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Worst-case time complexity of a lattice formation problem 44

Worst-case time complexity of a lattice formation problem

引用

44th Annual Allerton Conference on Communication, control, and Computing 2006

作者： Savla, Ketan Bullo, Francesco Center for Control Dynamical Systems and Computation University of California at Santa Barbara 2338 Engineering Bldg II Santa BarbaraCA93106-5070 United States

ISBN: (纸本)9781604237924

We consider a formation control problem for a robotic network with limited communication and controlled motion abilities. We propose a novel control structure that organizes the robots in concentric layers and that associates to each layer a local leader. Through a load balancing algorithm on the asynchronous network of layers we allocate the desired number of robots on each layer. A final uniform spreading algorithm leads the robots to a lattice-like formation. This novel distributed communication and control algorithm runs in linear time in the worst case.

关键词： Robots

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On the dubins traveling salesperson problems: Novel approximation algorithms 2nd

On the dubins traveling salesperson problems: Novel approxim...

引用

2nd International Conference on Robotics Science and Systems, RSS 2006

作者： Savla, Ketan Frazzoli, Emilio Bullo, Francesco Center for Control Dynamical Systems and Computation University of California at Santa Barbara United States Mechanical and Aerospace Engineering Department University of California Los Angeles United States

ISBN: (纸本)9780262693486

In this paper we study minimum-time motion planning and routing problems for the Dubins vehicle, i.e., a nonholonomic vehicle that is constrained to move along planar paths of bounded curvature, without reversing direction. Motivated by autonomous aerial vehicle applications, we consider the Traveling Salesperson Problem for the Dubins vehicle (DTSP): given n points on a plane, what is the shortest Dubins tour through these points and what is its length? Specifically, we study a stochastic version of the DTSP where the n targets are randomly sampled from a uniform distribution. We show that the expected length of such a tour is of order at least n2/3 and we propose a novel algorithm yielding a solution with length of order n2/3 with high probability. Additionally, we study a dynamic version of the DTSP: given a stochastic process that generates target points, is there a policy which guarantees that the number of unvisited points does not diverge over time? If such stable policies exist, what is the minimum expected time that a newly generated target waits before being visited by the vehicle? We propose a novel stabilizing algorithm such that the expected wait time is provably within a constant factor from the optimum.

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Moment closure techniques for stochastic models in population biology

Moment closure techniques for stochastic models in populatio...

引用

American control Conference (ACC)

作者： A. Singh J.P. Hespanha Center for Control Engineering Computation University of California Santa Barbara CA USA

Continuous-time birth-death Markov processes serve as useful models in population biology. In this paper, we present a procedure for constructing approximate stochastic models for these processes. This is done by representing the population of a species as the continuous state of a stochastic hybrid system (SHS). This SHS is characterized by reset maps that account for births and deaths, transition intensities that correspond to the birth-death rates, and trivial continuous dynamics. It has been shown that for this type of SHS the statistical moments of the continuous state evolve according to an infinite-dimensional linear ordinary differential equation (ODE). However, for analysis purposes it is convenient to approximate this infinite-dimensional linear ODE by a finite-dimensional nonlinear one. This procedure generally approximates some higher-order moments by a nonlinear function of lower-order moments and it is called moment closure. We obtain moment closures by matching time derivatives of the infinite-dimensional ODE with its finite-dimensional approximation at some time t 0 . This guarantees a good approximation, at-least locally in time. We provide explicit formulas to construct these approximations and compare this technique with alternative moment-closure methods available in the literature. This comparison takes into account both the transient and the steady-state regimens

关键词： Stochastic processes Biological system modeling computational biology Markov processes Evolution (biology) Stochastic systems Differential equations Polynomials Vectors Nonlinear dynamical systems

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Lognormal Moment Closures for Biochemical Reactions

Lognormal Moment Closures for Biochemical Reactions

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IEEE Conference on Decision and control

作者： Abhyudai Singh Joao Pedro Hespanha Center for Control Engineering and Computation University of California Santa Barbara CA USA

ISBN: (纸本)1424401704;9781424401703

In the stochastic formulation of chemical reactions, the dynamics of the first M-order moments of the species populations generally do not form a closed system of differential equations, in the sense that the time-derivatives of first M-order moments generally depend on moments of order higher than M. However, for analysis purposes, these dynamics are often made to be closed by approximating the needed derivatives of the first M-order moments by nonlinear functions of the same moments. These functions are called the moment closure functions. Recent results have introduced the technique of derivative-matching, where the moment closure functions are obtained by first assuming that they exhibit a certain separable form, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. However, for multi-species reactions these results have been restricted to second order truncations, i.e, M = 2. This paper extends these results by providing explicit formulas to construct moment closure functions for any arbitrary order of truncation M. We show that with increasing M the closed moment equations provide more accurate approximations to the exact moment equations. Striking features of these moment closure functions are that they are independent of the reaction parameters (reaction rates and stoichiometry) and moreover the dependence of higher-order moment on lower order ones is consistent with the population being jointly lognormally distributed. To illustrate the applicability of our results we consider a simple bi-molecular reaction. Moment estimates from a third order truncation are compared with estimates obtained from a large number of Monte Carlo simulations

关键词： Chemicals Stochastic systems Differential equations Stochastic processes Vectors control systems USA Councils Nonlinear dynamical systems Nonlinear equations Probability density function

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On the Continuity of Asymptotically Stable Compact Sets for Simulations of Hybrid Systems

On the Continuity of Asymptotically Stable Compact Sets for ...

