The explicit solution of model predictive control via multiparametric quadratic programming

The control based on online optimization, popularly known as model predictive control (MPC), has long been recognized as the winning alternative for constrained systems. The main limitation of MPC is, however, its online computational complexity. For discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly the state feedback control law associated with MPC, and show that it is piecewise linear and continuous. The controller inherits all the stability and performance properties of MPC, but the online computation is reduced to a simple linear function evaluation instead of the expensive quadratic program. The new technique is expected to enlarge the scope of applicability of MPC to small-size/fast-sampling applications which cannot be covered satisfactorily with anti-windup schemes.