The Explicit Linear Quadratic Regulator for Constrained Systems
Prof. Manfred Morari (ETH Zurich)
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 which minimizes a quadratic
performance criterion. We show that the control law is piecewise
linear and continuous for both the finite horizon problem (model
predictive control) and the usual infinite time measure (constrained
linear quadratic regulation). Thus, the on-line computation is
reduced to a simple linear function evaluation, instead of the
expensive quadratic program required up to now.
Control based on on-line optimization has long been recognized as a
superior alternative for constrained systems. The technique proposed
in this paper is attractive for a wide range of practical problems
where the computational complexity of on-line optimization is
prohibitive.
Speaker's bio:
In 1994 Manfred Morari was appointed head of the Automatic Control
Laboratory at the Swiss Federal Institute of Technology (ETH) in
Zurich. Before that he was the McCollum-Corcoran Professor and
Executive Officer for Control and Dynamical Systems at the California
Institute of Technology. He obtained the diploma from ETH Zurich and
the Ph.D. from the University of Minnesota. His interests are in
hybrid systems and the control of biomedical systems. In recognition
of his research he received numerous awards, among them the Eckman
Award of the AACC, the Colburn Award and the Professional Progress
Award of the AIChE and was elected to the National Academy of
Engineering (U.S.). Professor Morari has held appointments with Exxon
and ICI and has consulted internationally for a number of major
corporations.
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