(309e) Output-Feedback Predictive Control for Stochastic Nonlinear Systems
In this work, the generalized polynomial chaos (gPC) framework  is used for computationally efficient propagation of the uncertain initial conditions and parametric uncertainties in the system model through the nonlinear system dynamics. The main challenge in using the gPC framework is to enable efficient propagation of the stochastic system disturbances since this requires a large number of basis functions in the polynomial chaos (PC) expansions for describing the independent time-varying system disturbances. To overcome this limitation, this work uses a two-step approach  for propagation of the parametric uncertainties and additive disturbances in the space of the PC expansion coefficients under the assumption that these coefficients can be adequately described by a Gaussian distribution. The output-feedback approach is implemented by using a gPC-based histogram filter , which is a Bayesian state and parameter estimation algorithm for estimating the posterior probability density functions of the states and uncertain parameters using the available measurements. The constraints on the states are reformulated as a joint chance constraint (JCC), which is satisfied in with a certain probability. A tractable implementation of the JCC is obtained by using a sample-based approach .
The proposed SMPC approach is implemented for control of the thermal effects of an atmospheric pressure plasma jet (APPJ) simulation case . The system model consists of seven states (three of carrier gas temperature, three of carrier gas composition and one of target surface temperature) of which four are measured and three are unmeasured. The control objective is to regulate the target surface temperature. Chance constraints are imposed on the carrier gas temperature and surface temperature. The simulation results indicate that closed-loop control of the plasma device enables achieving the desired target surface temperature in the presence of system disturbances and modeling uncertainties, while maintaining the constraint satisfaction above the pre-specified probability level.
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