An Orthogonal Partitioning Approach to Simplify Robust Model Predictive Control

The main limitation of many robust model predictive control (MPC) algorithms is the formidable on-line computational complexity. For linear discrete-time systems with a polytopic uncertainty description, a new efficient algorithm to determine an approximate explicit state feedback solution to robust MPC is developed. It is shown that this control profile is, in fact, a piecewise affine (PWA) function of the initial state defined on an orthogonal partition of the state space. Robust exponential stability of the controller is established in terms of satisfaction of certain linear matrix inequalities (LMIs). The real-time computational effort required to implement the approximate controller can be reduced to a simple search in a finite-dimensional tree