Nonlinear Stochastic Model Predictive Control with Higher-order Moment-based Approximation of Chance Constraints

Abstract

This paper proposes non-conservative nonlinear stochastic model predictive control (SMPC) subject to time-invariant uncertainties in initial conditions and system parameters. SMPC imposes probabilistic constraints on the probability of satisfying constraints (chance constraints), which enable us to explicitly consider the trade-off between guaranteeing the constraint satisfaction and minimizing the cost function. This paper proposes a method to obtain non-conservative control inputs by deriving a probability inequality using higher-order moments for reformulating chance constraints. To estimate these moments, the proposed method adopts generalized polynomial chaos expansion. By applying the proposed method to a semibatch reactor system, we show that the generalized polynomial chaos expansion can estimate higher-order moments with fewer samples than the Monte Carlo method and that the proposed method performs better than SMPC using a probability inequality with only mean and variance.