Robust model predictive control as a class of semi-infinite programming problems

This thesis introduces a new interpretation of the problems arising in robust model predictive control (MPC). In practice, MPC algorithms are typically embedded within a multi-level hierarchy of control functions. The MPC algorithm itself is usually implemented in two pieces: a steady-state target calculation followed by a dynamic optimization. It is shown in this thesis that some of the most promising methods of imparting robustness to MPC algorithms result in semi-infinite programs. These programs arise from the addition of semi-infinite constraints to the nominal MPC algorithms which come from theoretical arguments that guarantee stability of the closed loop system or from requiring existing constraints to hold for an infinite set of plants. While the number of constrained variables is finite, the constraint must hold over an infinite set. This infinite set corresponds to a continuous uncertainty description for the model parameters.; In this dissertation it is also shown that the resulting optimization problems have a very unique structure. For some MPC algorithms the semi-infinite program (SIP) can be cast as an equivalent finite-dimensional nonlinear convex program. Primal-dual interior-point methods are used to efficiently solve the resulting optimization problem by exploiting its inherent convexity. Simulation examples illustrate the effects of uncertainty on nominal MPC algorithms and demonstrate the advantages of interior-point methods.