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Energy-Aware robotics 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Stramigioli, Stefano University of Twente Enschede Netherlands

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

This chapter has a tutorial nature in introducing a number of useful concepts which resulted by reasoning with power ports rather than with signals, as people usually do in control. Arjan is one of the Godfathers in this way of thinking and he has been a pioneer in bringing these concepts to a new level, introducing proper geometry, a sound system theoretic basis and divulgating these issues. This chapter shows how, by using these concepts, it is possible to address or solve certain problems in robotics, control and passivity in a simple and straightforward way. It also presents a formal proof of a claim which is often used as a conjecture and which gives theoretical arguments to counteract the statement which is often used against passivity and saying that passivity is too restrictive and stability is what should be looked for. Many of the concepts reported in the chapter have been the results of discussions with Arjan or are still issues that I am working on with Arjan. It is a great pleasure and honour to have the opportunity to contribute in this way to a recognition of the incredible career of a college and friend for which I have incredible respect from an intellectual and personal point of view. © Springer International Publishing Switzerland 2015.

关键词： Robotics

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Distributed line search for multiagent convex optimization 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Cortés, Jorge Martínez, Sonia Department of Mechanical and Aerospace Engineering UC San Diego 9500 Gilman Dr La JollaCA92093-0411 United States

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

This note considers multiagent systems seeking to optimize a convex aggregate *** assume that the gradient of this function is distributed, meaning that each agent can compute its corresponding partial derivative with information about its neighbors and itself only. In such scenarios, the discrete-time implementation of the gradient descent method poses the basic challenge of determining appropriate agent stepsizes that guarantee the monotonic evolution of the objective function. We provide a distributed algorithmic solution to this problem based on the aggregation of agent stepsizes via adaptive convex combinations. Simulations illustrate our results. © Springer International Publishing Switzerland 2015.

关键词： Multi agent systems

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A complement on elimination and realization in rational representations 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Trentelman, Harry L. Stegink, Tjerk W. Gottimukkala, Sasanka V. Johann Bernoulli Institute for Mathematics and Computer Science University of Groningen P. O Box 800 Groningen9700 AV Netherlands Hightech Solutions B.V. Apeldoorn Apeldoorn Netherlands

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

In this paper we study a number of problems in the context of rational representations of behaviors. In that context, a given proper real rational matrix can represent three behaviors. In the first place it can represent an input–output behavior. Second, it can represent the kernel behavior of the rational ‘differential operator’ associated with the rational matrix. Third, it can represent the image behavior asociated with the rational matrix. On the other hand, every proper real rational matrix admits a realization as a finite-dimensional linear state-space system. Such realization can represent three system behaviors: an input-state-output behavior, an output nulling behavior, or a driving variable behavior. In this paper we will study the relation between the three external behaviors of these state representations, and the behaviors given by the three rational representations associated with the underlying rational matrix. Preliminary results from [5] will be complemented to obtain necessary and sufficient conditions such that the respective external behaviors are equal. © Springer International Publishing Switzerland 2015.

关键词： Mathematical operators

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Modeling perspectives of hybrid systems and network systems 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Imura, Jun-Ichi Ishizaki, Takayuki Graduate School of Information Science and Engineering Tokyo Institute of Technology 2-12-1 Oh-Okayama MeguroTokyo152-8552 Japan

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

This article presents two topics, i.e., well-posedness of piecewise affine systems, and model reduction of network systems. The well-posedness problem, i.e., the problem of existence and uniqueness of solutions, of hybrid systems is one of the fundamental research topics, which the first author has collaborated with Prof. Arjan van der Schaft in 1998. Some results are revisited by focusing on the class of bimodal piecewise affine systems. The latter discusses the most recent topic that both Arjan and the first author have common interest in. In particular, the clustering-based H∞− and H2-model reduction approaches of large-scale network systems, which have been independently developed by the authors, are represented in a unified way. © Springer International Publishing Switzerland 2015.

关键词： Hybrid systems

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Modeling and analysis of energy distribution networks using switched differential systems 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Mayo-Maldonado, Jonathan C. Rapisarda, Paolo Vision Learning and Control Group School of Electronics and Computer Science University of Southampton SouthamptonSO17 1BJ United Kingdom

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

It is a pleasure to dedicate this contribution to Prof. Arjan van der Schaft on the occasion of his 60th birthday. We study the dynamics of energy distribution networks consisting of switching power converters and multiple (dis-)connectable modules. We use parsimonious models that deal effectively with the variant complexity of the network and the inherent switching phenomena induced by power converters. We also present the solution to instability problems caused by devices with negative impedance characteristics such as constant power loads. Elements of the behavioral system theory such as linear differential behaviors and quadratic differential forms are crucial in our analysis. © Springer International Publishing Switzerland 2015.

