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Polynomial chaos theory can be used to approximate a stochastic linear dynamical system by a deterministic linear system of larger dimension. This approximation enables the use of linear control theory tools for the analysis and design of controllers for the original stochastic system. The approximate system can, however, have stable moments while the moments of the original stochastic system are...
In many control problems, not all states can be measured and the system is subject to parametric uncertainties, measurement noise, and hard input constraints. To tackle such problems for linear systems, we propose to combine a recursive parameter and state estimator based on Bayes' theorem with a stochastic model predictive control approach. To efficiently obtain the probability density functions...
A computationally efficient approach is presented that quantifies the influence of parameter uncertainties on the states and outputs of finite-time control trajectories for nonlinear systems, based on the approximate representation of the model via polynomial chaos expansion. The approach is suitable for studying the uncertainty propagation in open-loop or closed-loop systems. A quantitative and qualitative...
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