The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Arjan Van Der Schaft - One of the best experts on this subject based on the ideXlab platform.
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Conditions on Shifted Passivity of Port-Hamiltonian Systems
Systems and Control Letters, 2019Co-Authors: Nima Monshizadeh, Pooya Monshizadeh, Romeo Ortega, Arjan Van Der SchaftAbstract:In this paper, we examine the shifted passivity property of port-Hamiltonian Systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus one is interested in passivity with respect to the shifted signals. We consider port-Hamiltonian Systems with strictly convex Hamiltonian, and derive conditions under which shifted passivity is guaranteed. In case the Hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices, our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix. Moreover, we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback, thus paving the path for controller design. Stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions. The utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system.
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interconnections of input output Hamiltonian Systems with dissipation
Conference on Decision and Control, 2016Co-Authors: Arjan Van Der SchaftAbstract:Negative imaginary and counter-clockwise Systems have attracted attention as an interesting class of Systems, which is well-motivated by applications. In this paper first the formulation and extension of negative imaginary and counter-clockwise Systems as (nonlinear) input-output Hamiltonian Systems with dissipation is summarized. Next it is shown how by considering the time-derivative of the outputs a port-Hamiltonian system is obtained, and how this leads to the consideration of alternate passive outputs for port-Hamiltonian Systems. Furthermore, a converse result to positive feedback interconnection of input-output Hamiltonian Systems with dissipation is obtained, stating that the positive feedback interconnection of two linear Systems is an input-output Hamiltonian system with dissipation if and only if the Systems themselves are input-output Hamiltonian Systems with dissipation. This implies that the Poisson and resistive structure matrices can be redefined in such a way that the interaction between the two Systems only takes place via the coupling term in the Hamiltonian of the interconnected system. Subsequently, it is shown how the positive feedback interconnection of two nonlinear input-output Hamiltonian Systems with dissipation can be extended to the network interconnection of such Systems, and how this leads to a stability analysis of the interconnected system in terms of the Hamiltonians and output mappings of the component Systems associated to the vertices, as well as of the network topology.
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interconnections of input output Hamiltonian Systems with dissipation
arXiv: Optimization and Control, 2016Co-Authors: Arjan Van Der SchaftAbstract:Recently, negative imaginary and counter-clockwise Systems have attracted attention as an interesting class of Systems, which is well-motivated by applications. In this paper first the formulation and extension of negative imaginary and counter-clockwise Systems as (nonlinear) input-output Hamiltonian Systems with dissipation is summarized. Next it is shown how by considering the time-derivative of the outputs a port-Hamiltonian system is obtained, and how this leads to the consideration of alternate passive outputs for port-Hamiltonian Systems. Furthermore, a converse result to positive feedback interconnection of input-output Hamiltonian Systems with dissipation is obtained, stating that the positive feedback interconnection of two linear Systems is an input-output Hamiltonian system with dissipation if and only if the Systems themselves are input-output Hamiltonian Systems with dissipation. This implies that the Poisson and resistive structure matrices can be redefined in such a way that the interaction between the two Systems only takes place via the coupling term in the Hamiltonian of the interconnected system. Subsequently, it is shown how network interconnection of (possibly nonlinear) input-output Hamiltonian Systems with dissipation results in another input-output Hamiltonian system with dissipation, and how this leads to a stability analysis of the interconnected system in terms of the Hamiltonians and output mappings of the Systems associated to the vertices, as well as the topology of the network.
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port Hamiltonian Systems on graphs
Siam Journal on Control and Optimization, 2013Co-Authors: Arjan Van Der Schaft, Bernhard MaschkeAbstract:In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian Systems on open graphs. The basic idea is to associate with the incidence matrix of any directed graph a Dirac structure relating the flow and effort variables associated to the edges and vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and the internal vertices. This allows for state variables associated to the edges and formalizes the interconnection of networks. Examples from different origins, such as consensus algorithms, that share the same structure are shown. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis and control of the resulting dynamics.
