Closed-Form Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density

Huber, Marco F.; Brunn, Dietrich; Hanebeck, Uwe D.

doi:10.1109/mfi.2006.265622

Cited by 13 publications

(20 citation statements)

References 10 publications

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“…the approach proposed by (Huber et al, 2006) allows to perform a closed-form prediction resulting in an approximate Gaussian mixture representation…”

Section: Scalar Systemsmentioning

confidence: 99%

“…Approximating these lower-dimensional transition densities is possible with decreased computational demand (Huber et al, 2006).…”

Section: Vector-valued Systemsmentioning

confidence: 99%

“…Therefore, in this paper a framework for discrete-time NMPC for continuous state spaces and a finite set of control inputs is presented that is based on the efficient state prediction of nonlinear stochastic models. Since an exact density representation in closed form and with constant complexity is preferable, a prediction method is applied that is founded on the approximation of the involved system transition densities by axis-aligned Gaussian mixture densities (Huber et al, 2006). To lower the computational demands for approximating multi-dimensional transition densities, the so-called modularization for complexity reduction purposes is proposed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Closed-Form Model Predictive Control Framework for Nonlinear Noise-Corrupted Systems

Weissel¹,

Huber²,

Hanebeck³

2007

Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics

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Abstract:In this paper, a framework for Nonlinear Model Predictive Control (NMPC) that explicitly incorporates the noise influence on systems with continuous state spaces is introduced. By the incorporation of noise, which results from uncertainties during model identification and the measurement process, the quality of control can be significantly increased. Since NMPC requires the prediction of system states over a certain horizon, an efficient state prediction technique for nonlinear noise-affected systems is required. This is achieved by using transition densities approximated by axis-aligned Gaussian mixtures together with methods to reduce the computational burden. A versatile cost function representation also employing Gaussian mixtures provides an increased freedom of modeling. Combining the prediction technique with this value function representation allows closed-form calculation of the necessary optimization problems arising from NMPC. The capabilities of the framework and especially the benefits that can be gained by considering the noise in the controller are illustrated by the example of a mobile robot following a given path.

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“…the approach proposed by (Huber et al, 2006) allows to perform a closed-form prediction resulting in an approximate Gaussian mixture representation…”

Section: Scalar Systemsmentioning

confidence: 99%

“…Approximating these lower-dimensional transition densities is possible with decreased computational demand (Huber et al, 2006).…”

Section: Vector-valued Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Closed-Form Model Predictive Control Framework for Nonlinear Noise-Corrupted Systems

Weissel¹,

Huber²,

Hanebeck³

2007

Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics

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show abstract

“…In this case the number of the components of the resulting transition density is increasing depending on the approximation of the process noise. If a nonlinear transition density model is used, it can be approximated with an algorithm, which is described in [10]. By using this transition density the predicted density…”

Section: Time Updatementioning

confidence: 99%

The Probabilistic Instantaneous Matching Algorithm

Beutler

Hanebeck

2006

2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems

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Abstract-A new Bayesian filtering technique for estimating signal parameters directly from discrete-time sequences is introduced. The so called probabilistic instantaneous matching algorithm recursively updates the probability density function of the parameters for every received sample and, thus, provides a high update rate up to the sampling rate with high accuracy. In order to do so, one of the signal sequences is used as part of a time-variant nonlinear measurement equation. Furthermore, the time-variant nature of the parameters is explicitly considered via a system equation, which describes the evolution of the parameters over time. An important feature of the probabilistic instantaneous matching algorithm is that it provides a probability density function over the parameter space instead of a single point estimate. This probability density function can be used in further processing steps, e.g. a range based localization algorithm in the case of time-of-arrival estimation.

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“…The application of adequate representations of the model like Gaussian mixtures with axis-aligned components (Huber et al, 2006), allows for efficient implementation of the filter steps.…”

Section: Introductionmentioning

confidence: 99%

A State Estimator for Nonlinear Stochastic Systems Based on Dirac Mixture Approximations

Schrempf¹,

Hanebeck²

2007

Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics

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Abstract:This paper presents a filter approach for estimating the state of nonlinear dynamic systems based on recursive approximation of posterior densities by means of Dirac mixture functions. The filter consists of a prediction step and a filter step. The approximation approach is based on a systematic minimization of a distance measure and is hence optimal and deterministic. In contrast to non-deterministic methods we are able to determine the optimal number of components in the Dirac mixture. A further benefit of the proposed approach is the consideration of measurements during the approximation process in order to avoid parameter degradation.

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Closed-Form Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density

Cited by 13 publications

References 10 publications

A Closed-Form Model Predictive Control Framework for Nonlinear Noise-Corrupted Systems

A Closed-Form Model Predictive Control Framework for Nonlinear Noise-Corrupted Systems

The Probabilistic Instantaneous Matching Algorithm

A State Estimator for Nonlinear Stochastic Systems Based on Dirac Mixture Approximations

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