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New filters are derived for estimating the n-dimensional state of a linear dynamic system based on uncertain m-dimensional observations, which suffer from two types of uncertainties simultaneously. The first uncertainty is a stochastic process with given distribution. The second uncertainty is only known to be bounded, the exact underlying distribution is unknown. The new estimators combine set theoretic...
In this paper, we consider state estimation for Stochastic Hybrid Systems (SHS). These are systems that possess both continuous-valued and discrete-valued dynamics. For SHS with nonlinear hybrid dynamics and/or non-Gaussian disturbances, state estimation can be implemented as an Interacting Multiple Model (IMM) particle filter. However, a disadvantage of particle filtering is the computational load...
In Model Predictive Control, the quality of control is highly dependent upon the model of the system under control. Therefore, a precise deterministic model is desirable. However, in real-world applications, modeling accuracy is typically limited and systems are generally affected by disturbances. Hence, it is important to systematically consider these uncertainties and to model them correctly. In...
A non-parametric conditional density estimation algorithm for nonlinear stochastic dynamic systems is proposed. The contributions are a novel support vector regression for estimating conditional densities, modeled by Gaussian mixture densities, and an algorithm based on cross-validation for automatically determining hyper-parameters for the regression. The conditional densities are employed with a...
The sample-based recursive prediction of discrete-time nonlinear stochastic dynamic systems requires a regular reapproximation of the Dirac mixture densities characterizing the state estimate with an exponentially increasing number of components. For that purpose, a systematic approximation method is proposed that is deterministic and guaranteed to minimize a new type distance measure, the so called...
This paper addresses the problem of model-based reconstruction and parameter identification of distributed phenomena characterized by partial differential equations. The novelty of the proposed method is the systematic approach and the integrated treatment of uncertainties, which naturally occur in the physical system and arise from noisy measurements. The main challenge of accurate reconstruction...
This paper introduces a new approach to the recursive propagation of probability density functions through discrete-time stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systematically...
Recursive prediction of the state of a nonlinear stochastic dynamic system cannot be efficiently performed in general, since the complexity of the probability density function characterizing the system state increases with every prediction step. Thus, representing the density in an exact closed-form manner is too complex or even impossible. So, an appropriate approximation of the density is required...
In this paper, an approach to the finite-horizon optimal state-feedback control problem of nonlinear, stochastic, discrete-time systems is presented. Starting from the dynamic programming equation, the value function will be approximated by means of Taylor series expansion up to second-order derivatives. Moreover, the problem will be reformulated, such that a minimum principle can be applied to the...
In this paper we attempt to lay the foundation for a novel filtering technique for the fusion of two random vectors with imprecisely known stochastic dependency. This problem mainly occurs in decentralized estimation, e.g., of a distributed phenomenon, where the stochastic dependencies between the individual states are not stored. Thus, we derive parameterized joint densities with both Gaussian marginals...
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