Shaping the Closed-Loop Behavior of Nonlinear Systems Under Probabilistic Uncertainty Using Arbitrary Polynomial Chaos

This paper presents a computationally efficient method for performance verification and tuning of model-based controllers in constrained nonlinear systems subject to probabilistic uncertainties with arbitrary distributions. The proposed method is based on an extension of generalized polynomial chaos, an asymptotically convergent spectral method for uncertainty propagation, to directly handle arbitrary uncertainty distributions. The proposed arbitrary polynomial chaos (aPC) method only requires knowledge of the statistical moments of the distribution, and is capable of estimating the aPC expansion coefficients using a minimal number of closed-loop simulations. Advantages of the proposed aPC method are demonstrated on a benchmark continuous reactor problem controlled by a scenario-based nonlinear model predictive controller.