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Application Uncertainty Propagation
Published in Bin Jia, Ming Xin, Grid-based Nonlinear Estimation and Its Applications, 2019
Note wj=v1,j2 with v1,j being the first component of the normalized jth eigenvector (Ahlfed et al. 2016). The above-described uncertainty quantification method is called the arbitrary polynomial chaos (aPC).
Differential flatness based design of robust controllers using polynomial chaos for linear systems
Published in International Journal of Control, 2023
Oladapo Ogunbodede, Tarunraj Singh
In this paper, a method to design a robust feedforward controller for linear differentially flat system with time invariant parametric uncertainties without employing a feedback controller is proposed. The notion of robustness here refers to the size of the bounding box which encloses the terminal state errors, where smaller the size of the box, greater the robustness. This corresponds to a trajectory planning problem in the presence of modelling uncertainties. The concept of polynomial chaos is used in propagating the uncertainties. It is also shown that for flat linear systems, the polynomial chaos surrogate model is also flat. The surrogate model is then used in a chance constrained optimisation framework to satisfy some control performance criterion. To illustrate this method, two examples are used. A single mass spring damper system is used with the performance criterion being the need to satisfy a bound on the final state configuration. Also a more practical example of the linearised longitudinal dynamics of a fixed wing Aerosonde UAV is used where the aim is to fly from point to point while maintaining certain bounds.
Multi-objective robust optimization of chassis system with polynomial chaos expansion method
Published in Engineering Optimization, 2021
Hanwei Gao, Louis Jézéquel, Eric Cabrol, Bernard Vitry
Adaptive–sparse polynomial chaos expansion (PCE) methods were proposed by Hu and Youn (2011) and Blatman and Sudret (2010). The term ‘chaos’ refers to the uncertain performance of the model due to stochastic input variables, while polynomial chaos aims to model this uncertainty by polynomials including random variables.