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structure preserving tangential interpolation for model reduction of port Hamiltonian Systems
Automatica, 2012Co-Authors: Serkan Gugercin, Rostyslav V Polyuga, Christopher Beattie, Arjan Van Der SchaftAbstract:Port-Hamiltonian Systems result from port-based network modeling of physical Systems and are an important example of passive state-space Systems. In this paper, we develop a framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian Systems via tangential rational interpolation. The resulting reduced model is a rational (tangential) interpolant that retains the port-Hamiltonian structure; hence it remains passive. We introduce an H"2-inspired algorithm for effective choice of interpolation points and tangent directions and present several numerical examples illustrating its effectiveness.
Eric Woillez - One of the best experts on this subject based on the ideXlab platform.
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Transport in Hamiltonian Systems with slowly changing phase space structure
Communications in Nonlinear Science and Numerical Simulation, 2019Co-Authors: Freddy Bouchet, Eric WoillezAbstract:Transport in Hamiltonian Systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian Systems with slowly changing phase space structure that are not order one perturbations of a given Hamiltonian. This class of problems is very important for many applications, for instance in celestial mechanics. As an example, we study a class of one-dimensional Hamiltonians that depend explicitly on time and on stochastic external parameters. The variations of the external parameters are responsible for a distortion of the phase space structures: chaotic, weakly chaotic and regular sets change with time. We show that theoretical predictions of transport rates can be made in the limit where the variations of the stochastic parameters are very slow compared to the Hamiltonian dynamics. Exact asymptotic results can be obtained in the classical case where the Hamiltonian dynamics is integrable for fixed values of the parameters. For the more interesting chaotic Hamiltonian dynamics case, we show that two mechanisms contribute to the transport. For some range of the parameter variations, one mechanism -called transport by migration together with the mixing regions - is dominant. We are then able to model transport in phase space by a Markov model, the local diffusion model, and to give reasonably good transport estimates.
Toshiharu Sugie - One of the best experts on this subject based on the ideXlab platform.
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passivity based control of a class of Hamiltonian Systems with nonholonomic constraints
Automatica, 2012Co-Authors: Kenji Fujimoto, Satoru Sakai, Toshiharu SugieAbstract:This paper is concerned with state and output feedback stabilization of a class of port-Hamiltonian Systems with nonholonomic constraints. First we study canonical forms for port-Hamiltonian Systems with nonholonomic constraints. Second, we give a new state feedback stabilization method by using non-smooth Hamiltonian functions via generalized canonical transformations. Third, we propose a dynamic output feedback stabilization method without measuring the velocity based on the corresponding state feedback result. Numerical examples demonstrate the effectiveness of the proposed method.
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Canonical transformation and stabilization of generalized Hamiltonian Systems
Systems & Control Letters, 2001Co-Authors: Kenji Fujimoto, Toshiharu SugieAbstract:Abstract This paper introduces generalized canonical transformations for generalized Hamiltonian Systems which convert a generalized Hamiltonian system into another one, and preserve the generalized Hamiltonian structure of the original. As in classical mechanics, it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those Systems. Firstly, the class of generalized canonical transformations and some of their properties are indicated. Secondly, it is shown how to stabilize the generalized Hamiltonian Systems using canonical transformations. In addition, some examples illustrate how such transformations are utilized for control Systems design.
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Canonical Transformation and Stabilization of Generalized Hamiltonian Systems
IFAC Proceedings Volumes, 1998Co-Authors: Kenji Fujimoto, Toshiharu SugieAbstract:Abstract This paper introduces the canonical transformation for the generalized Hamiltonian Systems, which preserves the generalized Hamiltonian structure of the original system and is expected to provide new insights and useful tools for analysis and synthesis of such Systems. First, the class of such transformations and some of their properties are clarified. Second, we show how to stabilize the generalized Hamiltonian Systems by using the transformation. This method works even when we can not stabilize them by conventional unity feedback without canonical transformation. Furthermore, it is shown that the proposed stabilization method includes the well-known one which exploits the virtual potential energy as a special case.
