Optimal control for stochastic systems with polynomial chaos

Assuring robustness of control system performance against model uncertainty is a significant component of control design. Current methods for developing a robust controller, however, are typically either too conservative or too computationally expensive. This thesis uses generalized polynomial chaos alongside finite-horizon optimal control as a new method of robust control design for a stochastic system. Since the equations for the mean and variance of the response can be expressed in terms of coefficients from a polynomial chaos expansion, optimizing a polynomial chaos expansion can be used to optimize the mean and variance, thus providing robust responses in a stochastic system. This thesis first provides a review of the concepts and literature then the rationale as well as the derivation of the proposed robust control method. Three examples are given to show the effectiveness of the new control method and are discussed. In particular, the final example demonstrates the applicability of using polynomial chaos to provide robust control for a stochastic soft landing problem.