Design of robust explicit model predictive controller via orthogonal search tree partitioning

Explicit piecewise linear state feedback solutions to the constrained linear model predictive control problem have been characterized and computed using multi-parametric quadratic programming. The piecewise linear state feedback is defined on a polyhedral partition of the state space, which may be quite complex. Recently, approximate multi-parametric quadratic programming approaches have been developed, which have the advantage that the state space partition is structured as an orthogonal search tree. This leads to more efficient real-time computations and admits implementation at high sampling frequencies in embedded systems with inexpensive processors and low software complexity. This paper presents an approximate multi-parametric quadratic programming algorithm that allows the explicit solution of robust model predictive control problems, by imposing an orthogonal search tree structure on the partition. Here, the robustness is defined in terms of satisfaction of the input and output constraints under all possible disturbance realizations.