Model Predictive Control

196 11 Receding Horizon Control
Model predictive control is the only advanced control technology that has made
a substantial impact on industrial control problems: its success is largely due to its
almost unique ability to handle, simply and effectively, hard constraints on control
and states.
(D.Mayne, 2001 [179])
11.1 Introduction
In the previous chapter we discussed the solution of constrained finite time and
infinite time optimal control problems for linear systems. An infinite horizon “suboptimal”
controller can be designed by repeatedly solving finite time optimal control
problems in a receding horizon fashion as described next.
Figure 11.1 Receding Horizon Idea
At each sampling time, starting at the current state, an open-loop optimal
control problem is solved over a finite horizon (top diagram in Figure 11.1). The
computed optimal manipulated input signal is applied to the process only during
the following sampling interval [t, t + 1]. At the next time step t +1 a new optimal
control problem based on new measurements of the state is solved over a shifted
horizon (bottom diagram in Figure 11.1). The resulting controller is referred to as
Receding Horizon Controller (RHC).
A receding horizon controller where the finite time optimal control law is computed
by solving an optimization problem on-line is usually referred to as Model
Predictive Control (MPC).
Since RHC requires to solve at each sampling time an open-loop constrained
finite time optimal control problem as a function of the current state, the results