An LMI approach to robust constrained model predictive control
An LMI approach to robust constrained model predictive control
M. Kothare, V. Balakrishnan and M. Morari
Automatica, vol. 32, no. 10, pages 1361-1379, November 1996
Abstract:
The primary disadvantage of current design techniques for
model predictive control (MPC) is their inability to deal {\em
explicitly} with plant model uncertainty. In this paper, we present
a new approach for robust MPC synthesis which allows explicit
incorporation of the description of plant uncertainty in the problem
formulation. The uncertainty is expressed both in the time and
frequency domains. The goal is to design, at each time step, a
state-feedback control law which minimizes a ``worst-case'' infinite
horizon objective function, subject to constraints on the control
input and plant output. Using standard techniques, the problem of
minimizing an upper bound on the ``worst-case'' objective function,
subject to input and output constraints, is reduced to a convex
optimization involving linear matrix inequalities (LMIs). It is
shown that the feasible receding horizon state-feedback control
design robustly stabilizes the set of uncertain plants. Several
extensions, such as application to systems with time-delays,
problems involving constant set-point tracking, trajectory tracking
and disturbance rejection, which follow naturally from our
formulation, are discussed. The controller design is illustrated
with two examples.
Download Postscript
PDF
Bibtex entry