Robust Linear Programming and Optimal Control

L. Vandenberghe, S. Boyd, and M. Nouralishahi

Proceedings of the 15th IFAC World Congress on Automatic Control, July 2002.

We describe an efficient method for solving an optimal control problem that arises in robust model-predictive control. The problem is to design the input sequence that minimizes the peak tracking error between the output of a linear dynamical system and a desired target output, subject to inequality constraints on the inputs. The system is uncertain, with an impulse response that can take arbitrary values in a given polyhedral set. The method is based on Mehrotra's interior-point method for linear programming, and takes advantage of the problem structure to achieve a complexity that grows linearly with the control horizon, and increases as a cubic polynomial as a function of the system order, the number of inputs, and the number of uncertainty parameters.