Generalized polynomial chaos expansion approaches to approximate stochastic receding horizon control with applications to probabilistic collision checking and avoidance

This paper studies the model predictive control of dynamic systems subject to stochastic parametric uncertainty due to plant/model mismatches and exogenous disturbance that corresponds to uncertain circumstance in operation of the system. Model and disturbance uncertainties are ubiquitous in any mathematical models of system and control theory. Parametric uncertainty propagation or quantification is approximated using a spectral method called polynomial chaos expansion and exogenous disturbance is assumed to be an additive Gaussian random process. With Gaussian approximation of resulting solution trajectory of a stochastic differential equation using polynomial chaos expansion, we solve convex finite-horizon model predictive control problems that are amenable to online computation of a stochastically robust control policy over the time-horizon. The proposed approach to chance-constrained model predictive control provides an explicit way to handle a stochastic system model in the presence of both model uncertainty and exogenous disturbances. Probabilistic constraints are replaced by convex deterministic constraints that approximate the probabilistic violations with a user-defined confidence level.