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Mathematical relationships between representations of structure in linear interconnected dynamical systems

Mathematical relationships between representations of struct...

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作者： Yeung, E. Gonçalves, J. Sandberg, H. Warnick, S. Control and Dynamical Systems California Institute of Technology United States Information and Decision Algorithms Laboratories Brigham Young University Provo UT United States Control Group Department of Engineering University of Cambridge Cambridge United Kingdom Automatic Control Laboratory KTH School of Electrical Engineering Stockholm Sweden

ISBN: (纸本)9781457700804

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relationships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. © 2011 AACC American Automatic control Council.

关键词： Dynamical systems

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Converse Results on Existence of Sum of Squares Lyapunov Functions

Converse Results on Existence of Sum of Squares Lyapunov Fun...

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IEEE Conference on decision and control

作者： Amir Ali Ahmadi Pablo A. Parrilo Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology

ISBN: (纸本)9781612848006

Despite the pervasiveness of sum of squares (sos) techniques in Lyapunov analysis of dynamical systems, the converse question of whether sos Lyapunov functions exist whenever polynomial Lyapunov functions exist has remained elusive. In this paper, we first show via an explicit counterexample that if the degree of the polynomial Lyapunov function is fixed, then sos programming can fail to find a valid Lyapunov function even though one exists. On the other hand, if the degree is allowed to increase, we prove that existence of a polynomial Lyapunov function for a homogeneous polynomial vector field implies existence of a polynomial Lyapunov function that is sos and that the negative of its derivative is also sos. The latter result is extended to develop a converse sos Lyapunov theorem for robust stability of switched linear systems.

关键词： Liapunov function Converse Polynomial Sum of squares Vector field Robust stability Linear system Explicit

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On Higher Order Derivatives of Lyapunov Functions

On Higher Order Derivatives of Lyapunov Functions

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2011 American control Conference (ACC)

作者： Amir Ali Ahmadi Pablo A. Parrilo Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology USA

This note is concerned with a class of differential inequalities in the literature that involve higher order derivatives of Lyapunov functions and have been proposed to infer asymptotic stability of a dynamical system without requiring the first derivative of the Lyapunov function to be negative definite. We show that whenever a Lyapunov function satisfies these conditions, we can explicitly construct another (standard) Lyapunov function that is positive definite and has a negative definite first derivative. Our observation shows that a search for a standard Lyapunov function parameterized by higher order derivatives of the vector field is less conservative than the previously proposed conditions. Moreover, unlike the previous inequalities, the new inequality can be checked with a convex program. This is illustrated with an example where sum of squares optimization is used.

关键词： Lyapunov methods Asymptotic stability Polynomials Trajectory Stability analysis Programming Optimization

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Dynamic vehicle routing for robotic systems

Dynamic vehicle routing for robotic systems

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作者： Bullo, Francesco Frazzoli, Emilio Pavone, Marco Savla, Ketan Smith, Stephen L. Center for Control Dynamical Systems and Computation Department of Mechanical Engineering University of California in Santa Barbara Santa Barbara CA 93106 United States Laboratory for Information and Decision Systems Department of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge MA 02139 United States Jet Propulsion Laboratory California Institute of Technology Pasadena CA 91109 United States Laboratory for Information and Decision Systems Massachusetts Institute of Technology Cambridge MA 02139 United States Department of Electrical and Computer Engineering University of Waterloo Waterloo ON N2L 3G1 Canada

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits. © 2011 IEEE.

关键词： Adaptive algorithms

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A Globally Asymptotically Stable Polynomial Vector Field with no Polynomial Lyapunov Function

A Globally Asymptotically Stable Polynomial Vector Field wit...

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IEEE Conference on decision and control

作者： Amir Ali Ahmadi Miroslav Krstic Pablo A. Parrilo Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cymer Center for Control Systems and Dynamics Department of Mechanical and Aerospace Engineering University of California at San Diego

We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.

ISBN: (纸本)9781612848006

We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.

关键词： Liapunov function Vector field Polynomial asymptotic

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ℋ2 performance bounds for voltage regulation on a spatially-invariant DC power grid

ℋ2 performance bounds for voltage regulation on a spatially...

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American control Conference (ACC)

作者： Michael Rinehart Mardavij Roozbehani Munther A. Dahleh Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge MA USA

Despite the importance of voltage regulation to operational reliability and safety of power grids, little is understood about how the topology of the physical layer, and the architecture of the communication and control layer impact the ability of the system to regulate the voltages. In this paper, we apply spatial-invariance analysis to develop analytical upper and lower bounds for the Hi gain of a DC power grid with respect to voltage regulation. These bounds establish a relation between network architecture and performance, and reveal fundamental limits to performance that cannot be overcome using feedback control.

