(585b) Adaptive Multiple-Model Stochastic Predictive Control
In this talk we present an adaptive multiple-model predictive control strategy with active learning of model structure for stochastic nonlinear systems. The controller considers a set of model hypotheses, each with different structural form. The uncertain time-invariant parameters in the model hypotheses are described with probability density functions (PDFs), and the temporal evolution of the state probability distributions is predicted using the generalized polynomial chaos framework . The uncertain parameters in each hypothesis are estimated online  and their distributions are updated as new measurements become available. The measurements are also used to estimate the validity probability of each model hypothesis using Bayesian statistics, providing the controller with a metric for the degree to which each hypothesis agrees with the data. In order to effectively determine which hypothesis best describes the system, we include a measure of model-hypothesis similarity in the control formulation and specify that the controller attempts to decrease the predicted output distribution overlap, thereby facilitating the task of reconciling the next data point with one of the models. In the talk, we review some dissimilarity metrics and argue that the Kolmogorov distance  is best suited for our purposes. This results in actively adaptive control with respect to structural uncertainty, or suboptimal dual control in the sense of Feldbaum . That is, the MPC algorithm simultaneously controls the process and performs active model discrimination.
We demonstrate the performance of the proposed adaptive multiple-model stochastic predictive control strategy through implementation on an atmospheric pressure plasma jet (based on ). The problem includes two model hypotheses, one for laminar flow and another for turbulent flow in the jet, and three uncertain parameters in each model hypothesis. The controller inputs will not only regulate the system dynamics, but also excite the system to effectively identify the flow regime (i.e., model hypothesis) in the presence of model parameter uncertainty.
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