关键词： Power converters

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Dirac structures and control by interconnection for distributed Port-Hamiltonian systems 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Macchelli, Alessandro Department of Electrical Electronic and Information Engineering University of Bologna Viale del Risorgimento 2 Bologna40136 Italy

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

The aim of this work is to show how the Dirac structure properties can be exploited in the development of energy-based boundary control laws for distributed port-Hamiltonian systems. Stabilisation of non-zero equilibria has been achieved by looking at, or generating, a set of structural invariants, namely Casimir functions, in closed-loop, and geometric conditions for the problem to be solved are determined. However, it is well known that this method fails when an infinite amount of energy is required at the equilibrium (dissipation obstacle). So, a novel approach that enlarges the class of stabilising controllers within the control by interconnection paradigm is also discussed. In this respect, it is shown how to determine a different control port that is instrumental for removing the intrinsic constraints imposed by the dissipative structure of the system. The general theory is illustrated with the help of two related examples, namely the boundary stabilisation of the shallow water equation with and without distributed dissipation. © Springer International Publishing Switzerland 2015.

关键词： Stabilization

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On geometric properties of triangularizations for nonlinear control systems 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Schöberl, Markus Schlacher, Kurt Institute of Automatic Control and Control Systems Technology Johannes Kepler University Linz Austria

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

We consider triangular decompositions for nonlinear control systems. For systems that are exactly linearizable by static feedback it is well known that a triangular structure exists in adapted coordinates using the Frobenius theorem to straighten out a nested sequence of involutive distributions. This triangular form is based on explicit ordinary differential equations from which it can be easily seen that exactly linearizable systems are also flat. We will analyze this triangularization also from a dual perspective using a Pfaffian system representation. This point of view allows the introduction of a triangular form corresponding to implicit ordinary differential equations. For systems that are flat but not exactly linearizable by static feedback, this modified triangular form turns out to be useful in setting up a constructive algorithm to compute so-called 1-flat outputs. © Springer International Publishing Switzerland 2015.

关键词： Ordinary differential equations

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Power-based methods for infinite-dimensional systems 1

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Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Kosaraju, Krishna Chaitanya Pasumarthy, Ramkrishna Department of Electrical Engineering Indian Institute of Technology Madras Chennai India

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

In this chapter we aim to extend the Brayton Moser (BM) framework for modeling infinite-dimensional systems. Starting with an infinite-dimensional port- Hamiltonian system we derive a BM equivalent which can be defined with respect to a non-canonical Dirac structure. Based on this model we derive stability and new passivity properties for the system. The state variables in this case are the "effort" variables and the storage function is a "power-like" function called the mixed potential. The new property is derived by "differentiating" one of the port variables. We present our results with the Maxwell’s equations, and the transmission line with non-zero boundary conditions as examples. © Springer International Publishing Switzerland 2015.

关键词： Hamiltonians

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Time-Varying phasors and their application to power analysis 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Stramigioli, Stefano Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 Delft2628 Netherlands

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

The classical complex phasor representation of sinusoidal voltages and currents is generalized to arbitrary waveforms. The method relies on the so-called analytic signal using the Hilbert *** naturally leads to the notion of a timevarying power triangle and its associated instantaneous power factor. Additionally, it is shown for linear systems that Budeanu’s reactive power can be related to energy oscillations, but only in an average sense. Furthermore, Budeanu’s distortion power is decomposed into a part representing a measure of the fluctuation of power around the active power and a part that represents the fluctuation of power around Budeanu’s reactive power. The results are presented for single-phase systems. © Springer International Publishing Switzerland 2015.

关键词： Reactive power

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On stabilization of mixed dimensional parameter port hamiltonian systems via energy shaping 1

引用

Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear control, 2015

作者： Rodríguez-Cortés, H. Departamento de Ingeniería Industrial y Operaciones Instituto Tecnológico Autónomo deMéxico Río Hondo 1 Col. Tizapan México D.f Mexico

ISBN: (数字)9783319209883

ISBN: (纸本)9783319209876

For systems described by Port-Hamiltonian (PH) equations, the control by Interconnection method, based on the existence of Casimir functions, provides a simple and elegant procedure for stabilization of nonlinear systems with finite dissipation. This work explores the possibility of extending this technique to the case where the plant contains an infinite-dimensional subsystem. Conditions for the existence of Casimir functions reveal the constraints for the application of the design procedure. A simple example of an RLC circuit coupled with an infinite-dimensional transmission line illustrates the main ideas of this paper. © Springer International Publishing Switzerland 2015.

关键词： Stabilization

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