The Experts below are selected from a list of 225 Experts worldwide ranked by ideXlab platform

Peter J Seiler - One of the best experts on this subject based on the ideXlab platform.

  • robust lpv estimator synthesis using integral quadratic constraints
    Advances in Computing and Communications, 2016
    Co-Authors: Raghu Venkataraman, Peter J Seiler
    Abstract:

    A method is presented for synthesizing output estimators for a class of continuous time, uncertain, linear parameter-varying (LPV) systems. The uncertain system is described as an interconnection of a nominal LPV system and a block structured perturbation. The nominal LPV system is “gridded” over the space of parameters, with the state matrices being arbitrary functions of the parameters. The input/output behavior of the perturbation is described by integral quadratic constraints. The main contribution of this paper is the derivation of convex conditions for the synthesis of output estimators for uncertain, grid-based LPV plants. Since LPV systems do not have valid frequency response interpretations, the time domain, Dissipation Inequality approach is followed. Robust performance is measured using the upper-bound on the worst-case induced-L2 gain of the closed loop. The effectiveness of the proposed method is demonstrated using a numerical example.

  • robustness analysis of linear parameter varying systems using integral quadratic constraints
    International Journal of Robust and Nonlinear Control, 2015
    Co-Authors: Harald Pfifer, Peter J Seiler
    Abstract:

    Summary A general approach is presented to analyze the worst case input/output gain for an interconnection of a linear parameter varying (LPV) system and an uncertain or nonlinear element. The LPV system is described by state matrices that have an arbitrary, that is not necessarily rational, dependence on the parameters. The input/output behavior of the nonlinear/uncertain block is described by an integral quadratic constraint (IQC). A Dissipation Inequality is proposed to compute an upper bound for this gain. This worst-case gain condition can be formulated as a semidefinite program and efficiently solved using available optimization software. Moreover, it is shown that this new condition is a generalization of the well-known bounded real lemma type result for LPV systems. The results contained in this paper complement known results that apply IQCs for analysis of LPV systems whose state matrices have a rational dependence on the parameters. The effectiveness of the proposed method is demonstrated on simple numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.

  • stability analysis with Dissipation inequalities and integral quadratic constraints
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Peter J Seiler
    Abstract:

    This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain Dissipation Inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the Dissipation Inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix Inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the Dissipation Inequality test, with an appropriate factorization, can be used with no additional conservatism.

  • robustness analysis of linear parameter varying systems using integral quadratic constraints
    Advances in Computing and Communications, 2014
    Co-Authors: Harald Pfifer, Peter J Seiler
    Abstract:

    A general approach is presented to analyze the worst case input/output gain for an interconnection of a linear parameter varying (LPV) system and an uncertain or nonlinear element. The input/output behavior of the nonlinear/uncertain block is described by an integral quadratic constraint (IQC). A Dissipation Inequality is proposed to compute an upper bound for this gain. This worst-case gain condition can be formulated as a semidefinite program and the result can be interpreted as a Bounded Real Lemma for uncertain LPV systems. The paper shows that this new condition is a generalization of the well known Bounded Real Lemma for LPV systems. The effectiveness of the proposed method is demonstrated on a simple numerical example.

  • robust synthesis for linear parameter varying systems using integral quadratic constraints
    Conference on Decision and Control, 2014
    Co-Authors: Shu Wang, Harald Pfifer, Peter J Seiler
    Abstract:

    A robust synthesis algorithm is proposed for a class of uncertain linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal (not-uncertain) LPV system and an uncertainty whose input/output behavior is described by an integral quadratic constraint (IQC). The proposed algorithm is a coordinate-wise ascent that is similar to the well-known DK iteration for μ-synthesis. In the first step, a nominal controller is designed for the LPV system without uncertainties. In the second step, the robustness of the designed controller is evaluated and a new scaled plant for the next synthesis step is created. The robust performance condition used in the analysis step is formulated as a Dissipation Inequality that incorporates the IQC and generalizes the Bounded Real Lemma like condition for performance of nominal LPV systems. Both steps can be formulated as a semidefinite program (SDP) and efficiently solved using available optimization software. The effectiveness of the proposed method is demonstrated on a simple numerical example.

Chiara Zanini - One of the best experts on this subject based on the ideXlab platform.

  • a quasilinear differential inclusion for viscous and rate independent damage systems in non smooth domains
    Nonlinear Analysis-real World Applications, 2015
    Co-Authors: Dorothee Knees, Riccarda Rossi, Chiara Zanini
    Abstract:

    Abstract This paper focuses on (incomplete) rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) vanishing-viscosity approach to rate-independent processes, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q -Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-Dissipation Inequality that is the starting point for the vanishing-viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime.