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IEEE Conference on Decision and control

作者： Ricardo G. Sanfelice Andrew R. Teel Center for Control Engineering and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

ISBN: (纸本)1424401704;9781424401703

We propose a hybrid model for simulations of hybrid systems and we establish conditions on its data so that the asymptotically stable sets observed in simulations are continuous. The most important components of the hybrid model for simulations are a discrete integration scheme for the computation of the flows and an approximated jump mapping for the computation of the jumps. Our main result is built on the facts that, on compact hybrid time domains, every simulation to a hybrid system is arbitrarily close (in the graphical sense) to some solution to the actual hybrid system, and that asymptotically stable compact sets of hybrid systems are semiglobally practically asymptotically stable compact sets for the hybrid model for simulations. We present these results and illustrate them in simulations of the bouncing ball system

关键词： computational modeling Differential equations State-space methods Numerical simulation Analytical models Military computing USA Councils Standards development control systems Packaging

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Lyapunov Analysis of Sample-and-Hold Hybrid Feedbacks

Lyapunov Analysis of Sample-and-Hold Hybrid Feedbacks

引用

IEEE Conference on Decision and control

作者： Ricardo G. Sanfelice Andrew R. Teel Center for Control Dynamical Systems and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

ISBN: (纸本)1424401704;9781424401703

For hybrid closed-loop systems arising from hybrid control of nonlinear systems, we show that the sample-and-hold implementation of the hybrid controller preserves (semiglobally and practically) the stability properties of the closed-loop system. We provide a general model for the hybrid closed-loop system where the hybrid controller is implemented digitally and it is interfaced to the nonlinear system through sample and hold devices. We model the sample device and the digital controller/hold device as single asynchronous hybrid systems with independent timing constants and data. The main result is established by means of a Lyapunov function for the hybrid closed-loop system resulting from the interconnection of its hybrid and nonlinear subsystems

关键词： Feedback control systems Nonlinear control systems Nonlinear systems Digital control Stability analysis Emulation control system synthesis Military computing Asymptotic stability

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Robust hybrid controllers for continuous-time systems with applications to obstacle avoidance and regulation to disconnected set of points

Robust hybrid controllers for continuous-time systems with a...

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American control Conference (ACC)

作者： R.G. Sanfelice M.J. Messina S. Emre Tuna A.R. Teel Center for Control Dynamical Systems and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

We give an elementary proof of the fact that, for continuous-time systems, it is impossible to use (even discontinuous) pure state feedback to achieve robust global asymptotic stabilization of a disconnected set of points or robust global regulation to a target while avoiding an obstacle. Indeed, we show that arbitrarily small, piecewise constant measurement noise can keep the trajectories away from the target. We give a constructive, Lyapunov-based hybrid state feedback that achieves robust regulation in the above mentioned settings

关键词： Robust control control systems Noise robustness Noise measurement State feedback Time measurement Hysteresis Differential equations Military computing Nonlinear control systems

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Approximate dynamic programming based on expansive projections

Approximate dynamic programming based on expansive projectio...

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45th IEEE Conference on Decision and control 2006, CDC

作者： Arruda, Edilson F. Do Val, João B. R. Center for Systems and Control National Laboratory for Scientific Computation - LNCC Av. Getulio Vargas 333 Petrópolis RJ 25651-075 Brazil School of Electrical and Computer Engineering State University of Campinas - UNICAMP Caixa Postal 6101 Campinas SP 13083-852 Brazil

ISBN: (纸本)1424401712

We present a general method to obtain convergent approximate value iteration algorithms with function approximation. The result is applicable to any arbitrary approximation architecture and generalizes existing results in the literature derived for particular approximation schemes. Additionally, we show how to obtain a convergent approximate mapping whose fixed point is the projection in the approximation space of a fixed point of the exact dynamic programming mapping with regards to a suitable subset norm. This result relies on evaluating the difference between successive iterates in the selected subset norm, which provides convergent procedures for any arbitrary approximation architecture. ©2006 IEEE.

关键词： Dynamic programming

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Distributed algorithms for polygonal approximation of convex contours

Distributed algorithms for polygonal approximation of convex...

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IEEE Conference on Decision and control

作者： Sara Susca Sonia Martinez Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara USA Mechanical and AeroSpace Engineering Department University of California San Diego USA

ISBN: (纸本)1424401704;9781424401703

We propose algorithms that compute polygon approximations for convex contours. This geometric problem is relevant in interpolation theory, data compression, and has potential applications in robotic sensor networks. The algorithms are based on simple feedback ideas, on limited nearest-neighbor information, and amount to gradient descent laws for appropriate cost functions. The approximations are based on intuitive performance metrics, such as the area of the inner, outer, and "outer minus inner" approximating polygons

关键词： Distributed algorithms Robot sensing systems Interpolation Data compression Measurement Force feedback Atomic force microscopy USA Councils Approximation algorithms Distributed computing

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Distributed consensus on enclosing shapes and minimum time rendezvous

Distributed consensus on enclosing shapes and minimum time r...

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IEEE Conference on Decision and control

作者： Giuseppe Notarstefano Francesco Bullo Department of Information Engineering Università di Padova Padova Italy Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

ISBN: (纸本)1424401704;9781424401703

In this paper we introduce the notion of optimization under control and communication constraint in a robotic network. Starting from a general setup, we focus our attention on the problem of achieving rendezvous in minimum time for a network of first order agents with bounded inputs and limited range communication. We propose two dynamic control and communication laws. These laws are based on consensus algorithms for distributed computation of the minimal enclosing ball and orthotope of a set of points. We prove that these control laws converge to the optimal solution of the centralized problem (i.e., when no communication constrains are enforced) as the bound on the control input goes to zero. Moreover, we give a bound for the time complexity of one of the two laws

关键词： Communication system control Optimal control Mobile communication Robot kinematics Distributed computing Centralized control Shape control Motion control Constraint optimization Network topology

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