关键词： Power grids Voltage control Discrete Fourier transforms Generators Feedback control Analytical models Distributed control

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An Optimal controller Architecture for Poset-Causal systems

An Optimal Controller Architecture for Poset-Causal Systems

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IEEE Conference on decision and control

作者： Parikshit Shah Pablo A. Parrilo Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge MA 02139

ISBN: (纸本)9781612848006

We propose a novel and natural architecture for decentralized control, that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the Mobius transform of the poset, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Mobius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on H_(2)-optimal decentralized control for arbitrary posets, we prove that the H_(2)-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture.

关键词： computer architecture Distributed control Context Architecture Vectors Indexing

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Degree Fluctuations and the Convergence Time of Consensus Algorithms

Degree Fluctuations and the Convergence Time of Consensus Al...

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IEEE Conference on decision and control

作者： Alex Olshevsky John N. Tsitsiklis Department of Mechanical and Aerospace Engineering Princeton University Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology

ISBN: (纸本)9781612848006

We consider a consensus algorithm in which every node in a time-varying undirected connected graph assigns equal weight to each of its neighbors. Under the assumption that the degree of any given node is constant in time, we show that the algorithm achieves consensus within a given accuracy E on n nodes in time O(n~(3)ln(n/E)). Because there is a direct relation between consensus algorithms in time-varying environments and inhomogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give simple proofs that the convergence time becomes exponentially large in the number of nodes n under slight relaxations of the above assumptions. We prove that exponential convergence time is possible for consensus algorithms on fixed directed graphs, and we use an example of Cao, Spielman, and Morse to give a simple argument that the same is possible if the constant degrees assumption is even slightly relaxed.

关键词： Converge time varying Random walk algorithms

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Tree-Structured Statistical Modeling via Convex Optimization

Tree-Structured Statistical Modeling via Convex Optimization

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IEEE Conference on decision and control

作者： James Saunderson Venkat Chandrasekaran Pablo A. Parrilo Alan S. Willsky Department of Electrical Engineering and Computer Science Laboratory of Information and Decision Systems Massachusetts Institute of Technology Cambridge MA 02139 USA

ISBN: (纸本)9781612848006

We develop a semidefinite-programming-based approach to stochastic modeling with multiscale autoregressive (MAR) processes--a class of stochastic processes indexed by the vertices of a tree. Given a tree and the covariance matrix of the variables corresponding to the leaves of the tree, our procedure aims to construct an MAR process with small state dimensions at each vertex that approximately realizes the given covariance at the leaves. Our method does not require prior specification of the state dimensions at each vertex. Furthermore, we establish a large class of MAR processes for which, given only the index tree and the leaf covariance of the process, our method can recover a parametrization that matches the leaf-covariance and has the correct state dimensions. Finally we demonstrate, using synthetic examples, that given i.i.d. samples of the leaf variables our method can recover the correct state dimensions of an underlying MAR process.

关键词： variance covariance matrix dimensions vertex head foliage statistical models (nuclear) Stochastic models Convex function Covariance corners Markov chain TREE LEAVES parameterization

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Modified Banker's algorithm for scheduling in multi-AGV systems

Modified Banker's algorithm for scheduling in multi-AGV syst...

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IEEE International Conference on Automation Science and engineering (CASE)

作者： Luka Kalinovcic Tamara Petrovic Stjepan Bogdan Vedran Bobanac Laboratory for Robotics and Intelligent Control Systems Department of Control and Computer Engineering Faculty of Electrical Engineering and Computing University of Zagreb Zagreb Croatia Laboratory for Renewable Energy Sources Department of Control and Computer Engineering Faculty of Electrical Engineering and Computing University of Zagreb Zagreb Croatia

In today's highly complex multi-AGV systems key research objective is finding a scheduling and routing policy that avoids deadlock while assuring that vehicle utilization is as high as possible. It is well known that finding such an optimal policy is a NP-hard task in general case. Therefore, big part of the research is oriented towards finding various suboptimal policies that can be applied to real world plants. In this paper we propose modified Banker's algorithm for scheduling in multi-AGV systems. A predetermined mission's path is executed in a way that some non-safe states are allowed in order to achieve better utilization of vehicles. A graph-based method of polynomial complexity for verification of these states is given. Algorithm is tested on a layout of a real plant for packing and warehousing palettes. Results shown at the end of the paper demonstrate advantages of the proposed method compared with other methods based on Banker's algorithm.

关键词： Vehicles System recovery Layout Resource management Job shop scheduling Workstations

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