  • a quasilinear differential inclusion for viscous and rate independent damage systems in non smooth domains
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Dorothee Knees, Riccarda Rossi, Chiara Zanini
    Abstract:

    This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) vanishing viscosity approach to rate-independent modeling, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q-Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-Dissipation Inequality that is the starting point for the vanishing viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime.

Dorothee Knees - One of the best experts on this subject based on the ideXlab platform.

  • a quasilinear differential inclusion for viscous and rate independent damage systems in non smooth domains
    Nonlinear Analysis-real World Applications, 2015
    Co-Authors: Dorothee Knees, Riccarda Rossi, Chiara Zanini
    Abstract:

    Abstract This paper focuses on (incomplete) rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) vanishing-viscosity approach to rate-independent processes, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q -Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-Dissipation Inequality that is the starting point for the vanishing-viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime.

  • a quasilinear differential inclusion for viscous and rate independent damage systems in non smooth domains
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Dorothee Knees, Riccarda Rossi, Chiara Zanini
    Abstract:

    This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) vanishing viscosity approach to rate-independent modeling, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q-Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-Dissipation Inequality that is the starting point for the vanishing viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime.

Riccarda Rossi - One of the best experts on this subject based on the ideXlab platform.

  • a quasilinear differential inclusion for viscous and rate independent damage systems in non smooth domains
    Nonlinear Analysis-real World Applications, 2015
    Co-Authors: Dorothee Knees, Riccarda Rossi, Chiara Zanini
    Abstract:

    Abstract This paper focuses on (incomplete) rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) vanishing-viscosity approach to rate-independent processes, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q -Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-Dissipation Inequality that is the starting point for the vanishing-viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime.

  • a quasilinear differential inclusion for viscous and rate independent damage systems in non smooth domains
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Dorothee Knees, Riccarda Rossi, Chiara Zanini
    Abstract:

    This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) vanishing viscosity approach to rate-independent modeling, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q-Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-Dissipation Inequality that is the starting point for the vanishing viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime.

Ian R. Petersen - One of the best experts on this subject based on the ideXlab platform.

  • STATE DISTRIBUTIONS AND MINIMUM RELATIVE ENTROPY NOISE SEQUENCES IN UNCERTAIN STOCHASTIC SYSTEMS: THE DISCRETE-TIME CASE ∗
    SIAM Journal on Control and Optimization, 2015
    Co-Authors: Igor G. Vladimirov, Ian R. Petersen
    Abstract:

    This paper is concerned with dissipativity theory and robust performance analysis and design of discrete-time stochastic systems driven by statistically uncertain random noise. The uncertainty is quantified by the conditional relative entropy of the actual probability law of the noise with respect to a nominal product measure corresponding to a white noise sequence. We discuss a balance equation, Dissipation Inequality, and superadditivity property for the corresponding conditional relative entropy supply as a function of time. The problem of minimizing the supply, required to drive the system between given state distributions over a specified time horizon, is considered. Such variational problems, involving entropy and probabilistic boundary conditions, are known in the literature as Schrodinger bridge problems. In application to control systems, the minimum required conditional relative entropy supply characterizes the robustness of the system with respect to a statistically uncertain random noise. We o...

  • State distributions and minimum relative entropy noise sequences in uncertain stochastic systems: the discrete time case
    arXiv: Systems and Control, 2012
    Co-Authors: Igor G. Vladimirov, Ian R. Petersen
    Abstract:

    The paper is concerned with a dissipativity theory and robust performance analysis of discrete-time stochastic systems driven by a statistically uncertain random noise. The uncertainty is quantified by the conditional relative entropy of the actual probability law of the noise with respect to a nominal product measure corresponding to a white noise sequence. We discuss a balance equation, Dissipation Inequality and superadditivity property for the corresponding conditional relative entropy supply as a function of time. The problem of minimizing the supply required to drive the system between given state distributions over a specified time horizon is considered. Such variational problems, involving entropy and probabilistic boundary conditions, are known in the literature as Schroedinger bridge problems. In application to control systems, this minimum required conditional relative entropy supply characterizes the robustness of the system with respect to an uncertain noise. We obtain a dynamic programming Bellman equation for the minimum required conditional relative entropy supply and establish a Markov property of the worst-case noise with respect to the state of the system. For multivariable linear systems with a Gaussian white noise sequence as the nominal noise model and Gaussian initial and terminal state distributions, the minimum required supply is obtained using an algebraic Riccati equation which admits a closed-form solution. We propose a computable robustness index for such systems in the framework of an entropy theoretic formulation of uncertainty and provide an example to illustrate this approach.