textCOMMENTO SCIENTIFICO CON ANALISI DEL PANORAMA DOTTRINALE E GIURISPRUDENZIALE DELLE NORME IN TEMA DI TRASCRIZIONE CON PARTICOLARE RIGUARDO ALLE CATEGORIE DI ATTI TRASCRIVIBIL
Regular Pairings for Nonquadratic Lyapunov Functions and Contraction Analysis
No full textRecent studies on stability and contractivity have highlighted the importance ofsemi-inner products, which we refer to as ``pairings,"" associated with general norms. A pairing isa binary operation that relates the derivative of a curve's norm to the radius vector of the curveand its tangent. This relationship, known as the curve norm derivative formula, is crucial whenusing the norm as a Lyapunov function. Another important property of the pairing, used in stabilityand contraction criteria, is the so-called Lumer inequality, which relates the pairing to the inducedlogarithmic norm. We prove that the curve norm derivative formula and Lumer's inequality are, infact, equivalent to each other and to several simpler properties. We then introduce and characterizeregular pairings that satisfy all of these properties. Our results unify several independent theoriesof pairings (semi-inner products) developed in previous work on functional analysis and controltheory. Additionally, we introduce the polyhedral max pairing and develop computational tools forpolyhedral norms, advancing contraction theory in non-Euclidean space
A distributed simplex algorithm for degenerate linear programs and multi-agent assignments
No full textIn this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer-to-peer networks with distributed information structures. We propose a distributed version of the well-known simplex algorithm for general degenerate linear programs. A network of agents, running our algorithm, will agree on a common optimal solution, even if the optimal solution is not unique, or will determine infeasibility or unboundedness of the problem. We establish how the multi-agent assignment problem can be efficiently solved by means of our distributed simplex algorithm. We provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the communication graph
The Yakubovich S-Lemma Revisited: Stability and Contractivity in Non-Euclidean Norms
No full textThe celebrated S-Lemma was originally proposed to ensure the existence of a
quadratic Lyapunov function in the Lur'e problem of absolute stability. A
quadratic Lyapunov function is, however, nothing else than a squared Euclidean
norm on the state space (that is, a norm induced by an inner product). A
natural question arises as to whether squared non-Euclidean norms
may serve as Lyapunov functions in stability problems. This
paper presents a novel non-polynomial S-Lemma that leads to constructive
criteria for the existence of such functions defined by weighted
norms. Our generalized S-Lemma leads to new absolute stability and absolute
contractivity criteria for Lur'e-type systems, including, for example, a new
simple proof of the Aizerman and Kalman conjectures for positive Lur'e systems
Visibility maintenance via controlled invariance for leader-follower vehicle formations
No full textThis paper studies the visibility maintenance problem (VMP) for a leaderfollower pair of Dubins-like vehicles with input constraints and proposes an original solution based on the notion of controlled invariance. The nonlinear model describing the relative dynamics of the vehicles is interpreted as a linear uncertain system, with the leader robot acting as an external disturbance. The VMP is then reformulated as a linear constrained regulation problem with additive disturbances (DLCRP). Positive D-invariance conditions for linear uncertain systems with parametric disturbance matrix are introduced and used to solve the VMP when box bounds on the state, control input and disturbance are considered. The proposed design procedure can be easily adapted to more general scenarios. Simulation results illustrate the theory and show the effectiveness of our approach
Non-Euclidean Contraction Analysis of Continuous-Time Neural Networks
No full textCritical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established via a contraction analysis. This paper develops a comprehensive non-Euclidean contraction theory for continuous-time neural networks. Specifically, we provide novel sufficient conditions for the contractivity of general classes of continuous-time neural networks including Hopfield, firing rate, Persidskii, Lur'e, and other neural networks with respect to the non-Euclidean norms. These sufficient conditions are based upon linear programming or, in some special cases, establishing the Hurwitzness of a particular Metzler matrix. To prove these sufficient conditions, we develop novel results on non-Euclidean logarithmic norms and a novel necessary and sufficient condition for contractivity of systems with locally Lipschitz dynamics. For each model, we apply our theoretical results to compute the optimal contraction rate and corresponding weighted non-Euclidean norm with respect to which the neural network is contracting
Non-Euclidean Contractivity of Recurrent Neural Networks
No full textCritical questions in dynamical neuroscience and machine learning are related to the study of recurrent neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established via a contraction analysis.This paper develops a comprehensive contraction theory for recurrent neural networks. First, for non-Euclidean l 1 /l ∞ logarithmic norms, we establish quasiconvexity with respect to positive diagonal weights and closed-form worst-case expressions over certain matrix polytopes. Second, for locally Lipschitz maps (e.g., arising as activation functions), we show that their one-sided Lipschitz constant equals the essential supremum of the logarithmic norm of their Jacobian. Third and final, we apply these general results to classes of recurrent neural circuits, including Hopfield, firing rate, Persidskii, Lur’e and other models. For each model, we compute the optimal contraction rate and corresponding weighted non-Euclidean norm via a linear program or, in some special cases, via a Hurwitz condition on the Metzler majorant of the synaptic matrix. Our non-Euclidean analysis establishes also absolute, connective, and total contraction properties
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