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Touri B.,Coordinated Science Laboratory | Nedic A.,Enterprise Systems
Automatica | Year: 2012

We study the ergodicity of backward product of stochastic and doubly stochastic matrices by introducing the concept of absolute infinite flow property. We show that this property is necessary for ergodicity of any chain of stochastic matrices, by defining and exploring the properties of a rotational transformation for a stochastic chain. Then, we establish that the absolute infinite flow property is equivalent to ergodicity for doubly stochastic chains. Furthermore, we develop a rate of convergence result for ergodic doubly stochastic chains. We also investigate the limiting behavior of a doubly stochastic chain and show that the product of doubly stochastic matrices is convergent up to a permutation sequence. Finally, we apply the results to provide a necessary and sufficient condition for the absolute asymptotic stability of a discrete linear inclusion driven by doubly stochastic matrices. © 2012 Published by Elsevier Ltd.

Paranjape A.A.,University of Illinois at Urbana - Champaign | Chung S.-J.,University of Illinois at Urbana - Champaign | Chung S.-J.,Coordinated Science Laboratory | Kim J.,University of Illinois at Urbana - Champaign
IEEE Transactions on Robotics | Year: 2013

We describe the design of an aerial robot inspired by birds and the underlying theoretical developments leading to novel control and closed-loop guidance algorithms for a perching maneuver. A unique feature of this robot is that it uses wing articulation to control the flight path angle as well as the heading angle. It lacks a vertical tail for improved agility, which results in unstable lateral-directional dynamics. New closed-loop motion planning algorithms with guaranteed stability are obtained by rewriting the flight dynamic equations in the spatial domain rather than as functions of time, after which dynamic inversion is employed. It is shown that nonlinear dynamic inversion naturally leads to proportional-integral-derivative controllers, thereby providing an exact method for tuning the gains. The capabilities of the proposed bioinspired robot design and its novel closed-loop perching controller have been successfully demonstrated with perched landings on a human hand. © 2004-2012 IEEE.

Law K.L.,University of Illinois at Urbana - Champaign | Law K.L.,TU Darmstadt | Do M.N.,Coordinated Science Laboratory | Do M.N.,University of Illinois at Urbana - Champaign
IEEE Transactions on Image Processing | Year: 2011

We study the theory and algorithms of an optimal use of multidimensional signal reconstruction from multichannel acquisition by using a filter bank setup. Suppose that we have an N-channel convolution system, referred to as N analysis filters, in M dimensions. Instead of taking all the data and applying multichannel deconvolution, we first reduce the collected data set by an integer M × M uniform sampling matrix D, and then search for a synthesis polyphase matrix which could perfectly reconstruct any input discrete signal. First, we determine the existence of perfect reconstruction (PR) systems for a given set of finite-impulse response (FIR) analysis filters. Second, we present an efficient algorithm to find a sampling matrix with maximum sampling rate and to find a FIR PR synthesis polyphase matrix for a given set of FIR analysis filters. Finally, once a particular FIR PR synthesis polyphase matrix is found, we can characterize all FIR PR synthesis matrices, and then find an optimal one according to design criteria including robust reconstruction in the presence of noise. © 2011 IEEE.

Yin H.,University of Illinois at Urbana - Champaign | Mehta P.G.,University of Illinois at Urbana - Champaign | Meyn S.P.,Coordinated Science Laboratory | Shanbhag U.V.,Enterprise Systems
Proceedings of the 2010 American Control Conference, ACC 2010 | Year: 2010

The purpose of this paper is to understand phase transition in noncooperative dynamic games with a large number of agents. Applications are found in neuroscience, biology, economics, as well as traditional engineering applications. The focus of analysis is a variation of the large population LQG model of Huang et. al. 2007 [6], comprised here of a controlled nonlinear N-dimensional stochastic differential equation model, coupled only through a nonlinear cost function. The states are interpreted as the phase angle for a collection of non-homogeneous oscillators, and in this way the model may be regarded as an extension of the classical coupled oscillator model of Kuramoto. A deterministic PDE model is proposed, which is shown to approximate the stochastic system as the population size approaches infinity. Key to the analysis of the PDE model is the existence of a particular Nash equilibrium in which the agents 'opt out' of the game, setting their controls to zero, resulting in the 'incoherence' equilibrium. Methods from dynamical systems theory are used in a bifurcation analysis, based on a linearization of the PDE model about the incoherence equilibrium. A critical value of the control cost parameter is identified: Above this value, the oscillators are incoherent; and below this value (when control is sufficiently cheap) the oscillators synchronize. These conclusions are illustrated with results from numerical experiments. © 2010 AACC.

Li L.,Indiana University - Purdue University Indianapolis | Hadjicostis C.N.,University of Cyprus | Hadjicostis C.N.,Coordinated Science Laboratory | Hadjicostis C.N.,University of Illinois at Urbana - Champaign
IEEE Transactions on Automation Science and Engineering | Year: 2011

This paper proposes an approach for estimating the least-cost transition firing sequence(s) that matches (match) the observation of a sequence of labels produced by transition activity in a given labeled Petri net. Each transition in the labeled net is associated with a (possibly empty) label and also with a nonnegative cost which captures its likelihood (e.g., in terms of the amount of workload or power required to execute the transition). Given full knowledge of the structure of the labeled Petri net and the observation of a sequence of labels, we aim at finding the transition firing sequence(s) that is (are) consistent with both the observed label sequence and the Petri net, and also has (have) the least total cost (i.e., the least sum of individual transition costs). The existence of unobservable transitions makes this task extremely challenging since the number of firing sequences that might be consistent can potentially be infinite. Under the assumption that the unobservable transitions in the net form an acyclic subnet and have strictly positive costs, we develop a recursive algorithm that is able to find the least-cost firing sequence(s) by reconstructing only a finite number of firing sequences. In particular, if the unobservable transitions in the net are contact-free, the proposed recursive algorithm finds the least-cost transition firing sequences with complexity that is polynomial in the length of the observed sequence of labels. © 2010 IEEE.

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