Freddy Bouchet - One of the best experts on this subject based on the ideXlab platform.
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Transport in Hamiltonian Systems with slowly changing phase space structure
Communications in Nonlinear Science and Numerical Simulation, 2019Co-Authors: Freddy Bouchet, Eric WoillezAbstract:Transport in Hamiltonian Systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian Systems with slowly changing phase space structure that are not order one perturbations of a given Hamiltonian. This class of problems is very important for many applications, for instance in celestial mechanics. As an example, we study a class of one-dimensional Hamiltonians that depend explicitly on time and on stochastic external parameters. The variations of the external parameters are responsible for a distortion of the phase space structures: chaotic, weakly chaotic and regular sets change with time. We show that theoretical predictions of transport rates can be made in the limit where the variations of the stochastic parameters are very slow compared to the Hamiltonian dynamics. Exact asymptotic results can be obtained in the classical case where the Hamiltonian dynamics is integrable for fixed values of the parameters. For the more interesting chaotic Hamiltonian dynamics case, we show that two mechanisms contribute to the transport. For some range of the parameter variations, one mechanism -called transport by migration together with the mixing regions - is dominant. We are then able to model transport in phase space by a Markov model, the local diffusion model, and to give reasonably good transport estimates.
Kenji Fujimoto - One of the best experts on this subject based on the ideXlab platform.
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on potential function design for path following control of port Hamiltonian Systems
Conference on Decision and Control, 2017Co-Authors: Yuki Okura, Kenji Fujimoto, Akio Saito, Hidetoshi IkedaAbstract:This paper describes a procedure to design potential functions for path following control of port-Hamiltonian Systems. The conventional path following control method needs to find a time invariant potential function which takes its minimum on the desired path. It is so difficult to find a potential function for a complex path. Inspired by the results of existing trajectory tracking control of port-Hamiltonian Systems, we propose an improved path following control method. By solving partial differential equations, a potential function for path following control is acquired.
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passivity based control of a class of Hamiltonian Systems with nonholonomic constraints
Automatica, 2012Co-Authors: Kenji Fujimoto, Satoru Sakai, Toshiharu SugieAbstract:This paper is concerned with state and output feedback stabilization of a class of port-Hamiltonian Systems with nonholonomic constraints. First we study canonical forms for port-Hamiltonian Systems with nonholonomic constraints. Second, we give a new state feedback stabilization method by using non-smooth Hamiltonian functions via generalized canonical transformations. Third, we propose a dynamic output feedback stabilization method without measuring the velocity based on the corresponding state feedback result. Numerical examples demonstrate the effectiveness of the proposed method.
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Canonical transformation and stabilization of generalized Hamiltonian Systems
Systems & Control Letters, 2001Co-Authors: Kenji Fujimoto, Toshiharu SugieAbstract:Abstract This paper introduces generalized canonical transformations for generalized Hamiltonian Systems which convert a generalized Hamiltonian system into another one, and preserve the generalized Hamiltonian structure of the original. As in classical mechanics, it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those Systems. Firstly, the class of generalized canonical transformations and some of their properties are indicated. Secondly, it is shown how to stabilize the generalized Hamiltonian Systems using canonical transformations. In addition, some examples illustrate how such transformations are utilized for control Systems design.
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Canonical Transformation and Stabilization of Generalized Hamiltonian Systems
IFAC Proceedings Volumes, 1998Co-Authors: Kenji Fujimoto, Toshiharu SugieAbstract:Abstract This paper introduces the canonical transformation for the generalized Hamiltonian Systems, which preserves the generalized Hamiltonian structure of the original system and is expected to provide new insights and useful tools for analysis and synthesis of such Systems. First, the class of such transformations and some of their properties are clarified. Second, we show how to stabilize the generalized Hamiltonian Systems by using the transformation. This method works even when we can not stabilize them by conventional unity feedback without canonical transformation. Furthermore, it is shown that the proposed stabilization method includes the well-known one which exploits the virtual potential energy as a special case.
