Prabhat K. Mishra

Prabhat K. Mishra, Joel A. Paulson, Richard D. Braatz

This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a computationally tractable way to perform complete and accurate uncertainty propagation through (smooth) nonlinear dynamic systems. As such, it represents a very useful computational tool for accelerating the computations needed in SMPC with time invariant uncertainties. It turns out that it can also be used to reduce complexity of chance constraints, which are an important component of SMPC. In this paper, we provide an overview of PCT and discuss how it can be applied in such time invariant settings.

Mateus V. Gasparino, Prabhat K. Mishra, Girish Chowdhary

This paper presents a deep learning based model predictive control (MPC) algorithm for systems with unmatched and bounded state-action dependent uncertainties of unknown structure. We utilize a deep neural network (DNN) as an oracle in the underlying optimization problem of learning based MPC (LBMPC) to estimate unmatched uncertainties. Generally, non-parametric oracles such as DNN are considered difficult to employ with LBMPC due to the technical difficulties associated with estimation of their coefficients in real time. We employ a dual-timescale adaptation mechanism, where the weights of the last layer of the neural network are updated in real time while the inner layers are trained on a slower timescale using the training data collected online and selectively stored in a buffer. Our results are validated through a numerical experiment on the compression system model of jet engine. These results indicate that the proposed approach is implementable in real time and carries the theoretical guarantees of LBMPC.