### Abstract

We present a new approach to describe the evolution of uncertainty in linear dynamic models with parametric and initial condition uncertainties, and driven by additive white Gaussian stochastic forcing. This is based on the polynomial chaos (PC) series expansion of second order random processes, which has been used in several domains to solve stochastic systems with parametric and initial condition uncertainties. The PC solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large systems with a relatively small number of uncertainties. However, when the dynamic system includes an additive stochastic forcing term varying with time, the computational cost of using the PC expansions for the stochastic forcing terms is expensive and increases exponentially with the increase in the number of time steps, due to the increase in the stochastic dimensionality. In this work, an alternative approach is proposed for uncertainty evolution in linear uncertain models driven by white noise. The uncertainty in the model states due to additive white Gaussian noise can be described by the mean and covariance of the states. This is combined with the PC based approach to propagate the uncertainty due to Gaussian stochastic forcing and model parameter uncertainties which can be non-Gaussian.

Original language | English (US) |
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Title of host publication | Proceedings of the 2010 American Control Conference, ACC 2010 |

Pages | 3118-3123 |

Number of pages | 6 |

State | Published - Oct 15 2010 |

Event | 2010 American Control Conference, ACC 2010 - Baltimore, MD, United States Duration: Jun 30 2010 → Jul 2 2010 |

### Publication series

Name | Proceedings of the 2010 American Control Conference, ACC 2010 |
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### Other

Other | 2010 American Control Conference, ACC 2010 |
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Country | United States |

City | Baltimore, MD |

Period | 6/30/10 → 7/2/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering

### Cite this

*Proceedings of the 2010 American Control Conference, ACC 2010*(pp. 3118-3123). [5531048] (Proceedings of the 2010 American Control Conference, ACC 2010).

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*Proceedings of the 2010 American Control Conference, ACC 2010.*, 5531048, Proceedings of the 2010 American Control Conference, ACC 2010, pp. 3118-3123, 2010 American Control Conference, ACC 2010, Baltimore, MD, United States, 6/30/10.

**State uncertainty propagation in the presence of parametric uncertainty and additive white noise.** / Kond, Umamaheswara; Singla, Puneet; Singh, Tarunraj; Scott, Peter.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - State uncertainty propagation in the presence of parametric uncertainty and additive white noise

AU - Kond, Umamaheswara

AU - Singla, Puneet

AU - Singh, Tarunraj

AU - Scott, Peter

PY - 2010/10/15

Y1 - 2010/10/15

N2 - We present a new approach to describe the evolution of uncertainty in linear dynamic models with parametric and initial condition uncertainties, and driven by additive white Gaussian stochastic forcing. This is based on the polynomial chaos (PC) series expansion of second order random processes, which has been used in several domains to solve stochastic systems with parametric and initial condition uncertainties. The PC solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large systems with a relatively small number of uncertainties. However, when the dynamic system includes an additive stochastic forcing term varying with time, the computational cost of using the PC expansions for the stochastic forcing terms is expensive and increases exponentially with the increase in the number of time steps, due to the increase in the stochastic dimensionality. In this work, an alternative approach is proposed for uncertainty evolution in linear uncertain models driven by white noise. The uncertainty in the model states due to additive white Gaussian noise can be described by the mean and covariance of the states. This is combined with the PC based approach to propagate the uncertainty due to Gaussian stochastic forcing and model parameter uncertainties which can be non-Gaussian.

AB - We present a new approach to describe the evolution of uncertainty in linear dynamic models with parametric and initial condition uncertainties, and driven by additive white Gaussian stochastic forcing. This is based on the polynomial chaos (PC) series expansion of second order random processes, which has been used in several domains to solve stochastic systems with parametric and initial condition uncertainties. The PC solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large systems with a relatively small number of uncertainties. However, when the dynamic system includes an additive stochastic forcing term varying with time, the computational cost of using the PC expansions for the stochastic forcing terms is expensive and increases exponentially with the increase in the number of time steps, due to the increase in the stochastic dimensionality. In this work, an alternative approach is proposed for uncertainty evolution in linear uncertain models driven by white noise. The uncertainty in the model states due to additive white Gaussian noise can be described by the mean and covariance of the states. This is combined with the PC based approach to propagate the uncertainty due to Gaussian stochastic forcing and model parameter uncertainties which can be non-Gaussian.

UR - http://www.scopus.com/inward/record.url?scp=77957805384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957805384&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:77957805384

SN - 9781424474264

T3 - Proceedings of the 2010 American Control Conference, ACC 2010

SP - 3118

EP - 3123

BT - Proceedings of the 2010 American Control Conference, ACC 2010

ER -